US2012300877A1PendingUtilityA1

Precoding method, transmitting device, and receiving device

Assignee: MURAKAMI YUTAKAPriority: May 27, 2011Filed: May 23, 2012Published: Nov 29, 2012
Est. expiryMay 27, 2031(~4.8 yrs left)· nominal 20-yr term from priority
H04L 1/0075H04L 1/0045H04L 25/03955H04B 7/0456H04L 25/03942
55
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Claims

Abstract

A transmission scheme for transmitting a first modulated signal and a second modulated signal in the same frequency at the same time. According to the transmission scheme, a precoding weight multiplying unit multiplies a precoding weight by a baseband signal after a first mapping and a baseband signal after a second mapping and outputs the first modulated signal and the second modulated signal. In the precoding weight multiplying unit, precoding weights are regularly hopped.

Claims

exact text as granted — not AI-modified
1 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
 selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and   generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being nine matrices expressed, using a positive real number α, as Equations 339 through 347.   
       
         
           
             
               
                 
                   
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                     340 
                   
                 
               
               
                 
                   
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                     341 
                   
                 
               
               
                 
                   
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                     343 
                   
                 
               
               
                 
                   
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                     344 
                   
                 
               
               
                 
                   
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                     346 
                   
                 
               
               
                 
                   
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                     9 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
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                     Equation 
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                     347 
                   
                 
               
             
           
         
       
     
     
         2 . The precoding method of  claim 1 , further comprising:
 generating coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes; and   generating a signal based on the selected modulation scheme from the coded data, wherein   the positive real number α is changed in accordance with the selected modulation scheme.   
     
     
         3 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
 selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and   generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being nine matrices expressed, as Equations 348 through 356.   
       
         
           
             
               
                 
                   
                     Math 
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                     10 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
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                     351 
                   
                 
               
               
                 
                   
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                     14 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
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                     352 
                   
                 
               
               
                 
                   
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                     15 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
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                     353 
                   
                 
               
               
                 
                   
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                     17 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
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                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     16 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     356 
                   
                 
               
             
           
         
       
     
     
         4 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
 selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and   generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 15 matrices expressed, using a positive real number α, as Equations 357 through 371.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     19 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                             
                               
                                  
                                 jπ 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     357 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     20 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     358 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     21 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           2 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     359 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     22 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           3 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     360 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     23 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           4 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     361 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     24 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           5 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     362 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     25 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           6 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     363 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     26 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           7 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     364 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     27 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     365 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     28 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           9 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       18 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           18 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     366 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     29 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           10 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       20 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           20 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     367 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     30 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           11 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       22 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           22 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     368 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     31 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           12 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       24 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           24 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     369 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     32 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           13 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       26 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           26 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     370 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     33 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           14 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       28 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           28 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     371 
                   
                 
               
             
           
         
       
     
     
         5 . The precoding method of  claim 4 , further comprising:
 generating coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes; and   generating a signal based on the selected modulation scheme from the coded data, wherein   the positive real number α is changed in accordance with the selected modulation scheme.   
     
     
         6 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
 selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and   generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 15 matrices expressed, as Equations 372 through 386.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     34 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 jπ 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     372 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     35 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     2 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     373 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     36 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           2 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     4 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     
                       Equation 
                        
                       
                           
                       
                        
                       374 
                     
                      
                     
                         
                     
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     37 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           3 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     6 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     375 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     38 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           4 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     8 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     376 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     39 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           5 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     10 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     377 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     40 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           6 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     12 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     378 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     41 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           7 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     14 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     379 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     42 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     16 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     380 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     43 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           9 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     18 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           18 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     381 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     44 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           10 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     20 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           20 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     382 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     45 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           11 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     22 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           22 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     383 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     46 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           12 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     24 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           24 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     384 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     47 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           13 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     26 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           26 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     385 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     48 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       f 
                        
                       
                         [ 
                         
                            
                           = 
                           14 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                  
                                 j0 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     28 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           28 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     386 
                   
                 
               
             
           
         
       
     
     
         7 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
 selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and   generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 18 matrices expressed, using a positive real number α, as Equations 387 through 404.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     49 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                             
                               
                                  
                                 jπ 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     387 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     50 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     388 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     51 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           2 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     389 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     52 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           3 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     390 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     53 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           4 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     391 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     54 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           5 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     392 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     55 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           6 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     393 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     56 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           7 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     394 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     57 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     395 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     58 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           9 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                             
                               
                                  
                                 jπ 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     396 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     59 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           10 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     397 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     60 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           11 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     398 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     61 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           12 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     399 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     62 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           13 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     400 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     63 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           14 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     401 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     64 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           15 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     402 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     65 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           16 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     403 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     66 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           17 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     404 
                   
                 
               
             
           
         
       
     
     
         8 . The precoding method of  claim 7 , further comprising:
 generating coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes; and   generating a signal based on the selected modulation scheme from the coded data, wherein   the positive real number α is changed in accordance with the selected modulation scheme.   
     
     
         9 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
 selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and   generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 18 matrices expressed, as Equations 405 through 422.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     67 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                             
                               
                                  
                                 jπ 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     405 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     68 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     406 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     69 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           2 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     407 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     70 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           3 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     408 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     71 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           4 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     409 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     72 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           5 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     410 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     73 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           6 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     411 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     74 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           7 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     412 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     75 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     413 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     76 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           9 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                             
                               
                                  
                                 jπ 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     414 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     77 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           10 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     415 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     78 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           11 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     416 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     79 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           12 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     417 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     80 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           13 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     418 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     81 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           14 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     419 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     82 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           15 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     420 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     83 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           16 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     421 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     84 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           17 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     422 
                   
                 
               
             
           
         
       
     
     
         10 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
 the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being nine matrices expressed, using a positive real number α, as Equations 339 through 347.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     85 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                             
                               
                                  
                                 jπ 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     339 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     86 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     340 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     87 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           2 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     341 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     88 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           3 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     342 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     89 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           4 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     343 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     90 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           5 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     344 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     91 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           6 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     345 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     92 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           7 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     346 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     93 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                            
                           = 
                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 j0 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   j0 
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     347 
                   
                 
               
             
           
         
       
     
     
         11 . The transmission device of  claim 10 , wherein
 the transmission device further generates coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes, and generates a signal based on the selected modulation scheme from the coded data, and   the positive real number a is changed in accordance with the selected modulation scheme.   
     
     
         12 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
 the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being nine matrices expressed, as Equations 348 through 356.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     94 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     348 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     95 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     2 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     349 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     96 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           2 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     4 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     350 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     97 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           3 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     6 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     351 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     98 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           4 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     8 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     352 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     99 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           5 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     10 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     353 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     100 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           6 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     12 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     354 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     101 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           7 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     14 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     355 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     102 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         
                           ( 
                           
                             
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                             
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             16 
                                             9 
                                           
                                            
                                           π 
                                         
                                         + 
                                         π 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                         . 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     356 
                   
                 
               
             
           
         
       
     
     
         13 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
 the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 15 matrices expressed, using a positive real number α, as Equations 357 through 371.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     103 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     357 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     104 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     358 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     105 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           2 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     359 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     106 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           3 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     360 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     107 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           4 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     361 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     108 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           5 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     362 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     109 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           6 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     363 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     110 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           7 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     364 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     111 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     365 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     112 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           9 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       18 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           18 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     366 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     113 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           10 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       20 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           20 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     367 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     114 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           11 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       22 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           22 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     368 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     115 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           12 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       24 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           24 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     369 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     116 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           13 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       26 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           26 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     370 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     117 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           14 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         
                           ( 
                           
                             
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                               
                                 
                                   α 
                                   × 
                                   
                                      
                                     
                                       j 
                                        
                                       
                                           
                                       
                                        
                                       0 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   α 
                                   × 
                                   
                                      
                                     
                                       j 
                                        
                                       
                                         28 
                                         15 
                                       
                                        
                                       π 
                                     
                                   
                                 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             28 
                                             15 
                                           
                                            
                                           π 
                                         
                                         + 
                                         π 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                         . 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     371 
                   
                 
               
             
           
         
       
     
     
         14 . The transmission device of  claim 13 , wherein
 the transmission device further generates coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes, and generates a signal based on the selected modulation scheme from the coded data, and   the positive real number α is changed in accordance with the selected modulation scheme.   
     
     
         15 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
 the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 15 matrices expressed, as Equations 372 through 386.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     118 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     372 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     119 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     2 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     373 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     120 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           2 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     4 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     374 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     121 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           3 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     6 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     375 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     122 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           4 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     8 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     376 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     123 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           5 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     10 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     377 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     124 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           6 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     12 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     378 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     125 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           7 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     14 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     379 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     126 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     16 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     380 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     127 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           9 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     18 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           18 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     381 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     128 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           10 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     20 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           20 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     382 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     129 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           11 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     22 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           22 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     383 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     130 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           12 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     24 
                                     9 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           24 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     384 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     131 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           13 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     26 
                                     15 
                                   
                                    
                                   π 
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           26 
                                           15 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     385 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     132 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           14 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         
                           ( 
                           
                             
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                             
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       28 
                                       15 
                                     
                                      
                                     π 
                                   
                                 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             28 
                                             15 
                                           
                                            
                                           π 
                                         
                                         + 
                                         π 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                         . 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     386 
                   
                 
               
             
           
         
       
     
     
         16 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
 the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 18 matrices expressed, using a positive real number α, as Equations 387 through 404.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     133 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     387 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     134 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     388 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     135 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           2 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     389 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     136 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           3 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     390 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     137 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           4 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     391 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     138 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           5 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     392 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     139 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           6 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     393 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     140 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           7 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     394 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     141 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           8 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     395 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     142 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           9 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     396 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     143 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           10 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     397 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     144 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           11 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     398 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     145 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           12 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     399 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     146 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           13 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     400 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     147 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           14 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     401 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     148 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           15 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     402 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     149 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           16 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     403 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     150 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           17 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                        
                       
                         
                           ( 
                           
                             
                               
                                 
                                   α 
                                   × 
                                   
                                      
                                     
                                       j 
                                        
                                       
                                         16 
                                         9 
                                       
                                        
                                       π 
                                     
                                   
                                 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             16 
                                             9 
                                           
                                            
                                           π 
                                         
                                         + 
                                         π 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                               
                                 
                                   α 
                                   × 
                                   
                                      
                                     
                                       j 
                                        
                                       
                                           
                                       
                                        
                                       0 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                         . 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     404 
                   
                 
               
             
           
         
       
     
     
         17 . The transmission device of  claim 16 , wherein
 the transmission device further generates coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes, and generates a signal based on the selected modulation scheme from the coded data, and   the positive real number α is changed in accordance with the selected modulation scheme.   
     
     
         18 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
 the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 18 matrices expressed, as Equations 405 through 422.   
       
         
           
             
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     151 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           0 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     405 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     152 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       F 
                        
                       
                         [ 
                         
                           i 
                           = 
                           1 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     406 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     153 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         2 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     407 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     154 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         3 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     408 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     155 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         4 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     409 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     156 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         5 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     410 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     157 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         6 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     411 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     158 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         7 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     412 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     159 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         8 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       16 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           16 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     413 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     160 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         9 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     414 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     161 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         10 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       2 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     415 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     162 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         11 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       4 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     416 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     163 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         12 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       6 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     417 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     164 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         13 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       8 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     418 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     165 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         14 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       10 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           10 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     419 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     166 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         15 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       12 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           12 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     420 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     167 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         16 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       14 
                                       9 
                                     
                                      
                                     π 
                                   
                                 
                               
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           14 
                                           9 
                                         
                                          
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                       
                                   
                                    
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     421 
                   
                 
               
               
                 
                   
                     Math 
                      
                     
                         
                     
                      
                     168 
                   
                 
                 
                   
                       
                   
                 
               
               
                 
                   
                     
                       [ 
                       
                         i 
                         = 
                         17 
                       
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                        
                       
                         
                           ( 
                           
                             
                               
                                 
                                   α 
                                   × 
                                   
                                      
                                     
                                       j 
                                        
                                       
                                         16 
                                         9 
                                       
                                        
                                       π 
                                     
                                   
                                 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             16 
                                             9 
                                           
                                            
                                           π 
                                         
                                         + 
                                         π 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                               
                                 
                                   α 
                                   × 
                                   
                                      
                                     
                                       j 
                                        
                                       
                                           
                                       
                                        
                                       0 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                         . 
                       
                     
                   
                 
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     422

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