US2020162142A1PendingUtilityA1

Method and apparatus to enable csi reporting in wireless communication systems

Assignee: SAMSUNG ELECTRONICS CO LTDPriority: Nov 15, 2018Filed: Nov 13, 2019Published: May 21, 2020
Est. expiryNov 15, 2038(~12.3 yrs left)· nominal 20-yr term from priority
H04B 7/0639H04L 5/0051H04B 7/0417H04B 7/0469H04B 7/0486H04B 7/0626H04B 7/0481H04B 7/0456
57
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Claims

Abstract

A method of a user equipment (UE) in a wireless communication system is provided. The method comprises: receiving, from a base station (BS), CSI feedback configuration information; and deriving, based on the CSI feedback configuration information, the CSI feedback including a precoding matrix indicator (PMI), transmitting, to the BS via an uplink channel, the CSI feedback including the PMI, wherein, for each layer l=1, 2, . . . , v, the PMI indicates KNZ,l non-zero (NZ) coefficients out of a total of 2LMv coefficients, each of which is represented as cl,i,m=pl,i,m(1)pl,i,m(2)ϕl,i,m, the KNZ,l NZ coefficients are partitioned into two groups (G0 and G1), and for each group Gr, rϵ{0,1}, one pl,i,m(1) value is indicated, where v is a rank value, pl,i,m(1) is a first amplitude coefficient, pl,i,m(2) is a second amplitude coefficient, and ϕl,i,m is a phase coefficient.

Claims

exact text as granted — not AI-modified
What is claimed is: 
     
         1 . A user equipment (UE) for a channel state information (CSI) feedback in a wireless communication system, the UE comprising:
 a transceiver configured to receive, from a base station (BS), CSI feedback configuration information; and   a processor operably connected to the transceiver, the processor configured to derive, based on the CSI feedback configuration information, the CSI feedback including a precoding matrix indicator (PMI),   wherein the transceiver is further configured to transmit, to the BS via an uplink channel, the CSI feedback including the PMI,   wherein, for each layer l=1, 2, . . . , v, the PMI indicates K NZ,l  non-zero (NZ) coefficients out of a total of 2LM v  coefficients, each of which is represented as c l,i,m =p l,i,m   (1) p l,i,m   (2) ϕ l,i,m  the K NZ,l  NZ coefficients are partitioned into two groups (G 0  and G 1 ), and for each group G r , rϵ{0,1}, one p l,i,m   (1)  value is indicated, where v is a rank value, p l,i,m   (1)  is a first amplitude coefficient, p l,i,m   (2)  is a second amplitude coefficient, and ϕ l,i,m  is a phase coefficient.   
     
     
         2 . The UE of  claim 1 , wherein:
 the total of 2LM v  coefficients forms a 2L×M v  coefficient matrix C l  comprising 2L rows and M v  columns;   the group G 0  comprises all coefficients c l,i,m  with an index iϵ{0,1, . . . ,L−1};   the group G 1  comprises all coefficients c l,i,m  with an index iϵ{L, L+1, . . . ,2L−1}; and   the one p l,i,m   (1)  value indicated for the group G r  is given by p l,i,m   (1) =p l,r   (1) , where   
       
         
           
             
               r 
               = 
               
                 
                   ⌊ 
                   
                     i 
                     L 
                   
                   ⌋ 
                 
                 . 
               
             
           
         
       
     
     
         3 . The UE of  claim 2 , wherein the PMI includes amplitude coefficient indicators i 2,3,l  and i 2,4,l  for first amplitude coefficients and second amplitude coefficients, respectively, given by:
     i   2,3,l =[ k   l,0   (1)    k   l,1   (1) ],       i   2,4,l =[ k   l,0   (2)    . . . k   l,M-1   (2) ],       k   l,m   (2) =[ k   l,0,m   (2)    . . . k   l,2L-1,m   (2) ],       k   l,r   (1) ϵ{1, . . . ,15}, and
       k   l,i,m   (2) ϵ{1, . . . ,7},
   
       where the first amplitude coefficients and the second amplitude coefficients are represented by:
     p   l   (1) =[ p   l,0   (1)    p   l,1   (1) ], 
     p   l   (2) =[ p   l,0   (2)    . . . p   l,M-1   (2) ], and 
     p   l,m   (2) =[ p   l,0,m   (2)    . . . p   l,2L-1,m   (2) ], 
 
       a mapping from k l,r   (1)  to the first amplitude coefficient p l,r   (1)  i s given by: 
       
         
           
                 
                 
                 
               
                     
                 
                     
                   k l,r   (1)    
                   p l,r   (1)   
                 
                     
                 
                     
                 
                 
                 
                 
               
                     
                   0 
                   Reserved 
                 
                     
                 
                     
                   1 
                   
                     
                       
                         
                           1 
                           
                             128 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   2 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               8192 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   3 
                   
                     
                       
                         
                           1 
                           8 
                         
                       
                     
                   
                 
                     
                 
                     
                   4 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               2048 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   5 
                   
                     
                       
                         
                           1 
                           
                             2 
                              
                             
                               8 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   6 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               512 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   7 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               128 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   8 
                   
                     
                       
                         
                           1 
                           
                             8 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   9 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               128 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   10 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               32 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   11 
                   
                     
                       
                         
                           1 
                           2 
                         
                       
                     
                   
                 
                     
                 
                     
                   12 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               8 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   13 
                   
                     
                       
                         
                           1 
                           
                             2 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   14 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               2 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   15 
                   1 
                 
                     
                 
             
                
                
                
               
               
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
               
            
           
         
       
       and a mapping from k l,i,m   (2)  to the second amplitude coefficient p l,i,m   (2)  is given by: 
       
         
           
                 
                 
                 
               
                     
                 
                     
                   k l,i,m   (2)   
                   p l,i,m   (2)   
                 
                     
                 
                     
                   0 
                   
                     
                       
                         
                           1 
                           
                             8 
                              
                             
                               2 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   1 
                   
                     
                       
                         
                           1 
                           8 
                         
                       
                     
                   
                 
                     
                 
                     
                   2 
                   
                     
                       
                         
                           1 
                           
                             4 
                              
                             
                               2 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   3 
                   
                     
                       
                         
                           1 
                           4 
                         
                       
                     
                   
                 
                     
                 
                     
                   4 
                   
                     
                       
                         
                           1 
                           
                             2 
                              
                             
                               2 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   5 
                   
                     
                       
                         
                           1 
                           2 
                         
                       
                     
                   
                 
                     
                 
                     
                   6 
                   
                     
                       
                         
                           1 
                           
                             2 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   7 
                   1 
                 
                     
                 
             
                
                
                
               
               
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
               
            
           
         
       
     
     
         4 . The UE of  claim 2 , wherein, for each layer l=1, . . . ,v:
 the processor is further configured to determine a strongest coefficient indicator i 1,8,l  indicating an index (i* l , m* l ) that jointly indicates:   a location of a strongest coefficient c l,i*     l     ,m*     l   =1, and   a first amplitude coefficient indicator k l,r*   (1)  indicating p l,r*   (1) =1 for the group G r*  to which the strongest coefficient belongs, where   
       
         
           
             
               
                 
                   r 
                   * 
                 
                 = 
                 
                   ⌊ 
                   
                     
                       i 
                       l 
                       * 
                     
                     L 
                   
                   ⌋ 
                 
               
               ; 
             
           
         
       
       and
 the transceiver is further configured to transmit, to the BS, the CSI feedback including the PMI that includes the determined strongest coefficient indicator i 1,8,l . 
 
     
     
         5 . The UE of  claim 4 , wherein, for each layer l=1, . . . , v:
 the processor is further configured to:
 determine another group G r , where r≠r*; and 
 determine a first amplitude coefficient indicator k l,r*   (1)  indicating p l,r*   (1)  for the other group G r ; and 
   the transceiver is further configured to transmit, to the BS, the CSI feedback including the PMI that includes i 2,3,l  indicating the first amplitude coefficient indicator for the other group.   
     
     
         6 . The UE of  claim 5 , wherein the transceiver is further configured to transmit, using the CSI feedback, the PMI including, for each layer l=1, . . . , v:
 one indicator for the first amplitude coefficient associated with the other group G r ;   K NZ,l −1 indicators for the second amplitude coefficients; and   K NZ,l −1 indicators for phase coefficients,   where for remaining 2LM v −K NZ,l  coefficients, the second amplitude coefficients and the phase coefficients are set to p l,i,m   (2) =ϕ l,i,m =0.   
     
     
         7 . The UE of  claim 2 , wherein the PMI further includes indicators for a spatial domain (SD) basis matrix A and a frequency domain (FD) basis matrix B l  for each layer l=1, . . . , v, and
 wherein:
 a precoding matrix for each FD unit of a total number (N 3 ) of FD units is determined by columns of 
   
       
         
           
             
               
                   
               
                
               
                 
                   W 
                   = 
                   
                     
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                         v 
                       
                     
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                           W 
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                          
                         … 
                          
                         
                             
                         
                          
                         
                           W 
                           v 
                         
                       
                       ] 
                     
                   
                 
                 , 
                 where 
               
             
           
         
         
           
             
               
                 W 
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               = 
               
                 
                   
                     [ 
                     
                       
                         
                           A 
                         
                         
                           0 
                         
                       
                       
                         
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                     ] 
                   
                    
                   
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                     l 
                   
                    
                   
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                     l 
                     H 
                   
                 
                 = 
                 
                   
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       is a pre-coding matrix for layer l, whose t-th column is a pre-coding matrix for FD unit t and is given by 
       
         
           
             
               
                 W 
                 t 
                 l 
               
               = 
               
                 
                   1 
                   
                     
                       
                         N 
                         1 
                       
                        
                       
                         N 
                         2 
                       
                        
                       
                         γ 
                         
                           t 
                           , 
                           l 
                         
                       
                     
                   
                 
                  
                 
                     
                   
                     
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                     , 
                     
                       
                         where 
                          
                         
                           
 
                         
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                            
                           
                             
                                
                               
                                 
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       normalizes t-th column to norm one;
 A=[a 0  a 1  . . . a L-1 ], a i =v m     1       (i)   , v m     1       (i)    is a N 1 N 2 ×1 column vector for SD antenna ports where N 1  and N 2  are number of antenna ports, respectively, with a same antenna polarization in a first and a second dimensions of a two-dimensional dual-polarized channel state information-reference signal (CSI-RS) antenna ports at the BS; 
 B l =[b l,0  b l,1  . . . b l,M     v     -1 ], b l,m  is a N 3 ×1 column vector for FD units, and y t,l   (m) =the t-th entry of m-th FD basis vector b l,m ; and 
 a number (L) of column vectors for the SD antenna ports, a number (M v ) of column vectors for the FD units, and the total number (N 3 ) of the FD units are configured via higher layer signaling. 
 
     
     
         8 . A base station (BS) in a wireless communication system, the BS comprising:
 a transceiver configured to:
 transmit, to a user equipment (UE), CSI feedback configuration information; and 
 receive, from the UE via an uplink channel, a CSI feedback including a precoding matrix indicator (PMI), 
   wherein, for each layer l=1, 2, . . . , v, the PMI indicates K NZ,l  non-zero (NZ) coefficients out of a total of 2 LM v  coefficients, each of which is represented as c l,i,m =p l,i,m   (1) p l,i,m   (2) ϕ l,i,m , the K NZ,l  NZ coefficients are partitioned into two groups (G 0  and G 1 ), and for each group G r , rϵ{0,1}, one p l,i,m   (1)  value is indicated, where v is a rank value, p l,i,m   (1)  is a first amplitude coefficient, p l,i,m   (2)  is a second amplitude coefficient, and ϕ l,i,m  is a phase coefficient, and   wherein the CSI feedback including the PMI is based on the CSI feedback configuration information.   
     
     
         9 . The BS of  claim 8 , wherein:
 the total of 2LM v  coefficients forms a 2L×M v  coefficient matrix C l  comprising 2L rows and M v  columns;   the group G 0  comprises all coefficients c l,i,m  with an index iϵ{0,1, . . . ,L−1};   the group G 1  comprises all coefficients c l,i,m  with an index iϵ{L, L+1, . . . ,2L−1}; and   the one p l,i,m   (1)  value indicated for the group G r  is given by p l,i,m   (1) =p l,r   (1) , where   
       
         
           
             
               r 
               = 
               
                 
                   ⌊ 
                   
                     i 
                     L 
                   
                   ⌋ 
                 
                 . 
               
             
           
         
       
     
     
         10 . The BS of  claim 9 , wherein the PMI includes amplitude coefficient indicators i 2,3,l  and i 2,4,l  for first amplitude coefficients and second amplitude coefficients, respectively, given by:
     i   2,3,l =[ k   l,0   (1)    k   l,1   (1) ],       i   2,4,l =[ k   l,0   (2)    . . . k   l,M-1   (2) ],       k   l,m   (2) =[ k   l,0,m   (2)    . . . k   l,2L-1,m   (2) ],       k   l,r   (1) ϵ{1, . . . ,15}, and
       k   l,i,m   (2) ϵ{1, . . . ,7},
   
       where the first amplitude coefficients and the second amplitude coefficients are represented by:
     p   l   (1) =[ p   l,0   (1)    p   l,1   (1) ], 
     p   l   (2) =[ p   l,0   (2)    . . . p   l,M-1   (2) ], and 
     p   l,m   (2) =[ p   l,0,m   (2)    . . . p   l,2L-1,m   (2) ], 
 
       a mapping from k l,r   (1)  to the first amplitude coefficient p l,r   (1)  i s given by: 
       
         
           
                 
                 
                 
               
                     
                 
                     
                   k l,r   (1)   
                   p l,r   (1)   
                 
                     
                 
                     
                 
                 
                 
                 
               
                     
                   0 
                   Reserved 
                 
                     
                 
                     
                   1 
                   
                     
                       
                         
                           1 
                           
                             128 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   2 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               8192 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   3 
                   
                     
                       
                         
                           1 
                           8 
                         
                       
                     
                   
                 
                     
                 
                     
                   4 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               2048 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   5 
                   
                     
                       
                         
                           1 
                           
                             2 
                              
                             
                               8 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   6 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               512 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   7 
                   
                     
                       
                         
                           1 
                           4 
                         
                       
                     
                   
                 
                     
                 
                     
                   8 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               128 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   9 
                   
                     
                       
                         
                           1 
                           
                             8 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   10 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               32 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   11 
                   
                     
                       
                         
                           1 
                           2 
                         
                       
                     
                   
                 
                     
                 
                     
                   12 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               8 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   13 
                   
                     
                       
                         
                           1 
                           
                             2 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   14 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               2 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   15 
                   1 
                 
                     
                 
             
                
                
                
               
               
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
               
            
           
         
         and a mapping from k l,i,m   (2)  to the second amplitude coefficient p l,i,m   (2)  is given by: 
       
       
         
           
                 
                 
                 
               
                     
                 
                     
                   k l,i,m   (2)   
                   p l,i,m   (2)   
                 
                     
                 
                     
                   0 
                   
                     
                       
                         
                           1 
                           
                             8 
                              
                             
                               2 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   1 
                   
                     
                       
                         
                           1 
                           8 
                         
                       
                     
                   
                 
                     
                 
                     
                   2 
                   
                     
                       
                         
                           1 
                           
                             4 
                              
                             
                               2 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   3 
                   
                     
                       
                         
                           1 
                           4 
                         
                       
                     
                   
                 
                     
                 
                     
                   4 
                   
                     
                       
                         
                           1 
                           
                             2 
                              
                             
                               2 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   5 
                   
                     
                       
                         
                           1 
                           2 
                         
                       
                     
                   
                 
                     
                 
                     
                   6 
                   
                     
                       
                         
                           1 
                           
                             2 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   7 
                   1 
                 
                     
                 
             
                
                
                
               
               
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
               
            
           
         
       
     
     
         11 . The BS of  claim 9 , wherein, for each layer l=1, . . . ,v, the transceiver is further configured to receive, from the UE, the CSI feedback including the PMI that includes a strongest coefficient indicator i 1,8,l , and
 wherein the strongest coefficient indicator i 1,8,l  indicates an index (i* l ,m* l ) that jointly indicates:   a location of a strongest coefficient c l,i*     l     ,m*     l   =1, and   a first amplitude coefficient indicator k l,r*   (1)  indicating p l,r*   (1) =1 for the group G r*  to which the strongest coefficient belongs, where   
       
         
           
             
               
                 r 
                 * 
               
               = 
               
                 
                   ⌊ 
                   
                     
                       i 
                       l 
                       * 
                     
                     L 
                   
                   ⌋ 
                 
                 . 
               
             
           
         
       
     
     
         12 . The BS of  claim 11 , wherein, for each layer l=1, . . . ,v, the transceiver is further configured to receive, from the UE, the CSI feedback including the PMI that includes i 2,3,l  indicating a first amplitude coefficient indicator k l,r   (1)  for another group G r , and wherein r≠r*; and the first amplitude coefficient indicator k l,r   (1)  indicates p l,r   (1)  for the other group G r . 
     
     
         13 . The BS of  claim 12 , wherein the transceiver is further configured to receive, using the CSI feedback, the PMI including, for each layer l=1, . . . , v:
 one indicator for the first amplitude coefficient associated with the other group G r ;   K NZ,l −1 indicators for the second amplitude coefficients; and   K NZ,l −1 indicators for the phase coefficients,   where for remaining 2LM v −K NZ,l  coefficients, the second amplitude coefficients and the phase coefficients are set to p l,i,m   (2) =ϕ l,i,m = 0 .   
     
     
         14 . The BS of  claim 9 , wherein the PMI further includes indicators for a spatial domain (SD) basis matrix A and a frequency domain (FD) basis matrix B 1  for each layer l=1, . . . , v, and
 wherein:
 a precoding matrix for each FD unit of a total number (N 3 ) of FD units is determined by columns of 
   
       
         
           
             
               
                   
               
                
               
                 
                   W 
                   = 
                   
                     
                       1 
                       
                         v 
                       
                     
                      
                     
                       [ 
                       
                         
                           W 
                           1 
                         
                          
                         
                             
                         
                          
                         
                           W 
                           2 
                         
                          
                         
                             
                         
                          
                         … 
                          
                         
                             
                         
                          
                         
                           W 
                           v 
                         
                       
                       ] 
                     
                   
                 
                 , 
                 where 
               
             
           
         
         
           
             
               
                 W 
                 l 
               
               = 
               
                 
                   
                     [ 
                     
                       
                         
                           A 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           A 
                         
                       
                     
                     ] 
                   
                    
                   
                     C 
                     l 
                   
                    
                   
                     B 
                     l 
                     H 
                   
                 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 0 
                               
                               
                                 L 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                 a 
                                 i 
                               
                                
                               
                                 
                                   ∑ 
                                   
                                     m 
                                     = 
                                     0 
                                   
                                   
                                     
                                       M 
                                       v 
                                     
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   
                                     C 
                                     
                                       l 
                                       , 
                                       i 
                                       , 
                                       m 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       b 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 0 
                               
                               
                                 L 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                 a 
                                 i 
                               
                                
                               
                                 
                                   ∑ 
                                   
                                     m 
                                     = 
                                     0 
                                   
                                   
                                     
                                       M 
                                       v 
                                     
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   
                                     C 
                                     
                                       l 
                                       , 
                                       
                                         i 
                                         + 
                                         L 
                                       
                                       , 
                                       m 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       b 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       [ 
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   0 
                                 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   a 
                                   i 
                                 
                                  
                                 
                                   p 
                                   
                                     l 
                                     , 
                                     0 
                                   
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       m 
                                       = 
                                       0 
                                     
                                     
                                       
                                         M 
                                         v 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       p 
                                       
                                         l 
                                         , 
                                         i 
                                         , 
                                         m 
                                       
                                       
                                         ( 
                                         2 
                                         ) 
                                       
                                     
                                      
                                     
                                       
                                         ϕ 
                                         
                                           l 
                                           , 
                                           i 
                                           , 
                                           m 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           b 
                                           
                                             l 
                                             , 
                                             m 
                                           
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   0 
                                 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   a 
                                   i 
                                 
                                  
                                 
                                   p 
                                   
                                     l 
                                     , 
                                     1 
                                   
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       m 
                                       = 
                                       0 
                                     
                                     
                                       
                                         M 
                                         v 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       p 
                                       
                                         l 
                                         , 
                                         
                                           i 
                                           + 
                                           L 
                                         
                                         , 
                                         m 
                                       
                                       
                                         ( 
                                         2 
                                         ) 
                                       
                                     
                                      
                                     
                                       
                                         ϕ 
                                         
                                           l 
                                           , 
                                           
                                             i 
                                             + 
                                             L 
                                           
                                           , 
                                           m 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           b 
                                           
                                             l 
                                             , 
                                             m 
                                           
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
             
           
         
       
       is a pre-coding matrix for layer l, whose t-th column is a pre-coding matrix for FD unit t and is given by 
       
         
           
             
               
                 W 
                 t 
                 l 
               
               = 
               
                 
                   1 
                   
                     
                       
                         N 
                         1 
                       
                        
                       
                         N 
                         2 
                       
                        
                       
                         γ 
                         
                           t 
                           , 
                           l 
                         
                       
                     
                   
                 
                  
                 
                     
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   0 
                                 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   a 
                                   i 
                                 
                                  
                                 
                                   p 
                                   
                                     l 
                                     , 
                                     0 
                                   
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       m 
                                       = 
                                       0 
                                     
                                     
                                       
                                         M 
                                         v 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       y 
                                       
                                         t 
                                         , 
                                         l 
                                       
                                       
                                         ( 
                                         m 
                                         ) 
                                       
                                     
                                      
                                     
                                       p 
                                       
                                         l 
                                         , 
                                         i 
                                         , 
                                         m 
                                       
                                       
                                         ( 
                                         2 
                                         ) 
                                       
                                     
                                      
                                     
                                       ϕ 
                                       
                                         l 
                                         , 
                                         i 
                                         , 
                                         m 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   0 
                                 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   a 
                                   i 
                                 
                                  
                                 
                                   p 
                                   
                                     l 
                                     , 
                                     1 
                                   
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       m 
                                       = 
                                       0 
                                     
                                     
                                       
                                         M 
                                         v 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       y 
                                       
                                         t 
                                         , 
                                         l 
                                       
                                       
                                         ( 
                                         m 
                                         ) 
                                       
                                     
                                      
                                     
                                       p 
                                       
                                         l 
                                         , 
                                         
                                           i 
                                           + 
                                           L 
                                         
                                         , 
                                         m 
                                       
                                       
                                         ( 
                                         2 
                                         ) 
                                       
                                     
                                      
                                     
                                       ϕ 
                                       
                                         l 
                                         , 
                                         
                                           i 
                                           + 
                                           L 
                                         
                                         , 
                                         m 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                     , 
                     
                       
                         where 
                          
                         
                           
 
                         
                          
                         
                           γ 
                           
                             t 
                             , 
                             l 
                           
                         
                       
                       = 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             0 
                           
                           
                             
                               2 
                                
                               L 
                             
                             - 
                             1 
                           
                         
                          
                         
                           
                             
                               ( 
                               
                                 p 
                                 
                                   l 
                                   , 
                                   
                                     ⌊ 
                                     
                                       i 
                                       L 
                                     
                                     ⌋ 
                                   
                                 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                               ) 
                             
                             2 
                           
                            
                           
                             
                                
                               
                                 
                                   ∑ 
                                   
                                     m 
                                     = 
                                     0 
                                   
                                   
                                     M 
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   
                                     y 
                                     
                                       t 
                                       , 
                                       l 
                                     
                                     
                                       ( 
                                       m 
                                       ) 
                                     
                                   
                                    
                                   
                                     p 
                                     
                                       l 
                                       , 
                                       i 
                                       , 
                                       m 
                                     
                                     
                                       ( 
                                       2 
                                       ) 
                                     
                                   
                                    
                                   
                                     ϕ 
                                     
                                       l 
                                       , 
                                       i 
                                       , 
                                       m 
                                     
                                   
                                 
                               
                                
                             
                             2 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       normalizes t-th column to norm one;
 A=[a 0  a 1  . . . a L-1 ], a i =v m     1       (i)   , v m     1       (i)    is a N 1 N 2 ×1 column vector for SD antenna ports where N 1  and N 2  are number of antenna ports, respectively, with a same antenna polarization in a first and a second dimensions of a two-dimensional dual-polarized channel state information-reference signal (CSI-RS) antenna ports at the BS; 
 B l =[b l,0  b l,1  . . . b l,M     v     -1 ], b l,m  is a N 3 ×1 column vector for FD units, and y t,l   (m) =the t-th entry of m-th FD basis vector b l,m ; and 
 a number (L) of column vectors for the SD antenna ports, a number (M v ) of column vectors for the FD units, and the total number (N 3 ) of the FD units are configured via higher layer signaling. 
 
     
     
         15 . A method of a user equipment (UE) in a wireless communication system, the method comprising:
 receiving, from a base station (BS), CSI feedback configuration information;   deriving, based on the CSI feedback configuration information, the CSI feedback including a precoding matrix indicator (PMI); and   transmitting, to the BS via an uplink channel, the CSI feedback including the PMI,   wherein, for each layer l=1, 2, . . . , v, the PMI indicates K NZ,l  non-zero (NZ) coefficients out of a total of 2 LM v  coefficients, each of which is represented as c l,i,m =p l,i,m   (1) p l,i,m   (2) ϕ l,i,m , the K NZ,l  NZ coefficients are partitioned into two groups (G 0  and G 1 ), and for each group G r , rϵ{0,1}, one p l,i,m   (1)  value is indicated, where v is a rank value, p l,i,m   (1)  is a first amplitude coefficient, p l,i,m   (2)  is a second amplitude coefficient, and ϕ l,i,m  is a phase coefficient.   
     
     
         16 . The method of  claim 15 , wherein:
 the total of 2LM v  coefficients forms a 2L×M v  coefficient matrix C l  comprising 2L rows and M v  columns;   the group G 0  comprises all coefficients c l,i,m  with an index iϵ{0,1, . . . ,L−1};   the group G 1  comprises all coefficients c l,i,m  with an index iϵ{L, L+1, . . . ,2L−1};   the one p l,i,m   (1)  value indicated for the group G r  is given by p l,i,m   (1) =p l,r   (1) , where   
       
         
           
             
               
                 r 
                 = 
                 
                   ⌊ 
                   
                     i 
                     L 
                   
                   ⌋ 
                 
               
               ; 
             
           
         
       
       and
 the PMI includes amplitude coefficient indicators i 2,3,l  and i 2,4,l  for first amplitude coefficients and second amplitude coefficients, respectively, given by:
     i   2,3,l =[ k   l,0   (1)    k   l,1   (1) ], 
     i   2,4,l =[ k   l,0   (2)    . . . k   l,M-1   (2) ], 
     k   l,m   (2) =[ k   l,0,m   (2)    . . . k   l,2L-1,m   (2) ], 
     k   l,r   (1) ϵ{1, . . . ,15}, and
 
     k   l,i,m   (2) ϵ{1, . . . ,7},
 
 
 
       where the first amplitude coefficients and the second amplitude coefficients are represented by:
     p   l   (1) =[ p   l,0   (1)    p   l,1   (1) ], 
     p   l   (2) =[ p   l,0   (2)    . . . p   l,M-1   (2) ], and 
     p   l,m   (2) =[ p   l,0,m   (2)    . . . p   l,2L-1,m   (2) ], 
 
       a mapping from k l,r   (1)  to the first amplitude coefficient p l,r   (1)  i s given by: 
       
         
           
                 
                 
                 
               
                     
                 
                     
                   k l,r   (1)   
                   p l,r   (1)   
                 
                     
                 
                     
                 
                 
                 
                 
               
                     
                   0 
                   Reserved 
                 
                     
                 
                     
                   1 
                   
                     
                       
                         
                           1 
                           
                             128 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   2 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               8192 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   3 
                   
                     
                       
                         
                           1 
                           8 
                         
                       
                     
                   
                 
                     
                 
                     
                   4 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               2048 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   5 
                   
                     
                       
                         
                           1 
                           
                             2 
                              
                             
                               8 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   6 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               512 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   7 
                   
                     
                       
                         
                           1 
                           4 
                         
                       
                     
                   
                 
                     
                 
                     
                   8 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               128 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   9 
                   
                     
                       
                         
                           1 
                           
                             8 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   10 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               32 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   11 
                   
                     
                       
                         
                           1 
                           2 
                         
                       
                     
                   
                 
                     
                 
                     
                   12 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               8 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   13 
                   
                     
                       
                         
                           1 
                           
                             2 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   14 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               2 
                             
                             ) 
                           
                           
                             1 
                             / 
                             4 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   15 
                   1 
                 
                     
                 
             
                
                
                
               
               
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
               
            
           
         
       
       and a mapping from k l,i,m   (2)  to the second amplitude coefficient p l,i,m   (2)  is given by: 
       
         
           
                 
                 
                 
               
                     
                 
                     
                   k l,i,m   (2)   
                   p l,i,m   (2)   
                 
                     
                 
                     
                   0 
                   
                     
                       
                         
                           1 
                           
                             8 
                              
                             
                               2 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   1 
                   
                     
                       
                         
                           1 
                           8 
                         
                       
                     
                   
                 
                     
                 
                     
                   2 
                   
                     
                       
                         
                           1 
                           
                             4 
                              
                             
                               2 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   3 
                   
                     
                       
                         
                           1 
                           4 
                         
                       
                     
                   
                 
                     
                 
                     
                   4 
                   
                     
                       
                         
                           1 
                           
                             2 
                              
                             
                               2 
                             
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   5 
                   
                     
                       
                         
                           1 
                           2 
                         
                       
                     
                   
                 
                     
                 
                     
                   6 
                   
                     
                       
                         
                           1 
                           
                             2 
                           
                         
                       
                     
                   
                 
                     
                 
                     
                   7 
                   1 
                 
                     
                 
             
                
                
                
               
               
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
                
               
            
           
         
       
     
     
         17 . The method of  claim 16 , wherein, for each layer l=1, . . . , v, further comprising:
 determining a strongest coefficient indicator i 1,8,l  indicating an index (i* l , m* l ) that jointly indicates:
 a location of a strongest coefficient c l,i*     l     ,m*     l   =1, and 
 a first amplitude coefficient indicator k l,r*   (1)  indicating p l,r*   (1) =1 for the group G r*  to which the strongest coefficient belongs, where 
   
       
         
           
             
               
                 
                   r 
                   * 
                 
                 = 
                 
                   ⌊ 
                   
                     
                       i 
                       l 
                       * 
                     
                     L 
                   
                   ⌋ 
                 
               
               ; 
             
           
         
       
       and
 which the strongest coefficient belongs, where and transmitting, to the BS, the CSI feedback including the PMI that includes the determined strongest coefficient indicator i 1,8,l . 
 
     
     
         18 . The method of  claim 17 , wherein, for each layer l=1, . . . , v, further comprising:
 determining another group G r , where r≠r*;   determining a first amplitude coefficient indicator k l,r   (1)  indicating p l,r   (1)  for the other group G r ; and   transmitting, to the BS, the CSI feedback including the PMI that includes i 2,3,l  indicating the first amplitude coefficient indicator for the other group.   
     
     
         19 . The method of  claim 15 , further comprising transmitting, using the CSI feedback, the PMI including, for each layer l=1, . . . , v:
 one indicator for the first amplitude coefficient associated with the other group G r ;   K NZ,l −1 indicators for the second amplitude coefficients; and   K NZ,l −1 indicators for phase coefficients,   where for remaining 2LM v −K NZ,l  coefficients, the second amplitude coefficients and the phase coefficients are set to p l,i,m   (2) =ϕ l,i,m =0.   
     
     
         20 . The method of  claim 16 , wherein the PMI further includes indicators for a spatial domain (SD) basis matrix A and a frequency domain (FD) basis matrix B l  for each layer l=1, . . . , v, and
 wherein:
 a precoding matrix for each FD unit of a total number (N 3 ) of FD units is determined by columns of 
   
       
         
           
             
               
                   
               
                
               
                 
                   W 
                   = 
                   
                     
                       1 
                       
                         v 
                       
                     
                      
                     
                       [ 
                       
                         
                           W 
                           1 
                         
                          
                         
                             
                         
                          
                         
                           W 
                           2 
                         
                          
                         
                             
                         
                          
                         … 
                          
                         
                             
                         
                          
                         
                           W 
                           v 
                         
                       
                       ] 
                     
                   
                 
                 , 
                 where 
               
             
           
         
         
           
             
               
                 W 
                 l 
               
               = 
               
                 
                   
                     [ 
                     
                       
                         
                           A 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           A 
                         
                       
                     
                     ] 
                   
                    
                   
                     C 
                     l 
                   
                    
                   
                     B 
                     l 
                     H 
                   
                 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 0 
                               
                               
                                 L 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                 a 
                                 i 
                               
                                
                               
                                 
                                   ∑ 
                                   
                                     m 
                                     = 
                                     0 
                                   
                                   
                                     
                                       M 
                                       v 
                                     
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   
                                     C 
                                     
                                       l 
                                       , 
                                       i 
                                       , 
                                       m 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       b 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 0 
                               
                               
                                 L 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                 a 
                                 i 
                               
                                
                               
                                 
                                   ∑ 
                                   
                                     m 
                                     = 
                                     0 
                                   
                                   
                                     
                                       M 
                                       v 
                                     
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   
                                     C 
                                     
                                       l 
                                       , 
                                       
                                         i 
                                         + 
                                         L 
                                       
                                       , 
                                       m 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       b 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                       H 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       [ 
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   0 
                                 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   a 
                                   i 
                                 
                                  
                                 
                                   p 
                                   
                                     l 
                                     , 
                                     0 
                                   
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       m 
                                       = 
                                       0 
                                     
                                     
                                       
                                         M 
                                         v 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       p 
                                       
                                         l 
                                         , 
                                         i 
                                         , 
                                         m 
                                       
                                       
                                         ( 
                                         2 
                                         ) 
                                       
                                     
                                      
                                     
                                       
                                         ϕ 
                                         
                                           l 
                                           , 
                                           i 
                                           , 
                                           m 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           b 
                                           
                                             l 
                                             , 
                                             m 
                                           
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   0 
                                 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   a 
                                   i 
                                 
                                  
                                 
                                   p 
                                   
                                     l 
                                     , 
                                     1 
                                   
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       m 
                                       = 
                                       0 
                                     
                                     
                                       
                                         M 
                                         v 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       p 
                                       
                                         l 
                                         , 
                                         
                                           i 
                                           + 
                                           L 
                                         
                                         , 
                                         m 
                                       
                                       
                                         ( 
                                         2 
                                         ) 
                                       
                                     
                                      
                                     
                                       
                                         ϕ 
                                         
                                           l 
                                           , 
                                           
                                             i 
                                             + 
                                             L 
                                           
                                           , 
                                           m 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           b 
                                           
                                             l 
                                             , 
                                             m 
                                           
                                           H 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
             
           
         
       
       is a pre-coding matrix for layer l, whose t-th column is a pre-coding matrix for FD unit t and is given by 
       
         
           
             
               
                 W 
                 t 
                 l 
               
               = 
               
                 
                   1 
                   
                     
                       
                         N 
                         1 
                       
                        
                       
                         N 
                         2 
                       
                        
                       
                         γ 
                         
                           t 
                           , 
                           l 
                         
                       
                     
                   
                 
                  
                 
                     
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   0 
                                 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   a 
                                   i 
                                 
                                  
                                 
                                   p 
                                   
                                     l 
                                     , 
                                     0 
                                   
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       m 
                                       = 
                                       0 
                                     
                                     
                                       
                                         M 
                                         v 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       y 
                                       
                                         t 
                                         , 
                                         l 
                                       
                                       
                                         ( 
                                         m 
                                         ) 
                                       
                                     
                                      
                                     
                                       p 
                                       
                                         l 
                                         , 
                                         i 
                                         , 
                                         m 
                                       
                                       
                                         ( 
                                         2 
                                         ) 
                                       
                                     
                                      
                                     
                                       ϕ 
                                       
                                         l 
                                         , 
                                         i 
                                         , 
                                         m 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   0 
                                 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   a 
                                   i 
                                 
                                  
                                 
                                   p 
                                   
                                     l 
                                     , 
                                     1 
                                   
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       m 
                                       = 
                                       0 
                                     
                                     
                                       
                                         M 
                                         v 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       y 
                                       
                                         t 
                                         , 
                                         l 
                                       
                                       
                                         ( 
                                         m 
                                         ) 
                                       
                                     
                                      
                                     
                                       p 
                                       
                                         l 
                                         , 
                                         
                                           i 
                                           + 
                                           L 
                                         
                                         , 
                                         m 
                                       
                                       
                                         ( 
                                         2 
                                         ) 
                                       
                                     
                                      
                                     
                                       ϕ 
                                       
                                         l 
                                         , 
                                         
                                           i 
                                           + 
                                           L 
                                         
                                         , 
                                         m 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                     , 
                     
                       
                         where 
                          
                         
                           
 
                         
                          
                         
                           γ 
                           
                             t 
                             , 
                             l 
                           
                         
                       
                       = 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             0 
                           
                           
                             
                               2 
                                
                               L 
                             
                             - 
                             1 
                           
                         
                          
                         
                           
                             
                               ( 
                               
                                 p 
                                 
                                   l 
                                   , 
                                   
                                     ⌊ 
                                     
                                       i 
                                       L 
                                     
                                     ⌋ 
                                   
                                 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                               ) 
                             
                             2 
                           
                            
                           
                             
                                
                               
                                 
                                   ∑ 
                                   
                                     m 
                                     = 
                                     0 
                                   
                                   
                                     M 
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   
                                     y 
                                     
                                       t 
                                       , 
                                       l 
                                     
                                     
                                       ( 
                                       m 
                                       ) 
                                     
                                   
                                    
                                   
                                     p 
                                     
                                       l 
                                       , 
                                       i 
                                       , 
                                       m 
                                     
                                     
                                       ( 
                                       2 
                                       ) 
                                     
                                   
                                    
                                   
                                     ϕ 
                                     
                                       l 
                                       , 
                                       i 
                                       , 
                                       m 
                                     
                                   
                                 
                               
                                
                             
                             2 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       normalizes t-th column to norm one;
 A=[a 0  a 1  . . . a L-1 ], a i =v m     1       (i)   , v m     1       (i)    is a N 1 N 2 ×1 column vector for SD antenna ports where N 1  and N 2  are number of antenna ports, respectively, with a same antenna polarization in a first and a second dimensions of a two-dimensional dual-polarized channel state information-reference signal (CSI-RS) antenna ports at the BS; 
 B l =[b l,0  b l,1  . . . b l,M     v     -1 ], b l,m  is a N 3 ×1 column vector for FD units, and y t,l   (m) =the t-th entry of m-th FD basis vector b l,m ; and 
 a number (L) of column vectors for the SD antenna ports, a number (M v ) of column vectors for the FD units, and the total number (N 3 ) of the FD units are configured via higher layer signaling.

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