GFSK receiver

Abstract

A method for synchronizing a receiver to a stream of transmitted symbols that includes a known synchronization word. The method includes receiving a signal in which the symbols, including the synchronization word, are encoded by frequency shift keying. The signal is sampled and digitized to generate a sequence of input samples. For each of the input samples, a phase difference is determined relative to a preceding input sample in the sequence, thereby generating a sequence of differential samples corresponding respectively to the input samples. The differential samples are then matched to the synchronization word.

1 . A method for synchronizing a receiver to a stream of transmitted symbols that includes a known synchronization word, the method comprising: 
 receiving a signal in which the symbols, including the synchronization word, are encoded by frequency shift keying;    sampling and digitizing the signal to generate a sequence of input samples;    determining, for each of the input samples, a phase difference relative to a preceding input sample in the sequence, thereby generating a sequence of differential samples corresponding respectively to the input samples; and    matching the differential samples to the synchronization word.    
     
     
         2 . A method according to  claim 1 , wherein receiving the signal comprises receiving the signal at a radio frequency having a frequency offset relative to a channel frequency designated for the signal, and wherein determining the phase difference comprises canceling the frequency offset out of the differential samples before matching the differential samples to the synchronization word.  
     
     
         3 . A method according to  claim 1 , wherein receiving the signal comprises receiving the stream of symbols encoded by Gaussian frequency shift keying.  
     
     
         4 . A method according to  claim 1 , wherein the symbols are transmitted at a given symbol rate, and wherein sampling and digitizing the signal comprises generating the input samples at a sample rate greater than the symbol rate, and wherein determining the phase difference comprises computing the phase difference between pairs of the input samples that are separated by an interval that is a reciprocal of the symbol rate.  
     
     
         5 . A method according to  claim 1 , wherein determining the phase difference comprises taking a complex cross product between each of the input samples and the preceding input sample.  
     
     
         6 . A method according to  claim 1 , wherein matching the differential samples comprises determining reference samples that correspond to frequency shift keying of the synchronization word, and correlating the sequence of differential samples with the reference samples.  
     
     
         7 . A method according to  claim 6 , wherein determining the reference samples comprises providing coefficients such that multiplication of the symbols in the synchronization word by the coefficients will generate the reference samples, and wherein correlating the sequence of differential samples comprises multiplying the differential samples by the coefficients.  
     
     
         8 . A method according to  claim 6 , wherein correlating the sequence of differential samples comprises computing a sequence of correlation values by correlating different, respective portions of the sequence of input samples with the synchronization word, and wherein matching the differential samples comprises choosing the portion of the sequence of input samples that best matches the synchronization word by finding a peak value among the correlation values corresponding to the chosen portion.  
     
     
         9 . A method according to  claim 8 , wherein sampling and digitizing the signal comprises generating complex samples, and wherein computing the sequence of correlation values comprises computing complex correlation values, and comprising determining a phase angle of the peak correlation value, and correcting a phase of the input samples of the signal subsequent to the synchronization word responsive to the phase angle.  
     
     
         10 . A method according to  claim 1 , wherein matching the differential samples comprises finding a time offset of the input samples relative to the synchronization word, and comprising decoding the input samples of the signal subsequent to the synchronization word responsive to the time offset.  
     
     
         11 . A method according to  claim 10 , wherein matching the differential samples comprises finding a frequency offset of the signal relative to an expected frequency, and wherein decoding the input samples comprises adjusting the decoding of the samples responsive to the frequency offset.  
     
     
         12 . A method according to  claim 10 , wherein decoding the input samples finding correlations between portions of the sequence of input samples and corresponding groups of symbols, so as to determine the symbols that were transmitted in the stream.  
     
     
         13 . A method for decoding a stream of transmitted symbols, comprising: 
 receiving a signal in which the symbols are encoded by frequency shift keying;    sampling and digitizing the signal to generate a sequence of input samples;    defining a plurality of hypotheses with respect to a selected group of the symbols occurring in succession in the stream, each such hypothesis comprising a different set of possible values of the symbols in the group;    finding a respective level of correlation between each of the plurality of hypotheses and the input samples in a portion of the sequence corresponding to the selected group of the symbols;    choosing one of the hypotheses responsive to the level of correlation thereof; and    for at least one of the symbols in the selected group, determining a decoded value of the symbol responsive to the value of the symbol in the chosen hypothesis.    
     
     
         14 . A method according to  claim 13 , wherein receiving the signal comprises receiving the stream of symbols encoded by Gaussian frequency shift keying.  
     
     
         15 . A method according to  claim 13 , wherein finding the respective level of correlation comprises determining reference samples that correspond to frequency shift keying of the symbol values in each of the hypotheses, and correlating the samples in the portion of the sequence with the reference samples.  
     
     
         16 . A method according to  claim 15 , wherein determining the reference samples comprises providing coefficients such that multiplication of the symbol values in each of the hypotheses by the coefficients will generate the reference samples, and wherein correlating the samples comprises multiplying the samples by the coefficients.  
     
     
         17 . A method according to  claim 16 , wherein sampling and digitizing the signal comprises generating complex samples, and wherein multiplying the samples comprises rotating a phase of each of the complex samples responsive to the coefficients.  
     
     
         18 . A method according to  claim 17 , wherein rotating the phase of each of the complex samples further comprises rotating the phase so as to correct for a frequency offset of the signal relative to an expected frequency.  
     
     
         19 . A method according to  claim 16 , wherein the symbols are transmitted at a given symbol rate, and wherein sampling and digitizing the signal comprises generating the input samples at a sample rate greater than the symbol rate, and wherein determining the reference samples comprises determining the reference samples at the sample rate.  
     
     
         20 . A method according to  claim 13 , wherein outputting the decoded value of the symbol comprises outputting the decoded value of a current symbol, and wherein defining the plurality of hypotheses comprises selecting the group of the symbols to include at least one symbol preceding the current symbol in the succession and at least one symbol following the current symbol in the succession.  
     
     
         21 . A method according to  claim 20 , wherein the at least one symbol preceding the current symbol comprises three symbols preceding the current symbol, and wherein the at least one symbol following the current symbol comprises three symbols following the current symbol.  
     
     
         22 . A method according to  claim 20 , wherein selecting the group of the symbols comprises selecting the at least one symbol preceding the current symbol such that the decoded value of the at least one symbol preceding the current symbol has already been determined, and wherein defining the plurality of hypotheses comprises using only the hypotheses that comprise the determined value of the at least one symbol preceding the current symbol.  
     
     
         23 . A method according to  claim 22 , and comprising repeating the step of defining the plurality of hypotheses with respect to the at least one symbol following the current symbol, using only the hypotheses that comprise the determined value of the current symbol, and repeating with respect to the at least one symbol following the current symbol the steps of finding the respective level of correlation, choosing one of the hypotheses, and determining the decoded value.  
     
     
         24 . A method according to  claim 13 , wherein choosing the one of the hypotheses comprises computing a correlation between each of the plurality of hypotheses and the input samples, and choosing the one of the hypotheses that has a maximal value of the correlation compared to the other hypotheses.  
     
     
         25 . A method according to  claim 13 , wherein sampling and digitizing the signal comprises generating complex samples of the signal, and wherein determining the decoded value comprises determining the decoded values of successive first and second ones of the symbols, and comprising comparing a phase difference between a first one of the samples, corresponding to the first symbol, and a second one of the samples, corresponding to the second symbol, to a difference between the first and second symbols so as to find a frequency offset of the signal relative to an expected frequency.  
     
     
         26 . A method according to  claim 25 , wherein finding the level of the correlation comprises applying a phase rotation to the complex samples responsive to the frequency offset.  
     
     
         27 . A method according to  claim 13 , wherein receiving the signal comprises receiving a packet of data transmitted from a transmitter to a receiver, the packet ending with a final symbol, and wherein sampling and digitizing the signal comprises adding to the samples at the receiver one or more tail samples corresponding to a tail symbol following the final symbol in the packet, for use in finding the respective level of correlation for the hypotheses used in determining the decoded value of the final symbol.  
     
     
         28 . A method according to  claim 13 , wherein receiving the signal comprises receiving a packet of data transmitted from a transmitter to a receiver, the packet comprising an error correcting code and ending with a final symbol, such that there is an increased level of uncertainty in the decoded value of the final symbol relative to the other symbols in the packet, and comprising performing an error check on the packet at the receiver based on the code in a manner that is insensitive to the decode value of the final symbol.  
     
     
         29 . A method for decoding a stream of transmitted symbols, comprising: 
 receiving a signal comprising a packet of data symbols transmitted from a transmitter to a receiver, the packet ending with a final symbol;    sampling and digitizing the signal to generate a sequence of input samples;    adding to the samples at the receiver one or more tail samples corresponding to a tail symbol following the final symbol in the packet; and    decoding the symbols by processing, for each of the symbols, a corresponding portion of the sequence of the samples, such that the portion corresponding to the final symbol comprises at least one of the tail samples.    
     
     
         30 . A method according to  claim 29 , wherein adding the one or more tail samples comprises identifying one of the input samples as a final sample, derived from the final symbol, and duplicating the final sample.  
     
     
         31 . A method according to  claim 29 , wherein the packet comprises a header indicating a length of the packet, and wherein adding the one or more tail samples comprises reading the length by decoding the header, and identifying the final symbol responsive to the length.  
     
     
         32 . A method according to  claim 29 , wherein decoding the symbols comprises finding, for each of the symbols, a correlation between the corresponding portion of the sequence of the samples and a hypothesis comprising possible values of a group of the symbols.  
     
     
         33 . A method according to  claim 29 , wherein decoding the symbols comprises processing the samples responsive to intersymbol interference between the symbols in the received signal.  
     
     
         34 . A method for decoding a stream of transmitted symbols, comprising: 
 receiving a signal at a transmission frequency, in which signal the symbols are encoded;    sampling and digitizing the signal to generate a sequence of complex input samples;    processing the samples so as to determine decoded values of successive first and second ones of the symbols;    computing a phase difference between a first one of the samples, corresponding to the first symbol, and a second one of the samples, corresponding to the second symbol; and    comparing the phase difference to a difference between the first and second symbols so as to find a frequency offset of the transmission frequency relative to an expected frequency.    
     
     
         35 . A method according to  claim 34 , wherein computing the phase difference comprises taking a complex cross product between the first and second samples.  
     
     
         36 . A method according to  claim 34 , wherein comparing the phase difference comprises determining reference samples that correspond to encoding of the first and second symbols, and taking a complex cross product between the reference samples and the first and second samples.  
     
     
         37 . A method according to  claim 34 , wherein processing the samples comprises computing a correlation between a hypothesis comprising possible values of a group of the symbols, including the first and second symbols, and a portion of the sequence of the samples including the first and second samples.  
     
     
         38 . A method according to  claim 37 , wherein computing the correlation comprises computing a plurality of correlations with respect to different hypotheses, and choosing the one of the hypotheses that has a maximal value of the correlation compared to the other hypotheses.  
     
     
         39 . A method according to  claim 34 , and comprising applying a phase rotation, responsive to the frequency offset, to the complex samples subsequent to the first and second samples in preparation for processing the subsequent samples to determine the decoded values of the symbols to which the subsequent samples correspond.  
     
     
         40 . A method according to  claim 34 , wherein receiving the signal comprises receiving the stream of symbols encoded by frequency shift keying.  
     
     
         41 . A receiver, for receiving a stream of transmitted symbols that includes a known synchronization word, the receiver comprising: 
 input circuitry, coupled to receive a signal in which the symbols, including the synchronization word, are encoded by frequency shift keying, and to sample and digitizing the signal to generate a sequence of input samples; and    a synchronization word detector, coupled to receive the sequence of input samples and adapted to determine, for each of the input samples, a phase difference relative to a preceding input sample in the sequence, thereby generating a sequence of differential samples corresponding respectively to the input samples, and to detect the synchronization word by matching the differential samples to the synchronization word.    
     
     
         42 . A receiver according to  claim 41 , wherein the signal comprises a radio frequency signal having a frequency offset relative to a channel frequency designated for the signal, and wherein the synchronization word detector is adapted to cancel the frequency offset out of the differential samples before matching the differential samples to the synchronization word.  
     
     
         43 . A receiver according to  claim 41 , wherein the stream of symbols is encoded by Gaussian frequency shift keying.  
     
     
         44 . A receiver according to  claim 41 , wherein the symbols are transmitted at a given symbol rate, and wherein the input circuitry is adapted to sample and digitize the signal at a sample rate greater than the symbol rate, and wherein the synchronization word detector is adapted to determine the phase difference between pairs of the input samples that are separated by an interval that is a reciprocal of the symbol rate.  
     
     
         45 . A receiver according to  claim 41 , wherein the synchronization word detector comprises at least one multiplier, which is adapted to compute a complex cross product between each of the input samples and the preceding input sample.  
     
     
         46 . A receiver according to  claim 41 , wherein the synchronization word detector is adapted to determine reference samples that correspond to frequency shift keying of the synchronization word, and comprises a correlator, which is coupled to correlate the sequence of differential samples with the reference samples.  
     
     
         47 . A receiver according to  claim 46 , wherein the reference samples are determined by coefficients provided to the synchronization word detector such that multiplication of the symbols in the synchronization word by the coefficients will generate the reference samples, and wherein the correlator is adapted to correlate the sequence of differential samples with the reference samples by multiplying the differential samples by the coefficients.  
     
     
         48 . A receiver according to  claim 46 , wherein the correlator is adapted to compute a sequence of correlation values by correlating different, respective portions of the sequence of input samples with the synchronization word, and wherein the synchronization word detector comprises a peak detector, coupled to find a peak value among the correlation values of the different portions, thus indicating the portion of the sequence of input samples that best matches the synchronization word.  
     
     
         49 . A receiver according to  claim 48 , wherein the input circuitry is adapted to generate complex samples, and wherein the correlator is adapted to compute complex correlation values, and comprising an automatic frequency control circuit, which is adapted to find a phase angle of the peak correlation value, and a rotator, which is coupled to the automatic frequency control circuit so as to correct a phase of the input samples of the signal subsequent to the synchronization word responsive to the phase angle.  
     
     
         50 . A receiver according to  claim 41 , wherein the synchronization word detector is adapted to find a time offset of the input samples relative to the synchronization word, and comprising a demodulator, which is coupled to receive the time offset from the synchronization word detector and to decode the input samples of the signal subsequent to the synchronization word responsive to the time offset.  
     
     
         51 . A receiver according to  claim 50 , wherein the synchronization word detector is adapted to generate a phase offset of the input samples relative to the synchronization word, and comprising an automatic frequency control circuit, which is coupled to find a frequency offset of the signal relative to an expected frequency responsive to the phase offset, and wherein the demodulator is coupled to adjust the decoding of the samples responsive to the frequency offset.  
     
     
         52 . A receiver according to  claim 50 , wherein the demodulator is adapted to find correlations between portions of the sequence of input samples and corresponding groups of symbols, so as to determine the symbols that were transmitted in the stream.  
     
     
         53 . A receiver for decoding a stream of transmitted symbols, comprising: 
 input circuitry, coupled to receive a signal in which the symbols are encoded by frequency shift keying, and to sample and digitize the signal to generate a sequence of input samples; and    a demodulator, adapted to process a plurality of hypotheses with respect to a selected group of the symbols occurring in succession in the stream, each such hypothesis comprising a different set of possible values of the symbols in the group, the demodulator comprising: 
 a correlator, adapted to find a respective level of correlation between each of the plurality of hypotheses and the input samples in a portion of the sequence corresponding to the selected group of the symbols; and  
 a selector, adapted to choose one of the hypotheses responsive to the level of correlation thereof, so as to determine, for at least one of the symbols in the selected group, a decoded value of the symbol responsive to the value of the symbol in the chosen hypothesis.  
   
     
     
         54 . A receiver according to  claim 53 , wherein the stream of symbols is encoded by Gaussian frequency shift keying.  
     
     
         55 . A receiver according to  claim 53 , wherein the demodulator is operative to determine reference samples that correspond to frequency shift keying of the symbol values in each of the hypotheses, and wherein the correlator is coupled to correlate the samples in the portion of the sequence with the reference samples.  
     
     
         56 . A receiver according to  claim 55 , wherein the demodulator is adapted to determine the reference samples by providing coefficients such that multiplication of the symbol values in each of the hypotheses by the coefficients will generate the reference samples, and wherein the correlator comprises at least one multiplier, which is coupled to multiply the samples by the coefficients.  
     
     
         57 . A receiver according to  claim 56 , wherein the input circuitry is adapted to generate complex samples, and wherein the at least one multiplier comprises a complex multiplier, which is coupled to rotate a phase of each of the complex samples responsive to the coefficients.  
     
     
         58 . A receiver according to  claim 57 , wherein the multiplier is further coupled to rotate the phase so as to correct for a frequency offset of the signal relative to an expected frequency.  
     
     
         59 . A receiver according to  claim 56 , wherein the symbols are transmitted at a given symbol rate, and wherein the input circuitry is adapted to sample and digitize the signal at a sample rate greater than the symbol rate, and wherein the demodulator is adapted to determine the reference samples at the sample rate.  
     
     
         60 . A receiver according to  claim 53 , wherein the decoded value of the symbol comprises the decoded value of a current symbol, and wherein the selected group of the symbols comprises at least one symbol preceding the current symbol in the succession and at least one symbol following the current symbol in the succession.  
     
     
         61 . A receiver according to  claim 60 , wherein the at least one symbol preceding the current symbol comprises three symbols preceding the current symbol, and wherein the at least one symbol following the current symbol comprises three symbols following the current symbol.  
     
     
         62 . A receiver according to  claim 60 , wherein the group is selected such that the decoded value of the at least one symbol preceding the current symbol has already been determined, and wherein the demodulator is arranged to process only the hypotheses that comprise the determined value of the at least one symbol preceding the current symbol.  
     
     
         63 . A receiver according to  claim 62 , wherein the demodulator is further arranged, after determining the decoded value of the current symbol, to decode the at least one symbol following the current symbol using only the hypotheses that comprise the determined value of the current symbol.  
     
     
         64 . A receiver according to  claim 53 , wherein the selector is adapted to select the one of the hypotheses that has a maximal value of the correlation level compared to the other hypotheses.  
     
     
         65 . A receiver according to  claim 53 , wherein the input circuitry is adapted to generate complex samples of the signal, and wherein the demodulator is operative to determine the decoded values of successive first and second ones of the symbols, and comprising an automatic frequency control circuit, which is coupled to compare a phase difference between a first one of the samples, corresponding to the first symbol, and a second one of the samples, corresponding to the second symbol, to a difference between the first and second symbols so as to find a frequency offset of the signal relative to an expected frequency.  
     
     
         66 . A receiver according to  claim 65 , and comprising at least one rotator, which is coupled to apply a phase rotation to the complex samples responsive to the frequency offset.  
     
     
         67 . A receiver according to  claim 53 , wherein the signal comprises a packet of data transmitted from a transmitter to a receiver, the packet ending with a final symbol, and wherein the demodulator is adapted to add to the samples that are input to the correlator one or more tail samples corresponding to a tail symbol following the final symbol in the packet, for use in finding the respective level of correlation for the hypotheses used in determining the decoded value of the final symbol.  
     
     
         68 . A receiver according to  claim 53 , wherein the signal comprises a packet of data transmitted from a transmitter to a receiver, the packet comprising an error correcting code and ending with a final symbol, such that there is an increased level of uncertainty in the decoded value of the final symbol relative to the other symbols in the packet, and comprising a processor, adapted to perform an error check on the packet at the receiver based on the code in a manner that is insensitive to the decode value of the final symbol.  
     
     
         69 . A receiver for decoding a stream of transmitted symbols, comprising: 
 input circuitry, coupled to receive a signal comprising a packet of data symbols transmitted from a transmitter to a receiver, the packet ending with a final symbol, and to sample and digitize the signal to generate a sequence of input samples; and    demodulation circuitry, which is adapted to add to the samples one or more tail samples corresponding to a tail symbol following the final symbol in the packet, and to decode the symbols by processing, for each of the symbols, a corresponding portion of the sequence of the samples, such that the portion corresponding to the final symbol comprises at least one of the tail samples.    
     
     
         70 . A receiver according to  claim 69 , wherein the receiver is adapted to identify one of the input samples as a final sample, derived from the final symbol, so that the demodulation circuitry duplicates the final sample to serve as the one or more tail samples.  
     
     
         71 . A receiver according to  claim 69 , wherein the packet comprises a header indicating a length of the packet, and comprising a processor, which is adapted to read the length by decoding the header, so as to identify the final symbol responsive to the length.  
     
     
         72 . A receiver according to  claim 69 , wherein the demodulator is adapted to find, for each of the symbols, a correlation between the corresponding portion of the sequence of the samples and a hypothesis comprising possible values of a group of the symbols.  
     
     
         73 . A receiver according to  claim 69 , wherein the demodulator is adapted to decode the samples responsive to intersymbol interference between the symbols in the received signal.  
     
     
         74 . A receiver for decoding a stream of transmitted symbols, comprising: 
 input circuitry, coupled to receive a signal at a transmission frequency, in which signal the symbols are encoded, and to sample and digitize the signal to generate a sequence of complex input samples;    a demodulator, which is coupled to process the samples so as to determine decoded values of successive first and second ones of the symbols; and    an automatic frequency control circuit, which is adapted to compute a phase difference between a first one of the samples, corresponding to the first symbol, and a second one of the samples, corresponding to the second symbol, and to compare the phase difference to a difference between the first and second symbols so as to find a frequency offset of the transmission frequency relative to an expected frequency.    
     
     
         75 . A receiver according to  claim 74 , wherein the automatic frequency control circuit comprises a complex multiplier, which is coupled to take a complex cross product between the first and second samples so as to determine the phase difference therebetween.  
     
     
         76 . A receiver according to  claim 74 , wherein the automatic frequency control circuit is adapted to determine reference samples that correspond to encoding of the first and second symbols, and comprises a complex multiplier, which is coupled to take a complex cross product between the reference samples and the first and second samples so as to find the frequency offset.  
     
     
         77 . A receiver according to  claim 74 , wherein the demodulator is adapted to decode the symbols by computing a correlation between a hypothesis comprising possible values of a group of the symbols, including the first and second symbols, and a portion of the sequence of the samples including the first and second samples.  
     
     
         78 . A receiver according to  claim 77 , wherein the demodulator is adapted to compute a plurality of correlations with respect to different hypotheses, and to choose the one of the hypotheses that has a maximal value of the correlation compared to the other hypotheses.  
     
     
         79 . A receiver according to  claim 74 , and comprising a rotator, which is coupled to apply a phase rotation, responsive to the frequency offset, to the complex samples subsequent to the first and second samples in preparation for processing the subsequent samples to determine the decoded values of the symbols to which the subsequent samples correspond.  
     
     
         80 . A receiver according to  claim 74 , wherein the stream of symbols are encoded by frequency shift keying.