CN114640562A - CPFSK/GFSK signal noncoherent demodulation method - Google Patents
CPFSK/GFSK signal noncoherent demodulation method Download PDFInfo
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Abstract
The invention provides a non-coherent demodulation method of a CPFSK/GFSK signal, which generates a matched filter group with a single symbol length and a phase correction factor according to the transmitted CPFSK/GFSK signal parameter; then, if the received CPFSK/GFSK signal is not spread spectrum, matching the received sample by K symbols, and performing modulo calculation on a matching result; if the received DSSS-CPFSK/DSSS-GFSK signals are directly subjected to sequence spread spectrum processing, the signals subjected to the spread spectrum processing are regarded as a whole, the received samples are matched with each other in length of spread spectrum codes, and the modulus value of the matching result is calculated; finally, if the received CPFSK/GFSK signals are not spread, each group decodes K bit information according to decoding requirements in a soft demodulation or hard demodulation mode; if the received signal is a DSSS-CPFSK/DSSS-GFSK signal, the corresponding non-spread original bit is solved.
Description
Technical Field
The invention relates to the technical field of communication of the Internet of things, in particular to a CPFSK/GFSK signal noncoherent demodulation method.
Background
With the rapid development of wireless communication technology and communication networks, the demand for communication between objects is rapidly increasing. In the fifth Generation mobile Communication technology (5th Generation,5G), mass Machine Type Communication (mtc) is listed as one of three application scenarios. In many physical layer technologies of the internet of things for mtc scenarios, Continuous Phase Shift Keying (CPFSK) is widely applied due to its excellent characteristics of constant envelope, Continuous Phase, and high spectrum efficiency. The Gaussian Frequency Shift Keying adds a low-pass Gaussian filter as a symbol phase shaping function on the basis of continuous phase modulation of CPFSK (Gaussian Frequency Shift Keying), so that the attenuation outside a Frequency spectrum band is faster and the Frequency spectrum efficiency is higher compared with the CPFSK signal, but the introduction of the Gaussian Frequency Shift Keying brings extra symbol crosstalk (Inter-symbol interference) and the realization is more complicated. Further, the CPFSK/GFSK modulation can be combined with Direct Sequence Spread Spectrum (DSSS) and channel coding to achieve coverage enhancement and rate adaptation, thereby meeting the requirements of long-distance internet of things communication.
In low-cost receiver design, the CPFSK/GFSK signal demodulation mode is usually implemented based on a non-coherent mode, because the mode has low requirement on synchronization accuracy and strong channel fading resistance, and is more suitable for low-cost implementation. The currently common non-coherent demodulation scheme is to use the changing polarity of the phase between single symbols to determine the information carried by the transmitted symbols, i.e. a differential demodulation algorithm. Although the implementation is simple, the Bit Error Rate (BER) performance is poor at a low Signal-to-Noise Radio (SNR), and it is difficult to meet the requirement of wide coverage. Another non-coherent envelope detection algorithm has better performance when the FSK signal modulation factor is larger, however, in order to reduce the actual occupied bandwidth of the signal, the CPFSK/GFSK modulation factor is usually smaller than 1, and the requirement of orthogonality between symbols is not satisfied, so the BER performance is also poor under low SNR. Since both CPFSK and GFSK are phase-continuous memory signals, the demodulation schemes with better BER performance are mostly multi-symbol Detection algorithms based on the Maximum Likelihood Sequence Detection (MLSD) idea, such as the optimal incoherent demodulation algorithm, however, the algorithm has very high computational complexity and storage complexity, and is difficult to adapt to practical engineering applications. Furthermore, the conventional demodulation despreading separation concept introduces a significant performance penalty in despreading demodulating a direct sequence spread spectrum DSSS-FSK signal.
The prior art discloses a CPFSK demodulating device with rapid automatic frequency compensation and a method thereof, wherein the CPFSK demodulating device is started firstly; then, processing the radio frequency signal by a CPFSK demodulation device to obtain an input signal; then, respectively transmitting the input signal and the orthogonal signal of the local oscillator to a CPFSK demodulating device to obtain an output signal; the method can realize the capture and tracking of the Doppler frequency offset in a large range, and can also realize the tracking of the Doppler change rate in a larger range; the other characteristic is that the calculation and updating time of each error voltage is short, and the algorithm convergence speed is high; the method has the advantages of simple structure, low hardware resource consumption, easy FPGA realization and the like. However, the patent is only concerned with achieving better performance with relatively low complexity by requiring only one symbol length of matched filter bank and phase correction factor.
Disclosure of Invention
The invention provides a CPFSK/GFSK signal noncoherent demodulation method, which can achieve better performance with relatively low complexity only by a matched filter bank with a symbol length and a phase correction factor, and the matched filter bank can multiplex a reference waveform used by a transmitting part of table look-up methods, thereby further reducing the storage complexity.
In order to achieve the technical effects, the technical scheme of the invention is as follows:
a non-coherent demodulation method of CPFSK/GFSK signal comprises the following steps:
s1: generating a matched filter group with a single symbol length and a phase correction factor according to the transmitted CPFSK/GFSK signal parameters;
s2: matching the received samples: if the received CPFSK/GFSK signal is not spread spectrum, matching the received sample by K symbols, and performing modulo operation on a matching result; if the received DSSS-CPFSK/DSSS-GFSK signals are directly subjected to sequence spread spectrum processing, the signals subjected to the spread spectrum processing are regarded as a whole, the received samples are matched with each other in length of spread spectrum codes, and the modulus value of the matching result is calculated;
s3: and demodulating the matching result: if the received CPFSK/GFSK signals are not spread, each group of the CPFSK/GFSK signals decodes K bit information according to decoding requirements in a soft demodulation or hard demodulation mode; if the received signal is a DSSS-CPFSK/DSSS-GFSK signal, the corresponding non-spread original bit is solved.
Further, the CPFSK/GFSK signal has a constant envelope, and the complex baseband signal model is:
wherein, alpha is a bit sequence to be modulated with a length L and alphaiE { -1,1} is the ith binary bipolar bit to be modulated; n is a single chip sampling factor, and N is a sampling subscript; h ism＝Δf/BwAs a modulation factor, ΔfIs the frequency difference of two frequency points, BwChip rate/transmission bandwidth; q (n) is the accumulation of the single sign phase shaping function h (n).
Further, for a full response CPFSK signal that is not phase shaped by a Gaussian filter, its shaping function hc(n) is the response length L c1, a rectangular filter of normalized symbol length, whose expression is:
thus, the expression for the kth symbol of the CPFSK signal is:
wherein θk-1Accumulated phase of the first k-1 term, akN/N is the phase change factor of the kth symbol, which is linearly changed under the full response CPFSK signal; and for the partial response GFSK signal which is subjected to phase shaping by the Gaussian filter, the shaping function hg(n) is a response length LgThe expression of the low-pass gaussian filter is:
gaussian filter bandwidth factor in the above equation
BT is the bandwidth-time factor of the 3dB attenuation, LgThe truncation 3 models intersymbol interference of the GFSK signal, namely, a single GFSK symbol mainly generates intersymbol interference with the front symbol and the rear symbol, so that the k-th symbol of the GFSK signal has the expression:
in the formula θk-1Is the accumulated phase of the first k-1 term, phi (n; BT; alpha)k-1αkαk+1) The phase change factor of the kth symbol under the current time-bandwidth factor is influenced by ISI of the preceding and following symbols, and the phase change factor is non-linearly changed under a partial response GFSK signal model.
Further, in step S1, the matched filter bank generating the length of a single symbol according to the transmitted CPFSK/GFSK signal parameters is:
wherein ,
permute the result of the inverse sample order for the reference complex baseband samples corresponding to CPFSK symbols q ∈ {0,1}, { }HRepresents the Hermitian transpose, {. The }TRepresenting a matrix transposition;
the CPFSK symbol q is represented as:
where N is 0,1,. N-1, N being an upsampling factor,hmthe CPFSK signal modulation factor is the sending end.
Further, in step S1, the phase correction factor for generating the length of a single symbol according to the transmitted CPFSK/GFSK signal parameter is expressed as:
Further, since the current symbol is affected by crosstalk between previous and next symbols, the generated and stored matched filter bank needs to consider the effect of the previous and next symbols, that is:
wherein 
For the symbol l ∈ {0, 1., 7} corresponding to the inverse of the reference complex baseband sample, and l is the current bit q1And two front and back bits q0q2Combining corresponding q0q1q2The highest decimal mapping on the right end, namely:
then each sample point of the symbol l is represented as:
wherein N is 0, 1.. cndot.N-1,. phi (N; BT; q)0q1q2) For phase change of current symbolBefore and after bit q0 and q2And the influence of the GFSK Gaussian shaping filter 3dB attenuation bandwidth parameter BT;
the phase correction factors generated and stored are expressed as:
a relative additional phase is introduced for the GFSK symbol l e {0, 1.
Further, in step S2, the processing of the non-spread CPFSK/GFSK signal includes:
and (3) reverse order arrangement: carrying out inverse sampling sequence arrangement on the received samples r to obtain inverse sequence samples
wherein 
A complex baseband signal sample point arranged in a reverse order for receiving a K-K +1 th symbol of a current packet;
single symbol matching: matching the first symbol sample (namely the original Kth sample) after the reverse order arrangement, wherein the matching result is as follows:
in the above formula, M denotes a modulation scheme: m ═ c' for CPFSK modulation, when the symbol shaping filter length LMThe matching result is a complex matching value of the symbol "0"/"1" when 1; m ═ g' for GPFSK modulation, when the symbol shaping filter length L isMThe matching result is a matching value of binary symbols representing '000' to '111', namely the current operation result needs to be stored for subsequent iteration and combination in consideration of the influence of the front and rear symbols on the phase change of the intermediate symbol;
then the 2 nd symbol after the reverse order, namely the K-1 st symbol of the order is processed according to the methodMatching is performed to obtain, for CPFSK symbols
For a GFSK symbol, obtaining
The matching result of (1);
merging: for a CPFSK symbol, two single-symbol matching results need to be transferred to the result of matching two sections of received symbols with a baseband reference waveform "00" "," 10 "", "01" ", and" 11 "of four symbol combinations, and for a GFSK signal, the influence of two symbols before and after the matching symbol needs to be additionally considered, that is, the matching results of two single symbols need to be extended to two received symbols and 16 symbol combinations" 0000 "," 1000 ", …", and "1111", wherein a black body is an intersymbol interference symbol at two ends of a matched observation part;
therefore, it is first necessary to match the matching results
The replication is performed, and the matrix for replication is:
wherein 
Is composed of
Then taking into account the phase continuity of the CPFSK/GFSK signal, except for the need for
The replication is performed by phase rotation to adapt the phase introduced by the previous matched symbol
The replica matrix is written as:
where blockdiag {. is the block diagonalization operation, and the phase rotation matrix is written as:
wherein 
Is a major diagonal element of
The square matrix of (A) is formed,
representing the additional phase introduced by the second matched symbol in reverse order, whereby the combined result is represented as:
wherein 
Because of the fact that
Is the first match result;
the said process only uses single symbol matching of each symbol and additional phase correction in symbol combination for complex multiplication, and the required number of complex multiplication is determined by
Is reduced to
Iteration: iterating the above steps, the result of matching and merging the k-th symbol after reverse order arrangement is:
wherein ,
is the single symbol matching result of the k-th symbol after the reverse order,
is the result of matching and merging k-1 symbols before and after the reverse order, and:
taking a mold: the final result of matching and merging K symbols is obtained, for CPFSK, the result is
Obtaining by modulo
For GFSK, are
Obtaining by modulo
Further, in step S2, the processing the spread spectrum CPFSK/GFSK signal includes:
and (3) reversing the sequence: carrying out reverse sequencing on the received samples r to obtain reverse sequence
wherein 
For receiving the Lth of the current packets-an inversely ordered complex baseband signal sample point of k +1 chip symbols;
single symbol matching: taking into account the spreading sequence DsKnown at the receiving end and therefore only needed for LsThe received complex baseband samples of chip length take into account two possible codeword combinations, namely a spreading sequence mapped by bit "1" and a spreading sequence mapped by bit "0", and thus for a CPFSK signal consider the following set of spreading mapping matrices:
wherein ,
spreading codes for ith bit
If the mapping matrix of
I.e. the mapped ith bit spreading code is the same as the original bit, the mapping matrix for selecting the matched filter bank and the phase correction factor
Otherwise, the mapped ith bit spread spectrum code is opposite to the original bit, then
For GFSK signals, consider the following set of mapping matrices:
wherein ,
for a mapping matrix of an ith bit of a spread spectrum sequence, the influence of the (i-1) th spread spectrum bit and the (i + 1) th spread spectrum bit on a symbol needs to be considered simultaneously; order to
For the decimal mapping of the i-1, i +1 bit, the subscript of 1 is:
representing the mapping of original information "1" and bits "0" to the ith chip, and the rest of the indexes are set with zero; chips outside the currently observed spreading sequence are defaulted to 0, i.e.
Single symbol matching: and matching the 1 st symbol sample and the 2 nd symbol sample after the reverse order, wherein the matching expression is as follows:
wherein the ratio of i to 1,2,
is based on the matched filter bank after chip mapping update, and the matching result
Representing a match result for an unspread bit of "0",
representing the matching result corresponding to the non-spread bit "1";
merging: for a DSSS-CPFSK symbol, the process of combining two single-symbol matching results is:
wherein 
Phase correction is needed for the phase correction factor after spread spectrum mapping, and in consideration of the phase continuity of the CPFSK/GFSK signal, the same-phase superposition is carried out after the phase correction;
iteration: iterating the above steps, the result of matching and combining the k-th chip after the reverse order is:
wherein 
The result of the combination of k-1 chips after the reverse order;
taking a mold: finally, the complete L of a single DSSS-FSK signal is obtainedsThe result of the length-chip match combining, for DSSS-CPFSK, is
Obtaining by modulo
For DSSS-GFSK, the
Obtaining by modulo calculation
Further, in step S3, if the hard demodulation method is adopted for the CPFSK/GFSK signal without spread spectrum, the subscript with the maximum matching modulus is selected first:
then, will
Inversely mapping the highest bit of the right end back to a binary sequence, wherein for CPFSK, the mapped sequence with the length of K bits is a demodulation result, for GFSK, the inversely mapped sequence with the length of K +2 bits needs to discard ISI bits before and after, and the middle K bit is taken as a demodulation result;
if soft demodulation is employed, the soft information for the kth bit among the K observed bits is written as:
wherein ,I0{. is a zero-order first-class modified Bessel function; SNRh＝|h|/σ2For the receiving end SNR, where | h | is the flat fading modulus, σ2Gaussian noise power for the receiver;
and
the branch index is matched for the kth bit as an inverse mapping to a set of 1 s and 0 s.
Further, in step S3, if the hard demodulation method is used for the spread DSSS-CPFSK/DSSS-GFSK signal, the information ratio before spreading is known as:
if soft demodulation is employed, the soft information is written as:
compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the method is suitable for non-spread spectrum CPFSK/GFSK signal demodulation and spread spectrum DSSS-CPFSK/DSSS-GFSK signal despreading and demodulation. Compared with the existing low-complexity low-performance differential demodulation/envelope detection scheme, the demodulation performance is greatly improved under the condition that the complexity is not remarkably improved. Compared with the existing multi-symbol detection scheme with high performance and high complexity, the method greatly reduces the calculation complexity at the cost of a small part of performance loss. And joint demodulation and de-spreading of the spread DSSS-CPFSK/DSSS-GFSK signals can obtain more spread spectrum gains under the condition of low complexity. The scheme is based on a non-coherent implementation mode, has low requirement on synchronization precision, and is suitable for the application of the Internet of things with low cost, low power consumption and long-distance transmission.
Drawings
FIG. 1 shows a block diagram of a CPFSK/GFSK signal matching calculation according to an embodiment of the invention;
FIG. 2 shows a block diagram of another embodiment of the present invention for DSSS-CPFSK/DSSS-GFSK signal matching calculation;
FIG. 3 is a schematic flow chart of CPFSK/GFSK demodulation according to an embodiment of the present invention;
fig. 4 is a graph showing the comparison of the demodulation performance of CPFSK/GFSK without channel coding under AWGN channel proposed in embodiment 1 of the present invention;
FIG. 5 is a graph showing the comparison of the performance of CPFSK/GFSK demodulation through (2,1,3) convolutional encoding and Viterbi soft decoding in AWGN channel proposed in embodiment 1 of the present invention;
fig. 6 is a graph showing the comparison of the performance of DSSS-CPFSK demodulation without channel coding under AWGN channel proposed in embodiment 2 of the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 3, a method for noncoherently demodulating a CPFSK/GFSK signal includes the following steps:
s1: generating a matched filter group with a single symbol length and a phase correction factor according to the transmitted CPFSK/GFSK signal parameters;
s2: matching the received samples: if the received signal is a CPFSK/GFSK signal without spread spectrum, matching the received sample by K symbols, and performing modulo calculation on a matching result; if the received DSSS-CPFSK/DSSS-GFSK signals are directly subjected to sequence spread spectrum processing, the signals subjected to the spread spectrum processing are regarded as a whole, the received samples are matched with each other in length of spread spectrum codes, and the modulus value of the matching result is calculated;
s3: and demodulating the matching result: if the received CPFSK/GFSK signals are not spread, each group of the CPFSK/GFSK signals decodes K bit information according to decoding requirements in a soft demodulation or hard demodulation mode; if the received signal is a DSSS-CPFSK/DSSS-GFSK signal, the corresponding non-spread original bit is solved.
The CPFSK/GFSK signal has a constant envelope, and the complex baseband signal model is as follows:
wherein, alpha is a bit sequence to be modulated with a length L and alphaiE { -1,1} is the ith binary bipolar bit to be modulated; n is a single chip sampling factor and N is a sampling subscript；hm＝Δf/BwAs modulation factor, ΔfIs the frequency difference of two frequency points, BwChip rate/transmission bandwidth; q (n) is the accumulation of the single sign phase shaping function h (n).
For a full response CPFSK signal that is not phase shaped by a Gaussian filter, the shaping function hc(n) is the response length L c1, a rectangular filter of normalized symbol length, whose expression is:
thus, the expression for the kth symbol of the CPFSK signal is:
wherein θk-1Accumulated phase of the first k-1 term, akN/N is the phase change factor of the kth symbol, which is linearly changed under the full response CPFSK signal; and for the partial response GFSK signal which is subjected to phase shaping by the Gaussian filter, the shaping function hg(n) is the response length LgThe expression of (3) is:
gaussian filter bandwidth factor in the above equation
BT is the bandwidth-time factor of 3dB attenuation, LgThe truncation 3 models intersymbol interference of the GFSK signal, namely, a single GFSK symbol mainly generates intersymbol interference with the front symbol and the rear symbol, so that the k-th symbol of the GFSK signal has the expression:
in the formula θk-1Is the accumulated phase of the first k-1 term, phi (n; BT; alpha)k-1αkαk+1) The phase change factor of the kth symbol under the current time-bandwidth factor is influenced by ISI of the preceding and following symbols, and the phase change factor is non-linearly changed under a partial response GFSK signal model.
In step S1, the matched filter bank with a single symbol length generated according to the transmitted CPFSK/GFSK signal parameters is:
wherein ,
permuting the result of the inverse sampling order of the reference complex baseband samples corresponding to the CPFSK symbol q ∈ {0,1}, }HRepresents the Hermitian transpose, {. The }TRepresenting a matrix transposition;
the CPFSK symbol q is represented as:
n-1, where N is 0,1mThe CPFSK signal modulation factor of the sending end is obtained.
Further, in step S1, the phase correction factor for generating the length of a single symbol according to the transmitted CPFSK/GFSK signal parameter is expressed as:
Since the current symbol is affected by crosstalk between previous and next symbols, the generated and stored matched filter bank needs to consider the effect of the previous and next symbols, that is:
wherein 
For the symbol l ∈ {0, 1., 7} corresponding to the inverse of the reference complex baseband sample, and l is the current bit q1With two preceding and succeeding bits q0q2Combining corresponding q0q1q2The highest decimal mapping at the right end is as follows:
then each sample point of the symbol l is represented as:
wherein N is 0, 1.. cndot.N-1,. phi (N; BT; q)0q1q2) For phase change of current symbol, subject to preceding and following bits q0 and q2And the influence of the GFSK Gaussian shaping filter 3dB attenuation bandwidth parameter BT;
the phase correction factors generated and stored are expressed as:
a relative additional phase is introduced for the GFSK symbol l e {0, 1.
In step S2, the process of processing the non-spread CPFSK/GFSK signal includes:
and (3) reverse order arrangement: carrying out inverse sampling sequence arrangement on the received samples r to obtain inverse sequence samples
wherein 
A complex baseband signal sample point arranged in a reverse order for receiving a K-K +1 th symbol of a current packet;
single symbol matching: matching the first symbol sample (namely the original Kth sample) after the reverse order arrangement, wherein the matching result is as follows:
in the above formula, M denotes a modulation scheme: m ═ c' for CPFSK modulation, when the symbol shaping filter length LMThe matching result is a complex matching value of the symbol "0"/"1" when 1; m ═ g' for GPFSK modulation, when the symbol shaping filter length L isMThe matching result is a matching value of binary symbols representing '000' to '111', namely the current operation result needs to be stored for subsequent iteration and combination in consideration of the influence of the front and rear symbols on the phase change of the intermediate symbol;
then, the 2 nd symbol after the reverse order, namely the K-1 th symbol of the order is matched according to the method, and the CPFSK symbol is obtained
For GFSK symbols, obtaining
The matching result of (1);
merging: for a CPFSK symbol, two single-symbol matching results need to be transferred to the result of matching two sections of received symbols with a baseband reference waveform "00" "," 10 "", "01" ", and" 11 "of four symbol combinations, and for a GFSK signal, the influence of two symbols before and after the matching symbol needs to be additionally considered, that is, the matching results of two single symbols need to be extended to two received symbols and 16 symbol combinations" 0000 "," 1000 ", …", and "1111", wherein a black body is an intersymbol interference symbol at two ends of a matched observation part;
therefore, it is first necessary to match the matching results
The replication is performed, and the matrix for replication is:
wherein 
Is composed of
Then taking into account the phase continuity of the CPFSK/GFSK signal, except for the need for
The replication is performed by phase rotation to adapt the phase introduced by the previous matched symbol
The replica matrix is written as:
where blockdiag {. is a block diagonalization operation, and the phase rotation matrix is written as:
wherein 
Is a main diagonal element of
The square matrix of (A) is formed,
represents the additional phase introduced by the second matched symbol in reverse order, whereby the combined result is represented as:
wherein 
Because of
Is the first match result;
the said process is really used for the single symbol matching of each symbol and the additional phase correction in symbol combination in the complex multiplication, and the number of complex multiplications required is determined by
Is reduced to
Iteration: iterating the above steps, the result of matching and merging the k-th symbol after reverse order arrangement is:
wherein ,
is the single symbol match result for the k-th symbol in reverse order,
combined for matching preceding k-1 symbols after reverse orderAs a result, and:
taking a mold: the final result of matching and merging K symbols is obtained, for CPFSK, the result is
Obtaining by modulo
For GFSK, are
Obtaining by modulo
In step S2, the process of processing the spread CPFSK/GFSK signal includes:
and (3) reversing: carrying out reverse sequencing on the received samples r to obtain reverse sequence
wherein 
For receiving the Lth of the current packets-complex baseband signal sample points of reverse order of k +1 chip symbols;
single symbol matching: taking into account the spreading sequence DsKnown at the receiving end and therefore only needs to be done for LsReceiving complex baseband samples of chip length takes into account two possibilitiesI.e. a spreading sequence mapped by bit "1" and a spreading sequence mapped by bit "0", thus for a CPFSK signal the following set of spreading mapping matrices is considered:
wherein ,
spreading codes for ith bit
If the mapping matrix of
I.e. the mapped ith bit spreading code is the same as the original bit, the mapping matrix for selecting the matched filter bank and the phase correction factor
Otherwise, the mapped ith bit spread spectrum code is opposite to the original bit, then
For GFSK signals, consider the following set of mapping matrices:
wherein ,
for a mapping matrix of an ith bit of a spread spectrum sequence, the influence of the (i-1) th spread spectrum bit and the (i + 1) th spread spectrum bit on a symbol needs to be considered simultaneously; order to
For decimal mapping of i-1, i +1 bit, 1 is setThe subscripts of (a) are:
representing the mapping of original information "1" and bits "0" to the ith chip, and the rest of the indexes are set with zero; chips outside the currently observed spreading sequence are defaulted to 0, i.e.
Single symbol matching: and matching the 1 st symbol sample and the 2 nd symbol sample after the reverse order, wherein the matching expression is as follows:
wherein the ratio of i to 1,2,
is based on the matched filter bank after chip mapping update, and the matching result
Representing a match result for an unspread bit of "0",
representing the matching result corresponding to the non-spread bit "1";
merging: for a DSSS-CPFSK symbol, the process of combining two single-symbol matching results is:
wherein 
For the phase correction factor after spread spectrum mapping, considerThe phase continuity of the CPFSK/GFSK signal needs to be subjected to phase correction and then in-phase superposition;
iteration: iterating the above steps, the result of matching and combining the k-th chip after the reverse order is:
wherein 
The result of the combination of k-1 chips after the reverse order;
taking a mold: finally, the complete L of a single DSSS-FSK signal is obtainedsThe result of the length-chip match combining, for DSSS-CPFSK, is
Obtaining by modulo calculation
For DSSS-GFSK, are
Obtaining by modulo
In step S3, if a hard demodulation method is adopted for the CPFSK/GFSK signal without spread spectrum, the subscript with the maximum matching modulus is selected:
then, will
Inversely mapping the highest bit of the right end back to the binary sequence, wherein the mapped K bit length sequence is the demodulation result for CPFSK, and the inversely mapped K +2 bit length sequence for GFSKDiscarding ISI bits before and after the sequence, and taking the middle K bit as a demodulation result;
if soft demodulation is employed, the soft information of the kth bit among the K observed bits is written as:
wherein ,I0{. is a zero-order first-class modified Bessel function; SNRh＝|h|/σ2For the receiving end SNR, where | h | is the flat fading modulus, σ2Gaussian noise power for the receiver;
and
the branch index is matched for the kth bit as an inverse mapping to a set of 1 s and 0 s.
In step S3, if the hard demodulation method is used for the spread DSSS-CPFSK/DSSS-GFSK signal, the ratio of the information before spreading is close up as:
if soft demodulation is employed, the soft information is written as:
example 2
As shown in fig. 3, a method for noncoherently demodulating a CPFSK/GFSK signal, the method comprising:
s1: generating a matched filter group with a single symbol length and a phase correction factor according to the transmitted CPFSK/GFSK signal parameters;
s2: matching the received samples: this step is compared by passing a symbol matching calculation instead of redundancy using the matching resultsLow complexity samples to be received
2 of sequences "00 … 0" to "11 … 1KMatching the baseband waveform combinations of continuous phases;
s3: and demodulating the matching result: and decoding the K bits of information from each group of K bits according to decoding requirements in a soft demodulation or hard demodulation mode.
In this embodiment, the CPFSK/GFSK signal has the excellent characteristics of constant envelope and continuous phase, and its complex baseband signal model is:
wherein, alpha is a bit sequence to be modulated with a length L and alphaiE { -1,1} is the ith binary bipolar bit to be modulated; n is a single chip sampling factor, and N is a sampling subscript; h isn＝Δf/BwAs a modulation factor, ΔfIs the frequency difference of two frequency points, BwChip rate/transmission bandwidth; q (n) is the accumulation of the single sign phase shaping function h (n). For a full response CPFSK signal that is not phase shaped by a Gaussian filter, the shaping function hc(n) is the response length Lc1 (normalized symbol length) rectangular filter, whose expression is:
thus, the expression for the kth symbol of the CPFSK signal is:
wherein θk-1Accumulated phase of the first k-1 term, akN/N is the phase change factor of the kth symbol, which is linearly changed in the case of a full response CPFSK signal. To is pairThe partial response GFSK signal is phase-shaped by a Gaussian filter and the shaping function hg(n) is the response length LgThe expression of the low-pass gaussian filter is:
gaussian filter bandwidth factor in the above equation
BT is the bandwidth-time factor of the 3dB attenuation. L is a radical of an alcoholgIn general, truncation 3 can model inter-symbol-interference (ISI) of the GFSK signal, that is, a single GFSK symbol mainly generates inter-horse crosstalk with two preceding and succeeding symbols, so that the k-th symbol of the GFSK signal is expressed as:
in the formula θk-1Is the accumulated phase of the first k-1 term, phi (n; BT; alpha)k-1αkαk+1) The phase change factor of the kth symbol under the current time-bandwidth factor is influenced by ISI of the preceding and following symbols, and the phase change factor is non-linearly changed under a partial response GFSK signal model.
Specifically, in step S1, for the full-response CPFSK signal, the pre-generated and stored matched filter bank is:
wherein ,{·}HRepresents the Hermitian transpose, {. The }TThe transpose of the matrix is represented,
an inversely ordered sequence of reference complex baseband samples corresponding to CPFSK symbols q ∈ {0,1 }. In particular, according to the signal model of CPFSK, the symbol q can be represented as:
wherein ,hmThe CPFSK signal modulation factor of the sending end is obtained. And the pre-generated and stored additional phase correction factors may be expressed as:
representing the relative additional phase introduced by the current matched symbol q e 0,1 to the subsequent matched symbol.
For a partial response GFSK signal, based on a signal model of the GFSK signal, a current symbol is affected by ISI from previous and subsequent symbols, so a pre-generated and stored matched filter bank needs to additionally consider the influence from the previous and subsequent symbols, that is:
where l is the inverse of the reference complex baseband sample corresponding to the symbol l ∈ {0, 1.., 7}, and l is the current bit q1With two preceding and succeeding bits q0q2Combining corresponding q0q1q2The highest decimal mapping on the right end, namely:
then each sample point of the symbol l can be represented as:
wherein phi (n; BT; q)0q1q2) For phase change of current symbol, subject to preceding and following bits q0 and q2And GFSK Gaussian shaped filtering 3dB attenuationThe impact of the bandwidth parameter BT. The pre-generated and stored additional phase correction factors may be expressed as:
a relative additional phase is introduced for the GFSK symbol l e {0, 1. The matching waveform can be multiplexed with a waveform stored by a Look-up-table (LUT) of a baseband modulation part, so that the storage space is further saved.
In step S2, for the CPFSK/GFSK signal without spreading, the received signal is divided into a group of every K symbols and demodulated. This step replaces the matching calculation of redundant symbols by the matching result delivery, and the received samples are processed with low complexity
2 of sequences "00 … 0" to "11 … 1KThe matching is performed by combining baseband waveforms of successive phases. The specific flow chart is shown in fig. 1, and the steps can be divided into reverse order, single symbol matching, merging, iteration and modular extraction;
and (3) reversing: carrying out reverse sequencing on the received samples r to obtain reverse sequence
wherein 
A complex baseband signal sample point arranged in a reverse order for receiving a K-K symbol of a current packet;
single symbol matching: and matching the first symbol sample (namely the original Kth sample) after the reverse order, wherein the matching result is as follows:
in the above formula, M denotes a modulation scheme: m ═ c' for CPFSK modulation, when the symbol shaping filter length L M1, matching knotThe result is a complex match of the symbols "0"/"1"; m ═ g' for GPFSK modulation, when the symbol shaping filter length L isMThe matching result is a matching value of symbols "000" to "111" (binary representation), that is, the influence of the preceding and following symbols on the phase change of the intermediate symbol is considered. The current operation result needs to be stored for subsequent iteration and combination.
Then, the 2 nd symbol sample (namely the original K-1 th sample) after the reverse order is matched according to the method, and the CPFSK symbol is obtained
For GFSK symbols, obtaining
The matching result of (2).
And for the CPFSK symbol, two single-symbol matching results need to be expanded to the results of matching two received symbols with four double-symbol combinations of '00', '10', '01' and '11'. For the GFSK signal, the influence of the two symbols before and after the GFSK signal needs to be considered, i.e. the matching result of the two single symbols needs to be extended to the combination of the two received symbols and the 16 symbols, "0000", "1000", …, "1111" (bold is the inter-symbol crosstalk term).
Therefore, it is first necessary to match the matching results
And copying, wherein a copy matrix is as follows:
wherein 
Is composed of
The unit matrix of (2). Then considering the phase continuity of CPFSK/GFSK signalExcept for the need for
The replication is performed and a phase rotation is also required to adapt to the phase introduced by the previous symbol, pair
The replica matrix can be written as:
wherein blockdiag {. is a block diagonalization operation. And the phase rotation matrix can be written as:
wherein 
Is a major diagonal element of
A square matrix of (a).
Representing the additional phase introduced by the second matched symbol in reverse order, whereby the combined result can be expressed as:
wherein 
The above process only uses single symbol matching of each symbol and additional phase correction in symbol combination for true complex multiplication, so that compared with traditional matching method, the required complex multiplication is performedNumber is given by
Is reduced to
Iteration: iterating the above steps, the result of matching and merging the kth symbol after the reverse order is:
wherein ,
is the result of the single symbol matching of the k-th symbol after the reverse order,
is the result of matching and merging k-1 symbols before and after the reverse order, and:
in summary, the number of Complex Multiplications (CMs) and Complex Additions (CAs) required for K symbol matching are both
The number of CM and CA times required for directly matching with all possible K symbol combinations
Compared with the prior art, the complexity of the scheme can be greatly reduced.
Taking a mold: the final result of matching and combining K symbols can be obtained, for CPFSK, the result is
Obtaining by modulo
For GFSK, are
Obtaining by modulo
The number of Real Multiplication (RM) required for modulo is
Real Addition (RA) times of
Specifically, in step S3, the final incoherent matching result needs to be demodulated to obtain the corresponding K bits of information. If a hard demodulation mode is adopted, firstly selecting a subscript with the maximum matching modulus:
where i represents the matching modulus index. Then, will
And inversely mapping the highest bit at the right end back to the binary sequence. For CPFSK, the mapped K-bit length sequence is the demodulation result. For GFSK, mapped sequences of K +2 bit length need to discard ISI bits before and after, and take the middle K bits as the demodulation result.
If it is notWith soft demodulation, the soft information of the K-th bit in the K observation bits can be written as
wherein ,I0{. is a zero-order first-class modified Bessel function; SNRh＝|h|/σ2For the receiving end SNR, where | h | is the flat fading modulus, σ2Is the gaussian noise power;
and
matching the set with branch subscripts of '1' and '0' for the kth bit after the highest inverse mapping at the right end.
In order to verify the effectiveness of the designed incoherent demodulation method provided in the embodiment of the present invention, a simulation experiment is further performed, specifically as follows:
under the AWGN channel, BER performance of different demodulation schemes is plotted along with SNR for CPFSK signal demodulation with h being 0.5 and GFSK signal demodulation with h being 0.5 and BT being 0.5 which are commonly used. Fig. 4 is a performance curve in an unencoded condition, and fig. 5 is a performance curve in (2,1,3) convolutional code encoding and soft viterbi decoding. The solid line represents GFSK demodulation performance and the dotted line represents CPFSK demodulation performance, the corresponding scheme of the present embodiment is labeled with "Δ", the optimal multi-symbol detection scheme is labeled with "□", the differential detection scheme is labeled with "good", the envelope detection scheme is labeled with "+", the theoretical performance of the orthogonal 2-FSK signal incoherent detection scheme under the uncoded condition is plotted with a dotted line, the abscissa represents SNR, and the ordinate represents BER. It can be seen that due to the non-orthogonality of the single symbol period, the envelope detection and differential detection performance under the uncoded condition are both inferior to the theoretical performance bound of the orthogonal 2-FSK signal non-coherent detection scheme, while the scheme and the optimal multi-symbol detection scheme are both superior to the theoretical performance bound of the orthogonal 2-FSK signal non-coherent detection scheme. Compared with the optimal multi-symbol detection scheme under the condition of no coding, the BER (bit error rate) required by the scheme to achieve reliable communication of the Internet of things is 10-4The performance loss for CPFSK demodulation is close to 2dB, the performance loss for GFSK demodulation is close to 1dB, and the BER is 10 under the coding condition-4The time performance loss is only 0.5dB, but the complexity of the receiver can be greatly reduced. Compared with envelope detection and differential detection with poor performance, BER of the scheme is 10 under the uncoded condition-4The performance gain of (2) is 3-6 dB, and the performance gain is 3dB under the coding condition.
To further illustrate the low complexity of the scheme, the complexity of different demodulation schemes is next compared, where 1 CM is equivalent to 4 RMs and one CA is equivalent to 2 RAs. The solution requires altogether
sub-RM and
sub-RA solves K bit information, optimal multi-symbol detection needs
sub-RM and
the information of the intermediate symbols of the K observation symbols can be solved by the secondary RA, and the envelope detection needs to be carried out
sub-RM and
the sub-RA solves the information of the current symbol, and the differential detection requires 4N +2 RM and 2N +1 RA to solve the information of the current symbol. In summary, the average per-symbol demodulation complexity statistics are as follows:
if the observation length K is 5 and the upsampling factor N is 4, then for GFSK demodulation, 10496 times of RMs and 5248 times of RA for optimal multi-symbol detection need to solve information of one symbol, 382.4 times of RMs and 191.2 times of RA for the scheme of the present invention need to solve information of one symbol, 144 times of RMs and 72 times of RA for envelope detection need to solve information of one symbol, and 18 times of RMs and 9 times of RA for differential detection need to solve information of one symbol. For CPFSK demodulation, optimal multi-symbol detection needs 2624 RM and 1312 RA to solve the information of one symbol, the scheme of the present invention needs 95.6 RM and 47.8 RA to solve the information of one symbol, envelope detection needs 36 RM and 18 RA to solve the information of one symbol, and differential detection needs 18 RM and 9 RA to solve the information of one symbol. In contrast, the inventive scheme is much less complex than the optimal multi-symbol detection scheme, and more complex than envelope detection and differential detection, but the performance gain compared to the receiver is still acceptable. In addition, the matched filter bank of the scheme can multiplex the reference waveform with single symbol length stored by the table look-up method of the baseband modulation part, thereby further reducing the space complexity of realization.
Example 3
As shown in fig. 3, a method for noncoherently demodulating a CPFSK/GFSK signal, the method comprising:
s1: generating a matched filter group with a single symbol length and a phase correction factor according to the transmitted CPFSK/GFSK signal parameters;
s2: matching the received samples: the step regards the DSSS-FSK after the spread spectrum as a complete symbol, wherein each receiving chip is matched with a matched filter group by a single chip, then the matching result after phase correction is superposed, and the modulus value of the final result is calculated;
s3: and demodulating the matching result: and decoding the K bits of information from each group of K bits according to decoding requirements in a soft demodulation or hard demodulation mode.
In this embodiment, the DSSS-CPFSK/DSSS-GFSK signal has the excellent characteristics of constant envelope and continuous phase, and its complex baseband signal model is the same as that of embodiment 1, but the bits to be modulated need to be first subjected to direct sequence spread spectrum processing and then to spreading sequence DsThe expression after the direct sequence spread processing is as follows:
b[kLs+i]＝a[k]·Ds[i],0≤i<Ls
wherein b [ i ] ∈ { -1,1} is the ith binary bipolar bit, and a [ i ] ∈ { -1,1} is the ith original information bit.
The processing flow of step S1 in this embodiment is exactly the same as that of step S1 in embodiment 1. In step S2, the length of the code is LSSpreading sequence D ofsAnd the spread DSSS-CPFSK/DSSS-GFSK signal is regarded as a complete symbol, each receiving chip is subjected to single chip matching with the matched filter bank, then the matching result subjected to phase correction is superposed, and the modulus value of the final result is obtained. The above process is equivalent to receiving a single DSSS-CPFSK/DSSS-GFSK symbol
The reference symbols corresponding to the "0", "1" information bits are matched and modulo. The specific flow chart is shown in fig. 2, and the steps can be divided into reverse order, single symbol matching, merging, iteration and modular extraction;
and (3) reversing: carrying out reverse sequencing on the received samples r to obtain reverse sequence
wherein 
For receiving the Lth of the current packets-an inverse order of k +1 symbols of complex baseband signal sample points.
Single symbol matching: taking into account the spreading sequence DsKnown, therefore, only need to be for LsThe chip-length received complex baseband samples take into account two possible codeword combinations, namely a bit "1" mapped spreading sequence and a bit "0" mapped spreading sequence. Thus for a CPFSK signal, consider the following set of spreading mapping matrices:
wherein ,
spreading codes for ith bit
If S is the mapping matrix of(i)1, i.e. the mapped ith bit spreading code is the same as the original bit, the mapping matrix for selecting the matched filter bank and the phase correction factor
Otherwise, the mapped ith bit spread spectrum code is opposite to the original bit, then
For GFSK signals, consider the following set of mapping matrices:
wherein ,
for the mapping matrix of the ith bit spreading code, the influence of the (i-1) th spreading bit and the (i + 1) th spreading bit on the symbol needs to be considered simultaneously. Order to
For the decimal mapping of the i-1, i +1 bit, the subscript of 1 is:
representing the mapping of the original information "1" and bits "0" to the ith chip.
Single symbol matching: and matching the 1 st symbol sample and the 2 nd symbol sample after the reverse order, wherein the matching expression is as follows:
wherein 
Is based on the matched filter bank after chip mapping update, and the matching result
Representing a match result for an unspread bit of "0",
representing the matching result for the non-spread bits "1".
Merging: for a DSSS-CPFSK symbol, the process of combining two single-symbol matching results is:
wherein 
For the phase correction factor after spread spectrum mapping, the phase continuity of the CPFSK/GFSK signal is considered, and the same-phase superposition is performed after the phase correction.
Iteration: iterating the above steps, the result of matching and combining the k-th chip after the reverse order is:
wherein 
Is the result of k-1 chip combining before and after the reverse order.
Taking a mold: finally, the complete L of a single DSSS-FSK signal can be obtainedsLength chip match combining resultFor DSSS-CPFSK, is
Obtaining by modulo
For DSSS-GFSK, the
Obtaining by modulo
Specifically, in step S3, for the spread DSSS-CPFSK/DSSS-GFSK signal, if the hard demodulation mode is adopted, the decoded information bits before spreading can be written as:
if soft demodulation is employed, the soft information can be written as:
in order to verify the effectiveness of the designed incoherent despreading demodulation method provided in the embodiment of the invention, a simulation experiment is further performed, which specifically comprises the following steps:
under AWGN channel, BER performance of different demodulation and despreading schemes under uncoded condition is plotted according to SNR variation curve for DSSS-CPFSK signal demodulation and despreading of commonly used h 0.5, as shown in FIG. 4, wherein the embodiment is marked by "+", the differential demodulation and soft decoding are combined and marked by "good", and different spreading code lengths L are distinguished by different line shapessThe abscissa represents SNR and the ordinate represents BER, for the performance curve under {4,8,16,32 }. As can be seen, in this embodiment, BER is 10-4Spread spectrum gain of about 3dB can be obtained, while the traditional scheme for separating de-spread spectrum from demodulation can only reach 1; a spreading gain of 2 dB. In a spreading codeWhen the length is 4, the scheme has 3dB performance gain compared with the comparison scheme, and when the length of the spread spectrum code is 32, the scheme has 6dB performance gain compared with the comparison scheme. And considering that the spreading code at the receiving end is known, the demodulation complexity of the scheme is similar to envelope detection, except for an additional phase correction step. The single symbol matched filter bank used in the scheme can multiplex the baseband waveform stored by the baseband modulation partial table look-up method, so that the storage complexity can be further saved. In addition, the length and the value of the spread spectrum code can be configured at will without the need of a receiving end to regenerate the matching reference waveform corresponding to the spread spectrum sequence, thereby further improving the flexibility.
The same or similar reference numerals correspond to the same or similar parts;
the positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. A non-coherent demodulation method of a CPFSK/GFSK signal is characterized by comprising the following steps:
s1: generating a matched filter group with a single symbol length and a phase correction factor according to the transmitted CPFSK/GFSK signal parameters;
s2: matching the received samples: if the received CPFSK/GFSK signal is not spread spectrum, matching the received sample by K symbols, and performing modulo operation on a matching result; if the received DSSS-CPFSK/DSSS-GFSK signals are directly subjected to sequence spread spectrum processing, the signals subjected to the spread spectrum processing are regarded as a whole, the received samples are matched with each other in length of spread spectrum codes, and the modulus value of the matching result is calculated;
s3: and demodulating the matching result: if the received CPFSK/GFSK signals are not spread, each group of the CPFSK/GFSK signals decodes K bit information according to decoding requirements in a soft demodulation or hard demodulation mode; if the received signal is a DSSS-CPFSK/DSSS-GFSK signal, the corresponding non-spread original bit is solved.
2. The method of claim 1, wherein the CPFSK/GFSK signal has a constant envelope and the complex baseband signal model is:
wherein, alpha is a bit sequence to be modulated with a length L and alphaiE { -1,1} is the ith binary bipolar bit to be modulated; n is a single chip sampling factor, and N is a sampling subscript; h ism＝Δf/BwAs a modulation factor, ΔfIs the frequency difference of two frequency points, BwChip rate/transmission bandwidth; q (n) is the accumulation of the single sign phase shaping function h (n).
3. The method of claim 2, wherein the shaping function h is applied to a full-response CPFSK signal that is not phase-shaped by a Gaussian filterc(n) is the response length Lc1, a rectangular filter of normalized symbol length, whose expression is:
the expression for the kth symbol of the CPFSK signal is thus:
wherein θk-1Accumulated phase of the first k-1 term, akN/N is the phase change factor of the kth symbol, which is linearly changed under the full response CPFSK signal; and for the partial response GFSK signal which is subjected to phase shaping by the Gaussian filter, the shaping function hg(n) is the response length LgThe expression of the low-pass gaussian filter is:
gaussian filter bandwidth factor in the above equation
BT is the bandwidth-time factor of 3dB attenuation, LgThe truncation 3 models intersymbol interference of the GFSK signal, namely, a single GFSK symbol mainly generates intersymbol interference with the front symbol and the rear symbol, so that the k-th symbol of the GFSK signal has the expression:
in the formula θk-1Is the accumulated phase of the first k-1 term, φ (n; BT; α)k-1αkαk+1) The phase change factor of the kth symbol under the current time-bandwidth factor is influenced by ISI of the preceding and following symbols, and the phase change factor is non-linearly changed under a partial response GFSK signal model.
4. The method according to claim 3, wherein in step S1, the step of generating the matched filter set with a single symbol length according to the transmitted CPFSK/GFSK signal parameters comprises:
wherein ,
permuting the result of the inverse sampling order of the reference complex baseband samples corresponding to the CPFSK symbol q ∈ {0,1}, }HRepresents the Hermitian transpose, {. The }TRepresenting a matrix transposition;
the CPFSK symbol q is represented as:
n-1, where N is 0,1mThe CPFSK signal modulation factor is the sending end.
5. The method according to claim 4, wherein in step S1, the phase correction factor for generating the single symbol length according to the transmitted CPFSK/GFSK signal parameter is expressed as:
6. The method of noncoherent demodulation of a CPFSK/GFSK signal according to claim 5,
since the current symbol is affected by crosstalk between previous and next symbols, the generated and stored matched filter bank needs to consider the effect of the previous and next symbols, that is:
wherein 
For the symbol l ∈ {0, 1., 7} corresponding to the inverse of the reference complex baseband sample, and l is the current bit q1With two preceding and succeeding bits q0q2Combining corresponding q0q1q2The highest decimal mapping at the right end is as follows:
then each sample point of the symbol l is represented as:
wherein N is 0, 1.. cndot.N-1,. phi (N; BT; q)0q1q2) For phase change of current symbol, subject to preceding and following bits q0 and q2And the influence of the GFSK Gaussian shaping filter 3dB attenuation bandwidth parameter BT;
the phase correction factor generated and stored is expressed as:
a relative additional phase is introduced for the GFSK symbol l e {0, 1.
7. The method according to claim 6, wherein the step S2 of processing the CPFSK/GFSK signal without spreading spectrum comprises:
and (3) reverse order arrangement: carrying out inverse sampling sequence arrangement on the received samples r to obtain inverse sequence samples
wherein 
A complex baseband signal sample point arranged in a reverse order for receiving a K-K +1 th symbol of a current packet;
single symbol matching: and matching the first symbol sample after the reverse order arrangement, namely the original Kth sample, wherein the matching result is as follows:
in the above formula, M denotes a modulation scheme: m ═ c' for CPFSK modulation, when the symbol shaping filter length LMThe matching result is a complex matching value of the symbol "0"/"1" when 1; m ═ g' for GPFSK modulation, when the symbol shaping filter length L isMThe matching result is a matching value of binary symbols representing '000' to '111', namely the current operation result needs to be stored for subsequent iteration and combination in consideration of the influence of the front and rear symbols on the phase change of the intermediate symbol;
then, the 2 nd symbol after the reverse order, namely the K-1 th symbol of the order is matched according to the method, and the CPFSK symbol is obtained
For GFSK symbols, obtaining
The matching result of (1);
merging: for a CPFSK symbol, two single-symbol matching results need to be transferred to the result of matching two sections of received symbols with a baseband reference waveform "00" "," 10 "", "01" ", and" 11 "of four symbol combinations, and for a GFSK signal, the influence of two symbols before and after the matching symbol needs to be additionally considered, that is, the matching results of two single symbols need to be extended to two received symbols and 16 symbol combinations" 0000 "," 1000 ", …", and "1111", wherein a black body is an intersymbol interference symbol at two ends of a matched observation part;
therefore, it is first necessary to match the matching results
The replication is performed, and the matrix for replication is:
wherein 
Is composed of
Then taking into account the phase continuity of the CPFSK/GFSK signal, except for the need for
The replication is performed by phase rotation to adapt the phase introduced by the previous matched symbol
The replica matrix is written as:
where blockdiag {. is a block diagonalization operation, and the phase rotation matrix is written as:
wherein 
Is a major diagonal element of
The square matrix of (a) is obtained,
represents the additional phase introduced by the second matched symbol in reverse order, whereby the combined result is represented as:
wherein 
Because of the fact that
Is the first match result;
the said process only uses single symbol matching of each symbol and additional phase correction in symbol combination for complex multiplication, and the required number of complex multiplication is determined by
Is reduced to
Iteration: iterating the above steps, and the result of matching and merging the k-th symbol after the reverse order arrangement is as follows:
wherein ,
is the single symbol match result for the k-th symbol in reverse order,
is the result of matching and merging k-1 symbols before and after the reverse order, and:
taking a mold: the final result of matching and merging K symbols is obtained, for CPFSK, the result is
Obtaining by modulo calculation
For GFSK, are
And (3) obtaining by modulus calculation:
8. the method according to claim 7, wherein the step S2 of processing the spread CPFSK/GFSK signal comprises:
and (3) reversing: carrying out reverse sequencing on the received samples r to obtain reverse sequence
wherein 
For receiving the Lth of the current packets-complex baseband signal sample points of reverse order of k +1 chip symbols;
single symbol matching: taking into account the spreading sequence DsKnown at the receiving end and therefore only needs to be done for LsThe received complex baseband samples of chip length take into account two possible codeword combinations, namely a spreading sequence mapped by bit "1" and a spreading sequence mapped by bit "0", and thus for a CPFSK signal consider the following set of spreading mapping matrices:
wherein ,
spreading codes for ith bit
If the mapping matrix of
I.e. the mapped ith bit spreading code is the same as the original bit, the mapping matrix for selecting the matched filter bank and the phase correction factor
Otherwise, the mapped ith bit spread spectrum code is opposite to the original bit, then
For GFSK signals, consider the following set of mapping matrices:
wherein ,
for a mapping matrix of an ith bit of a spread spectrum sequence, the influence of the (i-1) th spread spectrum bit and the (i + 1) th spread spectrum bit on a symbol needs to be considered simultaneously; order to
For the decimal mapping of the i-1, i +1 bit, the subscript of 1 is:
representing the mapping of original information "1" and bits "0" to the ith chip, and the rest of the indexes are set with zero; chips outside the currently observed spreading sequence are defaulted to 0, i.e.
Single symbol matching: and matching the 1 st symbol sample and the 2 nd symbol sample after the reverse order, wherein the matching expression is as follows:
wherein the ratio of i to 1,2,
is based on the matched filter bank after chip mapping update, and the matching result
Representing a match result for an unspread bit of "0",
representing the matching result corresponding to the non-spread bit "1";
merging: for a DSSS-CPFSK symbol, the process of combining two single-symbol matching results is:
wherein 
The phase correction factor after spread spectrum mapping is the same phase correction factor after phase correction and in-phase superposition in consideration of the phase continuity of the CPFSK/GFSK signal;
iteration: iterating the above steps, the result of matching and combining the k-th chip after the reverse order is:
wherein 
The result of the combination of k-1 chips after the reverse order;
taking a mold: finally, the complete L of a single DSSS-FSK signal is obtainedsThe result of the length-chip match combining, for DSSS-CPFSK, is
Obtaining by modulo calculation
For DSSS-GFSK, the
Obtaining by modulo
9. The method according to claim 8, wherein in step S3, if the hard demodulation method is adopted for the CPFSK/GFSK signal without spread spectrum, the subscript with the maximum matching modulus is selected first:
then, will
Inversely mapping the highest bit of the right end back to a binary sequence, wherein for CPFSK, the mapped sequence with the length of K bits is a demodulation result, for GFSK, the inversely mapped sequence with the length of K +2 bits needs to discard ISI bits before and after, and the middle K bit is taken as a demodulation result;
if soft demodulation is employed, the soft information of the kth bit among the K observed bits is written as:
wherein ,I0{. is a zero-order first-class modified Bessel function; SNRh＝|h|/σ2For the receiving end SNR, where | h | is the flat fading modulus, σ2Gaussian noise power for the receiver;
and
the branch index is matched for the kth bit as an inverse mapping to a set of 1 s and 0 s.
10. The CPFSK/GFSK signal noncoherent demodulation method according to claim 9, wherein in step S3, if the hard demodulation method is adopted for the spread DSSS-CPFSK/DSSS-GFSK signal, the ratio of the information before spreading is characterized as:
if soft demodulation is employed, the soft information is written as:
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