CN114640562B - Incoherent demodulation method for CPFSK/GFSK signals - Google Patents

Incoherent demodulation method for CPFSK/GFSK signals Download PDF

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CN114640562B
CN114640562B CN202210259019.2A CN202210259019A CN114640562B CN 114640562 B CN114640562 B CN 114640562B CN 202210259019 A CN202210259019 A CN 202210259019A CN 114640562 B CN114640562 B CN 114640562B
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CN114640562A (en
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张睿琦
伍沛然
夏明华
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Sun Yat Sen University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/10—Frequency-modulated carrier systems, i.e. using frequency-shift keying
    • H04L27/14—Demodulator circuits; Receiver circuits
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/10—Frequency-modulated carrier systems, i.e. using frequency-shift keying
    • H04L27/14—Demodulator circuits; Receiver circuits
    • H04L27/144—Demodulator circuits; Receiver circuits with demodulation using spectral properties of the received signal, e.g. by using frequency selective- or frequency sensitive elements
    • H04L27/148—Demodulator circuits; Receiver circuits with demodulation using spectral properties of the received signal, e.g. by using frequency selective- or frequency sensitive elements using filters, including PLL-type filters
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Abstract

The invention provides a CPFSK/GFSK signal incoherent demodulation method, which generates a matched filter bank with single symbol length and a phase correction factor according to transmitted CPFSK/GFSK signal parameters; then, if the received signal is the despreading CPFSK/GFSK signal, matching the received sample K symbols by K symbols, and modulo the matching result; if the received DSSS-CPFSK/DSSS-GFSK signal is subjected to direct sequence spread spectrum processing, the spread spectrum processed signal is regarded as a whole, the lengths of the spread spectrum codes of the received samples are matched, and the matching result is subjected to modulo value; finally, if the received CPFSK/GFSK signal is not spread, each group solves K bit information according to the decoding requirement and in a soft demodulation or hard demodulation mode; if a DSSS-CPFSK/DSSS-GFSK signal is received, the corresponding despread raw bits are demodulated.

Description

Incoherent demodulation method for CPFSK/GFSK signals
Technical Field
The invention relates to the technical field of Internet of things communication, in particular to a CPFSK/GFSK signal incoherent demodulation method.
Background
With the rapid development of wireless communication technologies and communication networks, the need for communication between objects is rapidly growing. In the fifth generation mobile communication technology (5th Generation,5G), large-scale machine type communication (Massive Machine Type Communication, mctc) is listed as one of three application scenarios. Among the physical layer technologies of the internet of things aiming at the mctc scene, continuous phase frequency shift keying (Continuous Phase Shift Keying modulation, CPFSK) is widely applied with the excellent characteristics of constant envelope, continuous phase and high spectrum efficiency. Gaussian filter frequency shift keying adds a low-pass gaussian filter as a symbol phase shaping function on the basis of continuous phase modulation in CPFSK (Gaussian Frequency Shift Keying, GFSK), and compared with CPFSK signals, the signal has quicker out-of-band attenuation and higher spectral efficiency, but the introduction of gaussian filter shaping can bring extra symbol crosstalk (Inter-symbol interference), and the implementation is more complex. Further, CPFSK/GFSK modulation can be combined with direct sequence spread spectrum techniques (Direct Sequence Spread Spectrum, DSSS) and channel coding techniques to achieve coverage enhancement and rate adaptation, thereby meeting the requirements of long-range Internet of things communications.
In low-cost receiver design, the CPFSK/GFSK signal demodulation mode is usually realized based on a non-coherent mode, because the mode has low requirements on synchronization precision and strong channel fading resistance, and is more suitable for low-cost realization. The currently used non-coherent demodulation scheme is to utilize the polarity of the phase change between single symbols to determine the information carried by the transmitted symbols, i.e. a differential demodulation algorithm. Although the implementation is simple, bit Error Rate (BER) performance is poor at a low received Signal-to-Noise ratio (SNR), and it is difficult to meet the requirement of wide coverage. Another incoherent envelope detection algorithm has better performance when the FSK signal modulation factor is large, 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 intersymbol orthogonality is not satisfied, so BER performance is also poor at low SNR. Because CPFSK and GFSK are memory signals with continuous phases, demodulation schemes with good BER performance are multi-symbol detection algorithms based on the concept of maximum likelihood sequence detection (Maximum Likelihood Sequence Detection, MLSD), such as optimal incoherent demodulation algorithms, and the like, however, the algorithm has very high operation complexity and storage complexity, and is difficult to adapt to practical engineering application. In addition, the conventional concept of demodulation despreading separation introduces a significant performance penalty in despreading a direct sequence spread spectrum DSSS-FSK signal.
The prior art discloses a CPFSK demodulation device with rapid automatic frequency compensation and a method thereof, which firstly starts the CPFSK demodulation device; then, the radio frequency signal is processed 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 demodulation device to obtain an output signal; the patent not only can realize the capture and tracking of the Doppler frequency offset in a large range, but also can realize the tracking of the Doppler change rate in a large range; the other characteristic is that the calculation and update 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 realization of the FPGA and the like. However, this patent is of little relevance for matched filter banks and phase correction factors that require only one symbol length to achieve good performance with relatively low complexity.
Disclosure of Invention
The invention provides a CPFSK/GFSK signal incoherent demodulation method, which can achieve better performance with relatively lower complexity only by a matched filter bank with a symbol length and a phase correction factor, and the matched filter bank can multiplex reference waveforms used by a transmission part table look-up method, thereby further reducing storage complexity.
In order to achieve the technical effects, the technical scheme of the invention is as follows:
a CPFSK/GFSK signal incoherent demodulation method comprises the following steps:
s1: generating a matched filter bank with 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 the despreading CPFSK/GFSK signal, matching the received sample by K symbols, and modulo the matching result; if the received DSSS-CPFSK/DSSS-GFSK signal is subjected to direct sequence spread spectrum processing, the spread spectrum processed signal is regarded as a whole, the lengths of the spread spectrum codes of the received samples are matched, and the matching result is subjected to modulo value;
s3: demodulating the matching result: if the received CPFSK/GFSK signal is not spread, each group according to the decoding requirement according to soft demodulation or hard demodulation mode to solve K bit information; if a DSSS-CPFSK/DSSS-GFSK signal is received, the corresponding despread raw bits are demodulated.
Further, the CPFSK/GFSK signal has a constant envelope, and a complex baseband signal model is as follows:
Figure BDA0003549983160000031
wherein alpha is a bit sequence to be modulated of length L and alpha i E { -1,1} is the ith binary bipolar bit to be modulated; n is a single chip sampling factor, N is a sampling index; h is a m ＝Δ f /B w As modulation factor, delta f Is the frequency difference of two frequency points, B w For chip rate/transmission bandwidth; q (n) is the accumulation of the single symbol phase shaping function h (n).
Further, for the lack ofFull response CPFSK signal phase shaped by Gaussian filter with shaping function h c (n) is the response length L c =1, rectangular filter of normalized symbol length, expressed as:
Figure BDA0003549983160000032
the expression for the kth symbol of the CPFSK signal is thus:
Figure BDA0003549983160000033
wherein θk-1 For the accumulated phase of the first k-1 terms, a k N/N is the phase change factor of the kth symbol, which varies linearly with the full response CPFSK signal; whereas for a partially-responsive GFSK signal phase-shaped by a gaussian filter, its shaping function h g (n) is the response length L g Is expressed as:
Figure BDA0003549983160000034
bandwidth factor of gaussian filter in above type
Figure BDA0003549983160000035
BT is a bandwidth-time factor of 3dB attenuation, L g The truncation 3 models inter-symbol interference of the GFSK signal, that is, a single GFSK symbol mainly generates inter-symbol interference with two front and rear symbols, so that the expression of the kth symbol of the GFSK signal is as follows:
Figure BDA0003549983160000036
in the formula θk-1 Is the accumulated phase of the first k-1 term, phi (n; BT; alpha) k-1 α k α k+1 ) Is the phase change factor of the kth symbol under the current time-bandwidth factor, and is subjected to the front and back symbols Which varies non-linearly under a partial response GFSK signal model.
Further, in the step S1, the generation of the matched filter bank with single symbol length according to the transmitted CPFSK/GFSK signal parameters is as follows:
Figure BDA0003549983160000041
wherein ,
Figure BDA0003549983160000042
the result of the reverse sampling sequence arrangement of the reference complex baseband samples corresponding to CPFSK symbol q epsilon {0,1}, { · } H Represents Hermitian transpose, {. Cndot. } T Representing a matrix transpose;
CPFSK symbol q is expressed as:
Figure BDA0003549983160000043
where n=0, 1..n-1, N is the upsampling factor, h m Is the modulation factor of CPFSK signal at the transmitting end.
Further, in the step S1, the generation of the phase correction factor of the single symbol length according to the transmitted CPFSK/GFSK signal parameter is expressed as:
Figure BDA0003549983160000044
Figure BDA0003549983160000045
representing the relative additional phase that the current symbol q e {0,1} introduces for subsequent symbols.
Further, since the current symbol is affected by the crosstalk between the symbols of the preceding and following symbols, the generated and stored matched filter bank needs to consider the influence of the preceding and following symbols, namely:
Figure BDA0003549983160000046
wherein
Figure BDA0003549983160000047
For the reverse order of the reference complex baseband samples corresponding to the symbol l e {0,1,., 7} and l is the current bit q 1 And two bits q 0 q 2 Combining the corresponding q 0 q 1 q 2 The right most significant decimal mapping, namely:
Figure BDA0003549983160000048
each sample point of the symbol/is expressed as:
Figure BDA0003549983160000049
Where n=0, 1..n-1, phi (N; BT; q) 0 q 1 q 2 ) For the phase change of the current symbol, the current symbol is subjected to front and back bits q 0 and q2 And the effect of GFSK gaussian shaping filtering 3dB attenuation bandwidth parameter BT;
the phase correction factor generated and stored is expressed as:
Figure BDA00035499831600000410
a relative additional phase is introduced for GFSK symbol i e {0,1,..7 }.
Further, in the step S2, the processing procedure for the non-spread CPFSK/GFSK signal includes:
reverse order arrangement: the received samples r are arranged in reverse sampling order to obtain reverse-order samples
Figure BDA0003549983160000051
wherein />
Figure BDA0003549983160000052
Complex baseband signal sample points arranged in reverse order for receiving the K-k+1 th symbol of the current packet;
single symbol matching: matching the first symbol sample (namely the original Kth sample) after the reverse sequence arrangement, wherein the matching result is as follows:
Figure BDA0003549983160000053
in the above formula, M refers to a modulation scheme: m= 'c' is CPFSK modulation, where the symbol shaping filter length L M =1, the matching result is complex matching value of the symbol "0"/"1"; m= 'g' is GPFSK modulation, at this time, the symbol shaping filter length L M =3, the matching result is a matching value of binary symbols representing "000" to "111", that is, 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 matching the 2 nd symbol after reverse sequence, namely the K-1 st symbol in sequence, according to the method, and obtaining CPFSK symbol
Figure BDA0003549983160000054
Is to obtain +.for the GFSK symbol>
Figure BDA0003549983160000055
Matching results of (2);
combining: for CPFSK symbols, two single-symbol matching results are required to be transferred into the results of matching the baseband reference waveforms of '00', '10', '01', '11' combined by two sections of received symbols and four symbols, and for GFSK signals, the influence of two symbols before and after the matching symbols is required to be additionally considered, namely, the matching results of the two single symbols are required to be expanded to the combination of the two received symbols and the 16 symbols of '0000', '1000', '…', '1111', wherein the blackbody is an intersymbol crosstalk symbol at two ends of a matching observation part;
thus, first of all, the matching result needs to be matched
Figure BDA0003549983160000056
Replication is performed, and the matrix for replication is:
Figure BDA0003549983160000057
wherein
Figure BDA0003549983160000058
Is->
Figure BDA0003549983160000059
Then consider the phase continuity of the CPFSK/GFSK signal except for the need for +.>
Figure BDA00035499831600000510
Copying, phase rotation is also needed to adapt the phase introduced by the previous matched symbol, for +.>
Figure BDA00035499831600000511
The replication matrix is written as:
Figure BDA00035499831600000512
where blockdiag {.cndot } is a block diagonalization operation and the phase rotation matrix is written as:
Figure BDA0003549983160000061
wherein
Figure BDA0003549983160000062
Is the main diagonal element +>
Figure BDA0003549983160000063
Square matrix of->
Figure BDA0003549983160000064
Representing the additional phase introduced by the second matched symbol after the reverse order, whereby the combined result is expressed as:
Figure BDA0003549983160000065
wherein
Figure BDA0003549983160000066
Because of->
Figure BDA0003549983160000067
Is the first matching result;
the complex multiplication number is determined by the single symbol matching of each symbol and the additional phase correction during symbol combination
Figure BDA0003549983160000068
Reduced to->
Figure BDA0003549983160000069
Iteration: iterating the steps, and matching and combining the k-th symbol after the reverse sequence arrangement:
Figure BDA00035499831600000610
wherein ,
Figure BDA00035499831600000611
for the result of the single-symbol matching of the kth symbol after the reverse order, < >>
Figure BDA00035499831600000612
Is the result of matching and combining the first k-1 symbols after the reverse sequence, and:
Figure BDA00035499831600000613
Figure BDA00035499831600000614
Figure BDA00035499831600000615
taking a mould: finally, K symbol matching and combining results are obtained, and CPFSK is
Figure BDA00035499831600000616
Obtaining by modulo calculation
Figure BDA00035499831600000617
For GFSK, is +.>
Figure BDA00035499831600000618
Modulo obtaining +.>
Figure BDA00035499831600000619
Further, in the step S2, the processing procedure for the spread CPFSK/GFSK signal includes:
reverse order: the received samples r are subjected to reverse order sorting to obtain reverse order
Figure BDA00035499831600000620
wherein />
Figure BDA00035499831600000621
To receive the L-th of the current packet s -complex baseband signal sample points of inverted sequence of k+1 chip symbols;
single symbol matching: taking into account the spreading sequence D s Known at the receiving end, and thus only need to be specific to L s The received complex baseband samples of chip length consider two possible codeword combinations, namely a spreading sequence mapped by bit "1" and a spreading sequence mapped by bit "0", and thus forIn CPFSK signals, consider the following set of spreading mapping matrices:
Figure BDA0003549983160000071
wherein ,
Figure BDA0003549983160000072
is the i bit spreading code +.>
Figure BDA0003549983160000073
If->
Figure BDA0003549983160000074
I.e. the i-th bit spreading code of the mapping is the same as the original bit, a mapping matrix for selecting a matched filter bank and a phase correction factor
Figure BDA0003549983160000075
Otherwise, the mapped i-th bit spreading code is opposite to the original bit, then +.>
Figure BDA0003549983160000076
For GFSK signals, consider the following set of mapping matrices:
Figure BDA0003549983160000077
wherein ,
Figure BDA0003549983160000078
for the mapping matrix of the ith bit of the spreading sequence, the i-1 th spreading bit and the influence of the (i+1) th spreading bit on the symbol need to be considered at the same time; let->
Figure BDA0003549983160000079
For the decimal mapping of the i-1, i, i+1 bits, the subscript of 1 is set as: />
Figure BDA00035499831600000710
Representing the mapping of original information "1" and bit "0" to the ith chip, the remaining subscripts being set to zero; chips outside the currently observed spreading sequence default to 0, i.e. +.>
Figure BDA00035499831600000711
Single symbol matching: matching the 1 st and 2 nd symbol samples after reverse sequence, wherein the matching expression is as follows:
Figure BDA00035499831600000712
where i=1, 2,
Figure BDA00035499831600000713
is based on the matching filter group after the updating of the chip mapping, the matching result +. >
Figure BDA00035499831600000714
Representing the matching result corresponding to the despread bit "0">
Figure BDA00035499831600000715
Representing the matching result corresponding to the non-spread bit 1;
combining: for DSSS-CPFSK symbols, the process of combining two single-symbol matching results is:
Figure BDA00035499831600000716
wherein
Figure BDA00035499831600000717
Figure BDA00035499831600000718
In order to consider the phase continuity of CPFSK/GFSK signals, the phase correction factor after spread spectrum mapping needs to be subjected to phase correctionThen carrying out in-phase superposition;
iteration: iterating the steps, and matching and combining the k-th chip after the reverse sequence:
Figure BDA00035499831600000719
wherein
Figure BDA0003549983160000081
The result of the combination of the front k-1 chips after the reverse sequence;
taking a mould: finally obtain the L with complete single DSSS-FSK signal s The result of the length chip matching combining is, for DSSS-CPFSK
Figure BDA0003549983160000082
Modulo obtaining +.>
Figure BDA0003549983160000083
For DSSS-GFSK, is +.>
Figure BDA0003549983160000084
Obtaining by modulo calculation
Figure BDA0003549983160000085
Further, in the step S3, if a hard demodulation mode is adopted for the CPFSK/GFSK signal without spread spectrum, the subscript with the largest matching modulus is selected first:
Figure BDA0003549983160000086
then, will
Figure BDA0003549983160000087
According to the inverse mapping of the highest bit at the right end back to the binary sequence, for CPFSK, the mapped sequence with the K bit length is the demodulation result, for GFSK, the inverse mapped sequence with the K+2 bit length needs to be discarded before and afterTaking the middle K bits as demodulation results;
If soft demodulation is employed, the soft information of the kth bit among the K observation bits is written as:
Figure BDA0003549983160000088
wherein ,I0 {. The first class of modified Bessel functions of zero order; SNR of h ＝|h|/σ 2 For the signal-to-noise ratio of the receiving end, wherein |h| is a flat attenuation module value, sigma 2 Gaussian noise power for the receiver;
Figure BDA0003549983160000089
and />
Figure BDA00035499831600000810
The index of the matching branch is inversely mapped to a set of 1 and 0 for the kth bit.
Further, in the step S3, for the spread DSSS-CPFSK/DSSS-GFSK signal, if a hard demodulation mode is adopted, the information bits before spreading are decoded as follows:
Figure BDA00035499831600000811
if soft demodulation is employed, the soft information is written as:
Figure BDA00035499831600000812
compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the method is suitable for despreading and demodulating the non-spread CPFSK/GFSK signal and the spread DSSS-CPFSK/DSSS-GFSK signal. 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 high-performance high-complexity multi-symbol detection scheme, the method greatly reduces the computational complexity at the cost of a small part of performance loss. The spread DSSS-CPFSK/DSSS-GFSK signal is subjected to joint demodulation and spread, so that more spread spectrum gain can be obtained 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 and low power consumption for long-distance transmission.
Drawings
FIG. 1 shows a block diagram of one embodiment of the present invention for CPFSK/GFSK signal matching computation;
FIG. 2 shows a block diagram of a calculation for DSSS-CPFSK/DSSS-GFSK signal matching according to another embodiment of the invention;
fig. 3 is a schematic flow chart of CPFSK/GFSK demodulation according to an embodiment of the invention;
FIG. 4 is a graph showing the comparison of CPFSK/GFSK demodulation performance without channel coding under AWGN channel proposed in example 1 of the present invention;
FIG. 5 is a graph showing CPFSK/GFSK demodulation performance versus Viterbi soft decoding (2, 1, 3) convolutional encoding under an AWGN channel as proposed in example 1 of the present invention;
fig. 6 shows a graph of DSSS-CPFSK demodulation performance versus channel coding without using an AWGN channel as proposed in example 2 of the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
for the purpose of better illustrating the embodiments, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the actual product dimensions;
it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 3, a non-coherent demodulation method of CPFSK/GFSK signal includes the following steps:
s1: generating a matched filter bank with 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 the despreading CPFSK/GFSK signal, matching the received sample by K symbols, and modulo the matching result; if the received DSSS-CPFSK/DSSS-GFSK signal is subjected to direct sequence spread spectrum processing, the spread spectrum processed signal is regarded as a whole, the lengths of the spread spectrum codes of the received samples are matched, and the matching result is subjected to modulo value;
s3: demodulating the matching result: if the received CPFSK/GFSK signal is not spread, each group according to the decoding requirement according to soft demodulation or hard demodulation mode to solve K bit information; if a DSSS-CPFSK/DSSS-GFSK signal is received, the corresponding despread raw bits are demodulated.
The CPFSK/GFSK signal has a constant envelope with a complex baseband signal model of:
Figure BDA0003549983160000101
wherein alpha is a bit sequence to be modulated of length L and alpha i E { -1,1} is the ith binary bipolar bit to be modulated; n is a single chip sampling factor, N is a sampling index; h is a m ＝Δ f /B w As modulation factor, delta f Is the frequency difference of two frequency points, B w For chip rate/transmission bandwidth; q (n) is the accumulation of the single symbol phase shaping function h (n).
For a full-response CPFSK signal which is not subjected to phase shaping by a Gaussian filter, a shaping function h of the full-response CPFSK signal c (n) is the response length L c =1, rectangular filter of normalized symbol length, expressed as:
Figure BDA0003549983160000102
the expression for the kth symbol of the CPFSK signal is thus:
Figure BDA0003549983160000103
wherein θk-1 For the accumulated phase of the first k-1 terms, a k N/N is the phase change factor of the kth symbol, which varies linearly with the full response CPFSK signal; whereas for a partially-responsive GFSK signal phase-shaped by a gaussian filter, its shaping function h g (n) is the response length L g Is expressed as:
Figure BDA0003549983160000104
bandwidth factor of gaussian filter in above type
Figure BDA0003549983160000105
BT is a bandwidth-time factor of 3dB attenuation, L g The truncation 3 models inter-symbol interference of the GFSK signal, that is, a single GFSK symbol mainly generates inter-symbol interference with two front and rear symbols, so that the expression of the kth symbol of the GFSK signal is as follows:
Figure BDA0003549983160000106
in the formula θk-1 Is the accumulated phase of the first k-1 term, phi (n; BT; alpha) k-1 α k α k+1 ) The phase change factor of the kth symbol at the current time-bandwidth factor is affected by ISI of the preceding and following symbols, which is non-linearly changing in the partial response GFSK signal model.
In step S1, the generation of the matched filter bank with single symbol length according to the transmitted CPFSK/GFSK signal parameters is:
Figure BDA0003549983160000111
wherein ,
Figure BDA0003549983160000112
the result of the reverse sampling sequence arrangement of the reference complex baseband samples corresponding to CPFSK symbol q epsilon {0,1}, { · } H Represents Hermitian transpose, {. Cndot. } T Representing a matrix transpose;
CPFSK symbol q is expressed as:
Figure BDA0003549983160000113
where n=0, 1..n-1, N is the upsampling factor, h m Is the modulation factor of CPFSK signal at the transmitting end.
Further, in the step S1, the generation of the phase correction factor of the single symbol length according to the transmitted CPFSK/GFSK signal parameter is expressed as:
Figure BDA0003549983160000114
Figure BDA0003549983160000115
representing the relative additional phase that the current symbol q e {0,1} introduces for subsequent symbols.
Since the current symbol is affected by the crosstalk between the symbols of the preceding and following symbols, the generated and stored matched filter bank needs to consider the influence caused by the preceding and following symbols, namely:
Figure BDA0003549983160000116
wherein
Figure BDA0003549983160000117
For the reverse order of the reference complex baseband samples corresponding to the symbol l e {0,1,., 7} and l is the current bit q 1 And two bits q 0 q 2 Combining the corresponding q 0 q 1 q 2 The right most significant decimal mapping, namely:
Figure BDA0003549983160000118
each sample point of the symbol/is expressed as:
Figure BDA0003549983160000119
where n=0, 1..n-1, phi (N; BT; q) 0 q 1 q 2 ) For the phase change of the current symbol, the current symbol is subjected to front and back bits q 0 and q2 And the effect of GFSK gaussian shaping filtering 3dB attenuation bandwidth parameter BT;
The phase correction factor generated and stored is expressed as:
Figure BDA0003549983160000121
a relative additional phase is introduced for GFSK symbol i e {0,1,..7 }.
In step S2, the processing procedure for the non-spread CPFSK/GFSK signal includes:
reverse order arrangement: the received samples r are arranged in reverse sampling order to obtain reverse-order samples
Figure BDA0003549983160000122
wherein />
Figure BDA0003549983160000123
Complex baseband signal sample points arranged in reverse order for receiving the K-k+1 th symbol of the current packet;
single symbol matching: matching the first symbol sample (namely the original Kth sample) after the reverse sequence arrangement, wherein the matching result is as follows:
Figure BDA0003549983160000124
in the above formula, M refers to a modulation scheme: m= 'c' is CPFSK modulation, where the symbol shaping filter lengthL M =1, the matching result is complex matching value of the symbol "0"/"1"; m= 'g' is GPFSK modulation, at this time, the symbol shaping filter length L M =3, the matching result is a matching value of binary symbols representing "000" to "111", that is, 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 matching the 2 nd symbol after reverse sequence, namely the K-1 st symbol in sequence, according to the method, and obtaining CPFSK symbol
Figure BDA0003549983160000125
Is to obtain +.for the GFSK symbol>
Figure BDA0003549983160000126
Matching results of (2);
combining: for CPFSK symbols, two single-symbol matching results are required to be transferred into the results of matching the baseband reference waveforms of '00', '10', '01', '11' combined by two sections of received symbols and four symbols, and for GFSK signals, the influence of two symbols before and after the matching symbols is required to be additionally considered, namely, the matching results of the two single symbols are required to be expanded to the combination of the two received symbols and the 16 symbols of '0000', '1000', '…', '1111', wherein the blackbody is an intersymbol crosstalk symbol at two ends of a matching observation part;
thus, first of all, the matching result needs to be matched
Figure BDA0003549983160000127
Replication is performed, and the matrix for replication is:
Figure BDA0003549983160000128
wherein
Figure BDA0003549983160000129
Is->
Figure BDA00035499831600001210
Then consider the phase continuity of the CPFSK/GFSK signal except for the need for +.>
Figure BDA00035499831600001211
Copying, phase rotation is also needed to adapt the phase introduced by the previous matched symbol, for +.>
Figure BDA0003549983160000131
The replication matrix is written as:
Figure BDA0003549983160000132
where blockdiag {.cndot } is a block diagonalization operation and the phase rotation matrix is written as:
Figure BDA0003549983160000133
wherein
Figure BDA0003549983160000134
Is the main diagonal element +>
Figure BDA0003549983160000135
Square matrix of->
Figure BDA0003549983160000136
Representing the additional phase introduced by the second matched symbol after the reverse order, whereby the combined result is expressed as:
Figure BDA0003549983160000137
wherein
Figure BDA0003549983160000138
Because of->
Figure BDA0003549983160000139
Is the first matching result;
the complex multiplication number is determined by the single symbol matching of each symbol and the additional phase correction during symbol combination
Figure BDA00035499831600001310
Reduced to->
Figure BDA00035499831600001311
Iteration: iterating the steps, and matching and combining the k-th symbol after the reverse sequence arrangement:
Figure BDA00035499831600001312
wherein ,
Figure BDA00035499831600001313
for the result of the single-symbol matching of the kth symbol after the reverse order, < >>
Figure BDA00035499831600001314
Is the result of matching and combining the first k-1 symbols after the reverse sequence, and:
Figure BDA00035499831600001315
Figure BDA00035499831600001316
Figure BDA00035499831600001317
/>
taking a mould: finally, K symbol matching and combining results are obtained, and CPFSK is
Figure BDA00035499831600001318
Obtaining by modulo calculation
Figure BDA00035499831600001319
For GFSK, is +.>
Figure BDA00035499831600001320
Modulo obtaining +.>
Figure BDA00035499831600001321
In step S2, the process of processing the spread CPFSK/GFSK signal includes:
reverse order: the received samples r are subjected to reverse order sorting to obtain reverse order
Figure BDA00035499831600001322
wherein />
Figure BDA00035499831600001323
To receive the L-th of the current packet s -complex baseband signal sample points of inverted sequence of k+1 chip symbols;
single symbol matching: taking into account the spreading sequence D s Known at the receiving end, and thus only need to be specific to L s The received complex baseband samples of chip length consider two possible codeword combinations, namely a spreading sequence mapped by bit "1" and a spreading sequence mapped by bit "0", and thus consider the following set of spreading mapping matrices for the CPFSK signal:
Figure BDA0003549983160000141
wherein ,
Figure BDA0003549983160000142
is the i bit spreading code +.>
Figure BDA0003549983160000143
If->
Figure BDA0003549983160000144
I.e. the i-th bit spreading code of the mapping is the same as the original bit, a mapping matrix for selecting a matched filter bank and a phase correction factor
Figure BDA0003549983160000145
Otherwise, the mapped i-th bit spreading code is opposite to the original bit, then +.>
Figure BDA0003549983160000146
For GFSK signals, consider the following set of mapping matrices:
Figure BDA0003549983160000147
wherein ,
Figure BDA0003549983160000148
for the mapping matrix of the ith bit of the spreading sequence, the i-1 th spreading bit and the influence of the (i+1) th spreading bit on the symbol need to be considered at the same time; let->
Figure BDA0003549983160000149
For the decimal mapping of the i-1, i, i+1 bits, the subscript of 1 is set as: />
Figure BDA00035499831600001410
Representing the mapping of original information "1" and bit "0" to the ith chip, the remaining subscripts being set to zero; chips outside the currently observed spreading sequence default to 0, i.e. +.>
Figure BDA00035499831600001411
Single symbol matching: matching the 1 st and 2 nd symbol samples after reverse sequence, wherein the matching expression is as follows:
Figure BDA00035499831600001412
where i=1, 2,
Figure BDA00035499831600001413
is based on the updated matched filter group of the chip mapping, and the matching result
Figure BDA00035499831600001414
Representing the matching result corresponding to the despread bit "0">
Figure BDA00035499831600001415
Representing the matching result corresponding to the non-spread bit 1;
combining: for DSSS-CPFSK symbols, the process of combining two single-symbol matching results is:
Figure BDA00035499831600001416
wherein
Figure BDA00035499831600001417
Figure BDA00035499831600001418
Taking the phase continuity of CPFSK/GFSK signals into consideration for the phase correction factors after spread spectrum mapping, carrying out in-phase superposition after phase correction;
iteration: iterating the steps, and matching and combining the k-th chip after the reverse sequence:
Figure BDA0003549983160000151
wherein
Figure BDA0003549983160000152
The result of the combination of the front k-1 chips after the reverse sequence; />
Taking a mould: finally, a single DSS is obtainedL with complete S-FSK signal s The result of the length chip matching combining is, for DSSS-CPFSK
Figure BDA0003549983160000153
Modulo obtaining +.>
Figure BDA0003549983160000154
For DSSS-GFSK, is +.>
Figure BDA0003549983160000155
Obtaining by modulo calculation
Figure BDA0003549983160000156
In step S3, for the CPFSK/GFSK signal without spread spectrum, if a hard demodulation mode is adopted, firstly, selecting the subscript with the largest matching modulus value:
Figure BDA0003549983160000157
then, will
Figure BDA0003549983160000158
Inversely mapping the highest bit at 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 sequence with the length of K+2 bits inversely mapped back needs to discard the ISI bits before and after, and the middle K bits are taken as the demodulation result;
if soft demodulation is employed, the soft information of the kth bit among the K observation bits is written as:
Figure BDA0003549983160000159
wherein ,I0 {. The first class of modified Bessel functions of zero order; SNR of h ＝|h|/σ 2 For the signal-to-noise ratio of the receiving end, wherein |h| is a flat attenuation module value, sigma 2 Gaussian noise power for the receiver;
Figure BDA00035499831600001510
and />
Figure BDA00035499831600001511
The index of the matching branch is inversely mapped to a set of 1 and 0 for the kth bit.
In step S3, for the spread DSSS-CPFSK/DSSS-GFSK signal, if a hard demodulation mode is adopted, the information bits before spreading that are demodulated are written as follows:
Figure BDA00035499831600001512
if soft demodulation is employed, the soft information is written as:
Figure BDA00035499831600001513
example 2
As shown in fig. 3, a method for incoherent demodulation of a CPFSK/GFSK signal, the method comprising:
s1: generating a matched filter bank with single symbol length and a phase correction factor according to the transmitted CPFSK/GFSK signal parameters;
s2: matching the received samples: this step replaces redundant symbol matching calculations by using the matching result transfer to lower complexity received samples
Figure BDA0003549983160000161
And the sequence "00 … 0" to "11 … 1" 2 K Matching the baseband waveform combination of the continuous phases;
s3: demodulating the matching result: and solving the K bits of information according to the decoding requirement and the soft demodulation or hard demodulation mode.
In this embodiment, the CPFSK/GFSK signal has a constant envelope, and excellent phase continuity, and the complex baseband signal model is:
Figure BDA0003549983160000162
wherein alpha is a bit sequence to be modulated of length L and alpha i E { -1,1} is the ith binary bipolar bit to be modulated; n is a single chip sampling factor, N is a sampling index; h is a n ＝Δ f /B w As modulation factor, delta f Is the frequency difference of two frequency points, B w For chip rate/transmission bandwidth; q (n) is the accumulation of the single symbol phase shaping function h (n). For a full-response CPFSK signal which is not subjected to phase shaping by a Gaussian filter, a shaping function h of the full-response CPFSK signal c (n) is the response length L c =1 (normalized symbol length) rectangular filter, whose expression is:
Figure BDA0003549983160000163
the expression for the kth symbol of the CPFSK signal is thus:
Figure BDA0003549983160000164
wherein θk-1 For the accumulated phase of the first k-1 terms, a k N/N is the phase change factor of the kth symbol, which varies linearly with the full response CPFSK signal. Whereas for a partially-responsive GFSK signal phase-shaped by a gaussian filter, its shaping function h g (n) is the response length L g Is expressed as:
Figure BDA0003549983160000165
bandwidth factor of gaussian filter in above type
Figure BDA0003549983160000166
BT is the bandwidth-time factor of 3dB attenuation. L (L) g The inter-code crosstalk of the GFSK signal can be modeled by cutting off 3(inter-symbol-interference, ISI), i.e., a single GFSK symbol primarily creates inter-symbol interference with two symbols before and after, so the expression for the kth symbol of the GFSK signal is:
Figure BDA0003549983160000171
in the formula θk-1 Is the accumulated phase of the first k-1 term, phi (n; BT; alpha) k-1 α k α k+1 ) The phase change factor of the kth symbol at the current time-bandwidth factor is affected by ISI of the preceding and following symbols, which is non-linearly changing in the partial response GFSK signal model.
Specifically, in step S1, for the full response CPFSK signal, the pre-generated and stored matched filter bank is:
Figure BDA0003549983160000172
wherein ,{·}H Represents Hermitian transpose, {. Cndot. } T The transpose of the matrix is represented,
Figure BDA0003549983160000173
the reverse ordered sequence of reference complex baseband samples corresponding to CPFSK symbol q ε {0,1 }. Specifically, according to the signal model of CPFSK, symbol q can be expressed as:
Figure BDA0003549983160000174
wherein ,hm Is the modulation factor of CPFSK signal at the transmitting end. And the additional phase correction factors pre-generated and stored can be expressed as:
Figure BDA0003549983160000175
representing the relative additional phase that the current matching symbol q e {0,1} introduces to the subsequent matching symbols.
For partial response GFSK signals, based on the signal model of GFSK signals, the current symbol is affected by the ISI of the preceding and following symbols, so the pre-generated and stored matched filter bank needs to additionally consider the effects of the preceding and following symbols, namely:
Figure BDA0003549983160000176
where the reverse order of the reference complex baseband samples corresponding to the symbol l e {0,1,., 7} is the current bit q 1 And two bits q 0 q 2 Combining the corresponding q 0 q 1 q 2 The right most significant decimal mapping, namely:
Figure BDA0003549983160000177
each sample point of the symbol/can be expressed as:
Figure BDA0003549983160000181
wherein phi (n; BT; q) 0 q 1 q 2 ) For the phase change of the current symbol, the current symbol is subjected to front and back bits q 0 and q2 And the effect of GFSK gaussian shaping filtering 3dB attenuation bandwidth parameter BT. The additional phase correction factors pre-generated and stored may be expressed as:
Figure BDA0003549983160000182
a relative additional phase is introduced for GFSK symbol i e {0,1,..7 }. The matching waveform can multiplex waveforms 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 despread CPFSK/GFSK signal, the received signal is divided into a group of K symbols for demodulation. This step is carried out by using the matching resultMatching computation to replace redundant symbols to lower complexity received samples
Figure BDA0003549983160000183
And the sequence "00 … 0" to "11 … 1" 2 K The baseband waveform combinations of successive phases are matched. The specific flow chart is shown in fig. 1, and the steps can be divided into reverse order, single symbol matching, merging, iteration and modulo;
reverse order: the received samples r are subjected to reverse order sorting to obtain reverse order
Figure BDA0003549983160000184
wherein />
Figure BDA0003549983160000185
Complex baseband signal sample points arranged in reverse order for receiving the K-th symbol of the current packet;
single symbol matching: matching the first symbol sample (namely the original Kth sample) after the reverse sequence, wherein the matching result is as follows:
Figure BDA0003549983160000186
in the above formula, M refers to a modulation scheme: m= 'c' is CPFSK modulation, where the symbol shaping filter length L M =1, the matching result is complex matching value of the symbol "0"/"1"; m= 'g' is GPFSK modulation, at this time, the symbol shaping filter length L M =3, the matching result is the matching value of the symbols "000" to "111" (binary representation), i.e. taking into account the influence of the preceding and following symbols on the phase change of the intermediate symbol. The current operation result needs to be stored for subsequent iteration and combination.
Then the samples of the 2 nd symbol (namely the original K-1 st sample) after the reverse sequence are matched according to the method, and CPFSK symbols are obtained
Figure BDA0003549983160000187
For GFSK symbols, getTo->
Figure BDA0003549983160000188
Is a result of the matching of (a).
Combining-for CPFSK symbols, two single-symbol matching results need to be extended to the result of matching two received symbols with four double-symbol combinations "00", "10", "01", "11". For GFSK signals, however, the influence of two symbols before and after needs to be considered additionally, that is, the matching result of two single symbols needs to be extended to the combination of two received symbols and 16 symbols, "0000", "1000", …, "1111" (bold is inter-symbol interference term).
Thus, first of all, the matching result needs to be matched
Figure BDA0003549983160000191
Copying, wherein the copy matrix is as follows:
Figure BDA0003549983160000192
wherein
Figure BDA0003549983160000193
Is->
Figure BDA0003549983160000194
Is a unit array of (a) units. Then taking into account the phase continuity of the CPFSK/GFSK signal except for the need for +.>
Figure BDA0003549983160000195
Copying, phase rotation is also needed to adapt the phase introduced by the previous symbol, for +.>
Figure BDA0003549983160000196
The replication matrix can be written as:
Figure BDA0003549983160000197
where blockdiag {.cndot } is the block diagonalization operation. And the phase rotation matrix can be written as:
Figure BDA0003549983160000198
wherein
Figure BDA0003549983160000199
Is the main diagonal element +>
Figure BDA00035499831600001910
Is a square matrix of (c). />
Figure BDA00035499831600001911
Representing the additional phase introduced by the second matched symbol after the reverse order, whereby the combined result can be expressed as:
Figure BDA00035499831600001912
wherein
Figure BDA00035499831600001913
The above process is truly used for single-symbol matching of each symbol and additional phase correction during symbol combination, so compared with the traditional matching mode, the required complex multiplication times are calculated by
Figure BDA00035499831600001914
Is reduced to
Figure BDA00035499831600001915
Iteration: iterating the steps, and matching and combining the k-th symbol after the reverse sequence:
Figure BDA00035499831600001916
wherein ,
Figure BDA00035499831600001917
For the k-th symbol single symbol matching result after the reverse order,/>
Figure BDA00035499831600001918
Is the result of matching and combining the first k-1 symbols after the reverse sequence, and:
Figure BDA00035499831600001919
Figure BDA00035499831600001920
Figure BDA00035499831600001921
in summary, the number of complex multiplications (complex multiplication, CM) and Complex Additions (CA) required for K symbol matches are
Figure BDA00035499831600001922
The CM times and CA times needed for matching directly with K possible symbol combinations are +.>
Figure BDA0003549983160000201
The complexity of the scheme can be greatly reduced compared with that of the scheme.
Taking a mould: the result of matching and combining K symbols can be finally obtained, and for CPFSK, the result is that
Figure BDA0003549983160000202
Obtaining by modulo calculation
Figure BDA0003549983160000203
For GFSK, is +.>
Figure BDA0003549983160000204
Modulo obtaining +.>
Figure BDA0003549983160000205
The number of real multiplications (real multiplication, RM) required for modulo is +.>
Figure BDA0003549983160000206
The number of Real Additions (RA) is
Figure BDA0003549983160000207
Specifically, in step S3, the final incoherent matching and combining result needs to demodulate the corresponding K-bit information. If a hard demodulation mode is adopted, firstly selecting the subscript with the largest matching modulus value:
Figure BDA0003549983160000208
where i represents the matched modulus index. Then, will
Figure BDA0003549983160000209
The binary sequence is mapped back according to the inverse of the top most bits on the right. For CPFSK, the mapped sequence with K bit length is the demodulation result. For GFSK, the mapped k+2-bit length sequence needs to discard the ISI bits before and after, taking the middle K bits as the demodulation result.
If soft demodulation is employed, the soft information of the kth bit of the K observation bits can be written as
Figure BDA00035499831600002010
wherein ,I0 {. The first class of modified Bessel functions of zero order; SNR of h ＝|h|/σ 2 For the signal-to-noise ratio of the receiving end, wherein |h| is a flat attenuation module value, sigma 2 Is Gaussian noise power;
Figure BDA00035499831600002011
and />
Figure BDA00035499831600002012
The k-th bit matching branch after the highest inverse mapping at the right end is marked with a set of '1' and '0'.
In order to verify the effectiveness of the incoherent demodulation method of the design provided by the embodiment of the invention, a simulation experiment is further carried out, and the simulation experiment is specifically as follows:
BER performance versus SNR for different demodulation schemes is plotted for the common CPFSK signal demodulation of h=0.5 and GFSK signal demodulation of h=0.5, bt=0.5 under AWGN channel. Fig. 4 is a performance curve in an uncoded condition, and fig. 5 is a performance curve in (2, 1, 3) convolutional code coding and soft viterbi decoding. Wherein the solid line represents GFSK demodulation performance and the dash-dot line represents CPFSK demodulation performance, the corresponding scheme in this 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 uncoded conditions is plotted with a dashed 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 performances under the uncoded condition are both worse than the theoretical boundary of the orthogonal 2-FSK signal incoherent detection scheme, and the theoretical performance boundary of the scheme and the optimal multi-symbol detection scheme are better than the theoretical performance boundary of the orthogonal 2-FSK signal incoherent detection scheme. Compared with the optimal multi-symbol detection scheme under the uncoded condition, the scheme achieves BER=10 required by reliable communication of the Internet of things -4 The performance loss for CPFSK demodulation is close to 2dB, the performance loss for GFSK demodulation is close to 1dB, and the scheme is characterized in that ber=10 under coding conditions -4 The 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=10 in uncoded condition -4 The 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 the different demodulation schemes is next compared, where 1 CM is equivalent to 4 RMs and one CA is equivalent to 2 RA. The scheme totally needs
Figure BDA0003549983160000211
Secondary RM +.>
Figure BDA0003549983160000212
The secondary RA solves K bit information, and the optimal multi-symbol detection needs
Figure BDA0003549983160000213
Secondary RM +.>
Figure BDA0003549983160000214
The information of the intermediate symbols of the K observation symbols can be solved only by RA, and the envelope detection needs +.>
Figure BDA0003549983160000215
Secondary RM +.>
Figure BDA0003549983160000216
The secondary RA solves for the information of the current symbol, and the differential detection requires 4n+2 secondary RMs and 2n+1 secondary RA to solve for the information of the current symbol. In summary, the demodulation complexity statistics for each symbol are averaged as follows:
Figure BDA0003549983160000217
taking the observation length k=5 and the up-sampling factor n=4, for GFSK demodulation, the optimal multi-symbol detection needs 10496 times of RM and 5248 times of RA to solve the information of one symbol, the scheme of the invention needs 382.4 times of RM and 191.2 times of RA to solve the information of one symbol, the envelope detection needs 144 times of RM and 72 times of RA to solve the information of one symbol, and the differential detection needs 18 times of RM and 9 times of RA to solve the information of one symbol. For CPFSK demodulation, the optimal multi-symbol detection needs 2624 times of RM and 1312 times of RA to solve the information of one symbol, the scheme of the invention needs 95.6 times of RM and 47.8 times of RA to solve the information of one symbol, the envelope detection needs 36 times of RM and 18 times of RA to solve the information of one symbol, and the differential detection needs 18 times of RM and 9 times of RA to solve the information of one symbol. In contrast, the inventive scheme is far less complex than the optimal multi-symbol detection scheme, higher 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 reference waveforms with single symbol length stored by a base band modulation part table look-up method, and further reduces the space complexity of implementation.
Example 3
As shown in fig. 3, a method for incoherent demodulation of a CPFSK/GFSK signal, the method comprising:
s1: generating a matched filter bank with single symbol length and a phase correction factor according to the transmitted CPFSK/GFSK signal parameters;
s2: matching the received samples: the step regards spread DSSS-FSK as a complete symbol, wherein each receiving chip is matched with a matched filter group in a single chip mode, then the matched result after phase correction is overlapped, and the final result is subjected to modular value;
s3: demodulating the matching result: and solving the K bits of information according to the decoding requirement and the soft demodulation or hard demodulation mode.
In this embodiment, the DSSS-CPFSK/DSSS-GFSK signal has a constant envelope and a continuous phase, and has the same complex baseband signal model as in embodiment 1, but the bits to be modulated are first subjected to direct sequence spread spectrum processing and to spread spectrum sequence D s The expression after the direct expansion process is:
b[kL s +i]＝a[k]·D s [i],0≤i<L s
where b [ i ] e { -1,1} is the i-th binary bipolar bit and a [ i ] e { -1,1} is the i-th original information bit.
The processing flow of step S1 in this embodiment is exactly the same as step S1 of embodiment 1. In step S2, for a length L S Is a spread sequence D of (2) s The spread DSSS-CPFSK/DSSS-GFSK signal is regarded as a complete symbol, wherein each receiving chip is matched with a matched filter group in a single chip manner, then the matched results after phase correction are overlapped, and the final result is moduloValues. The above procedure is equivalent to a single DSSS-CPFSK/DSSS-GFSK symbol to be received
Figure BDA0003549983160000221
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 modulo;
reverse order: the received samples r are subjected to reverse order sorting to obtain reverse order
Figure BDA0003549983160000222
wherein />
Figure BDA0003549983160000223
To receive the L-th of the current packet s -k+1 complex baseband signal sample points arranged in reverse order of symbols.
Single symbol matching: taking into account the spreading sequence D s Is known, therefore only to L s The received complex baseband samples of chip length consider two possible codeword combinations, namely a spreading sequence mapped by bit "1" and a spreading sequence mapped by bit "0". Thus for CPFSK signals, consider the following set of spreading mapping matrices:
Figure BDA0003549983160000231
wherein ,
Figure BDA0003549983160000232
is the i bit spreading code +.>
Figure BDA0003549983160000233
If S (i) =1, i.e. the mapped i-th spreading code is identical to the original bit, then the mapping matrix for selecting the matched filter bank and the phase correction factor
Figure BDA0003549983160000234
Otherwise, mappedThe i-th bit spreading code is opposite to the original bit, then +.>
Figure BDA0003549983160000235
For GFSK signals, consider the following set of mapping matrices:
Figure BDA0003549983160000236
wherein ,
Figure BDA0003549983160000237
for the mapping matrix of the i-th bit spreading code, the i-1 th spreading bit and the i+1 th spreading bit influence on the symbol need to be considered at the same time. Let->
Figure BDA0003549983160000238
For the decimal mapping of the i-1, i, i+1 bits, the subscript of 1 is set as: />
Figure BDA0003549983160000239
Representing the mapping of the original information "1" and bit "0" to the ith chip.
Single symbol matching: matching the 1 st and 2 nd symbol samples after reverse sequence, wherein the matching expression is as follows:
Figure BDA00035499831600002310
wherein
Figure BDA00035499831600002311
Is based on the matching filter group after the updating of the chip mapping, the matching result +.>
Figure BDA00035499831600002312
Representing the matching result corresponding to the despread bit "0">
Figure BDA00035499831600002313
Representing the matching result corresponding to the despread bit "1".
Combining: for DSSS-CPFSK symbols, the process of combining two single-symbol matching results is:
Figure BDA00035499831600002314
wherein
Figure BDA00035499831600002315
Figure BDA00035499831600002316
In order to consider the phase continuity of CPFSK/GFSK signals, the phase correction factors after the spread spectrum mapping are subjected to phase correction and then in-phase superposition is required.
Iteration: iterating the steps, and matching and combining the kth chip after the reverse sequence:
Figure BDA0003549983160000241
wherein
Figure BDA0003549983160000242
Is the result of the first k-1 chip combinations after the reverse order.
Taking a mould: the complete L of the single DSSS-FSK signal can be finally obtained s The result of the length chip matching combining is, for DSSS-CPFSK
Figure BDA0003549983160000243
Modulo obtaining +.>
Figure BDA0003549983160000244
For DSSS-GFSK, is +.>
Figure BDA0003549983160000245
Modulo obtaining +.>
Figure BDA0003549983160000246
Specifically, in step S3, for the spread DSSS-CPFSK/DSSS-GFSK signal, if a hard demodulation manner is adopted, the information bits before spreading that are decoded may be written as:
Figure BDA0003549983160000247
if soft demodulation is employed, the soft information may be written as:
Figure BDA0003549983160000248
in order to verify the effectiveness of the designed incoherent despreading demodulation method in the embodiment of the invention, a simulation experiment is further carried out, and the method is specifically as follows:
under AWGN channel, for the common DSSS-CPFSK signal demodulation spreading with h=0.5, different demodulation despreading schemes draw curves of BER performance with SNR under uncoded condition, as shown in fig. 4, where this embodiment is marked with "+" and the combination of differential demodulation and soft decoding is marked with "h", and different spreading code lengths L are distinguished by different lines s The performance curve at = {4,8,16,32}, the abscissa indicates SNR, and the ordinate indicates BER. As can be seen from the figure, the present embodiment is shown at ber=10 -4 The spread spectrum gain of about 3dB can be obtained, and the traditional scheme for separating despreading and demodulation can only reach 1; spread spectrum gain of 2 dB. When the length of the spreading code is 4, the scheme has a performance gain of 3dB compared with the comparison scheme, and when the length of the spreading code is 32, the scheme has a performance gain of 6dB compared with the comparison scheme. And considering that the spreading code at the transmitting and receiving end is known, the demodulation complexity of the scheme is similar to the envelope detection except for the additional phase correction step. The single-symbol matched filter bank used in the scheme can multiplex the baseband waveforms stored by the baseband modulation part 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 of the scheme can be arbitrarily configured without receiving end repetitionAnd matching reference waveforms corresponding to the spread spectrum sequences are newly generated, so that the flexibility is further improved.
The same or similar reference numerals correspond to the same or similar components;
the positional relationship depicted in the drawings is for illustrative purposes only and is not to be construed as limiting the present patent;
it is to be understood that the above examples of the present invention are provided by way of illustration only and not by way of limitation of the embodiments of the present invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.

Claims (10)

1. The incoherent demodulation method for the CPFSK/GFSK signal is characterized by comprising the following steps of:
s1: generating a matched filter bank with 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 the despreading CPFSK/GFSK signal, matching the received sample by K symbols, and modulo the matching result; if the received DSSS-CPFSK/DSSS-GFSK signal is subjected to direct sequence spread spectrum processing, the spread spectrum processed signal is regarded as a whole, the lengths of the spread spectrum codes of the received samples are matched, and the matching result is subjected to modulo value;
s3: demodulating the matching result: if the received CPFSK/GFSK signal is not spread, each group according to the decoding requirement according to soft demodulation or hard demodulation mode to solve K bit information; if a DSSS-CPFSK/DSSS-GFSK signal is received, the corresponding despread raw bits are demodulated.
2. The method for incoherent demodulation of CPFSK/GFSK signal according to claim 1, wherein the CPFSK/GFSK signal has a constant envelope with complex baseband signal model:
Figure FDA0003549983150000011
wherein alpha is a bit sequence to be modulated of length L and alpha i E { -1,1} is the ith binary bipolar bit to be modulated; n is a single chip sampling factor, N is a sampling index; h is a m ＝Δ f /B w As modulation factor, delta f Is the frequency difference of two frequency points, B w For chip rate/transmission bandwidth; q (n) is the accumulation of the single symbol phase shaping function h (n).
3. The method for incoherent demodulation of CPFSK/GFSK signals according to claim 2, wherein the shaping function h is a full-response CPFSK signal that has not been phase-shaped by a gaussian filter c (n) is the response length L c =1, rectangular filter of normalized symbol length, expressed as:
Figure FDA0003549983150000012
the expression for the kth symbol of the CPFSK signal is thus:
Figure FDA0003549983150000013
wherein θk-1 For the accumulated phase of the first k-1 terms, a k N/N is the phase change factor of the kth symbol, which varies linearly with the full response CPFSK signal; whereas for a partially-responsive GFSK signal phase-shaped by a gaussian filter, its shaping function h g (n) is the response length L g Is expressed as:
Figure FDA0003549983150000021
bandwidth factor of gaussian filter in above type
Figure FDA0003549983150000022
BT is a bandwidth-time factor of 3dB attenuation, L g The truncation 3 models inter-symbol interference of the GFSK signal, that is, a single GFSK symbol mainly generates inter-symbol interference with two front and rear symbols, so that the expression of the kth symbol of the GFSK signal is as follows:
Figure FDA0003549983150000023
in the formula θk-1 Is the accumulated phase of the first k-1 term, phi (n; BT; alpha) k-1 α k α k+1 ) The phase change factor of the kth symbol at the current time-bandwidth factor is affected by ISI of the preceding and following symbols, which is non-linearly changing in the partial response GFSK signal model.
4. The method of incoherent demodulation of CPFSK/GFSK signal according to claim 3, wherein in step S1, the generation of the matched filter bank of single symbol length according to the transmitted CPFSK/GFSK signal parameters is:
Figure FDA0003549983150000024
wherein ,
Figure FDA0003549983150000025
the result of the reverse sampling sequence arrangement of the reference complex baseband samples corresponding to CPFSK symbol q epsilon {0,1}, { · } H Represents Hermitian transpose, {. Cndot. } T Representing a matrix transpose;
CPFSK symbol q is expressed as:
Figure FDA0003549983150000026
where n=0, 1..n-1, N is the upsampling factor, h m Is the modulation factor of CPFSK signal at the transmitting end.
5. The method for incoherent demodulation of CPFSK/GFSK signal according to claim 4, wherein in step S1, the generation of the phase correction factor of single symbol length from the transmitted CPFSK/GFSK signal parameters is expressed as:
Figure FDA0003549983150000027
Figure FDA0003549983150000028
representing the relative additional phase that the current symbol q e {0,1} introduces for subsequent symbols.
6. The method for incoherent demodulation of a CPFSK/GFSK signal according to claim 5, wherein,
since the current symbol is affected by the crosstalk between the symbols of the preceding and following symbols, the generated and stored matched filter bank needs to consider the influence caused by the preceding and following symbols, namely:
Figure FDA0003549983150000031
wherein
Figure FDA0003549983150000032
For the reverse order of the reference complex baseband samples corresponding to the symbol l e {0,1,., 7} and l is the current bit q 1 And two bits q 0 q 2 Combining the corresponding q 0 q 1 q 2 The right most significant decimal mapping, namely:
Figure FDA0003549983150000033
each sample point of the symbol/is expressed as:
Figure FDA0003549983150000034
where n=0, 1..n-1, phi (N; BT; q) 0 q 1 q 2 ) For the phase change of the current symbol, the current symbol is subjected to front and back bits q 0 and q2 And the effect of GFSK gaussian shaping filtering 3dB attenuation bandwidth parameter BT;
the phase correction factor generated and stored is expressed as:
Figure FDA0003549983150000035
a relative additional phase is introduced for GFSK symbol i e {0,1,..7 }.
7. The method according to claim 6, wherein in the step S2, the processing of the non-spread CPFSK/GFSK signal comprises:
reverse order arrangement: the received samples r are arranged in reverse sampling order to obtain reverse-order samples
Figure FDA0003549983150000036
wherein />
Figure FDA0003549983150000037
Complex baseband signal sample points arranged in reverse order for receiving the K-k+1 th symbol of the current packet;
single symbol matching: matching the first symbol sample after reverse sequence arrangement, namely the original Kth sample, wherein the matching result is as follows:
Figure FDA0003549983150000038
in the above formula, M refers to a modulation scheme: m= 'c' is CPFSK modulation, where the symbol shaping filter length L M =1, the matching result is complex matching value of the symbol "0"/"1"; m= 'g' is GPFSK modulation, at this time, the symbol shaping filter length L M =3, the matching result is a matching value of binary symbols representing "000" to "111", that is, 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 matching the 2 nd symbol after reverse sequence, namely the K-1 st symbol in sequence, according to the method, and obtaining CPFSK symbol
Figure FDA0003549983150000041
Is to obtain +.for the GFSK symbol>
Figure FDA0003549983150000042
Matching results of (2);
combining: for CPFSK symbols, two single-symbol matching results are required to be transferred into the results of matching the baseband reference waveforms of '00', '10', '01', '11' combined by two sections of received symbols and four symbols, and for GFSK signals, the influence of two symbols before and after the matching symbols is required to be additionally considered, namely, the matching results of the two single symbols are required to be expanded to the combination of the two received symbols and the 16 symbols of '0000', '1000', '…', '1111', wherein the blackbody is an intersymbol crosstalk symbol at two ends of a matching observation part;
thus, first of all, the matching result needs to be matched
Figure FDA0003549983150000043
Replication is performed, and the matrix for replication is:
Figure FDA0003549983150000044
wherein
Figure FDA0003549983150000045
Is->
Figure FDA0003549983150000046
Then consider the phase continuity of the CPFSK/GFSK signal except for the need for +.>
Figure FDA0003549983150000047
Replication, phase rotation is also needed to adapt the phase introduced by the previous matched symbol, pair
Figure FDA0003549983150000048
The replication matrix is written as:
Figure FDA0003549983150000049
where blockdiag {.cndot } is a block diagonalization operation and the phase rotation matrix is written as:
Figure FDA00035499831500000410
wherein
Figure FDA00035499831500000411
Is the main diagonal element +>
Figure FDA00035499831500000412
Square matrix of->
Figure FDA00035499831500000413
Representing the additional phase introduced by the second matched symbol after the reverse order, whereby the combined result is expressed as:
Figure FDA00035499831500000414
wherein
Figure FDA00035499831500000415
Because of->
Figure FDA00035499831500000416
Is the first matching result;
the complex multiplication number is determined by the single symbol matching of each symbol and the additional phase correction during symbol combination
Figure FDA00035499831500000417
Reduced to->
Figure FDA00035499831500000418
Iteration: iterating the steps, and matching and combining the k-th symbol after the reverse sequence arrangement:
Figure FDA00035499831500000419
/>
wherein ,
Figure FDA00035499831500000420
for the result of the single-symbol matching of the kth symbol after the reverse order, < >>
Figure FDA00035499831500000421
Is the result of matching and combining the first k-1 symbols after the reverse sequence, and:
Figure FDA0003549983150000051
Figure FDA0003549983150000052
Figure FDA0003549983150000053
taking a mould: finally, K symbol matching and combining results are obtained, and CPFSK is
Figure FDA0003549983150000054
Obtaining by modulo calculation
Figure FDA0003549983150000055
For GFSK, is +.>
Figure FDA0003549983150000056
And (5) obtaining the model: / >
Figure FDA0003549983150000057
8. The method according to claim 7, wherein the processing of the spread CPFSK/GFSK signal in step S2 comprises:
reverse order: the received samples r are subjected to reverse order sorting to obtain reverse order
Figure FDA0003549983150000058
wherein />
Figure FDA0003549983150000059
To receive the L-th of the current packet s -complex baseband signal sample points of inverted sequence of k+1 chip symbols;
single symbol matching: taking into account the spreading sequence D s Known at the receiving end, and thus only need to be specific to L s The received complex baseband samples of chip length consider two possible codeword combinations, namely the spreading sequence mapped by bit "1" and the bitsThe "0" mapped spreading sequence, therefore for CPFSK signals, consider the following set of spreading mapping matrices:
Figure FDA00035499831500000510
wherein ,
Figure FDA00035499831500000511
is the i bit spreading code +.>
Figure FDA00035499831500000512
If->
Figure FDA00035499831500000513
I.e. the i-th bit spreading code of the mapping is the same as the original bit, a mapping matrix for selecting a matched filter bank and a phase correction factor
Figure FDA00035499831500000514
Otherwise, the mapped i-th bit spreading code is opposite to the original bit, then +.>
Figure FDA00035499831500000515
For GFSK signals, consider the following set of mapping matrices:
Figure FDA00035499831500000516
wherein ,
Figure FDA00035499831500000517
for the mapping matrix of the ith bit of the spreading sequence, the i-1 th spreading bit and the influence of the (i+1) th spreading bit on the symbol need to be considered at the same time; let- >
Figure FDA00035499831500000518
For the decimal mapping of the i-1, i, i+1 bits, the subscript of 1 is set as: />
Figure FDA0003549983150000061
Representing the mapping of original information "1" and bit "0" to the ith chip, the remaining subscripts being set to zero; chips outside the currently observed spreading sequence default to 0, i.e. +.>
Figure FDA0003549983150000062
Single symbol matching: matching the 1 st and 2 nd symbol samples after reverse sequence, wherein the matching expression is as follows:
Figure FDA0003549983150000063
where i=1, 2,
Figure FDA0003549983150000064
is based on the matching filter group after the updating of the chip mapping, the matching result +.>
Figure FDA0003549983150000065
Representing the matching result corresponding to the despread bit "0">
Figure FDA0003549983150000066
Representing the matching result corresponding to the non-spread bit 1;
combining: for DSSS-CPFSK symbols, the process of combining two single-symbol matching results is:
Figure FDA0003549983150000067
wherein
Figure FDA0003549983150000068
Taking the phase continuity of CPFSK/GFSK signals into consideration for the phase correction factors after spread spectrum mapping, carrying out in-phase superposition after phase correction;
iteration: iterating the steps, and matching and combining the k-th chip after the reverse sequence:
Figure FDA0003549983150000069
wherein
Figure FDA00035499831500000610
The result of the combination of the front k-1 chips after the reverse sequence;
taking a mould: finally obtain the L with complete single DSSS-FSK signal s The result of the length chip matching combining is, for DSSS-CPFSK
Figure FDA00035499831500000611
Modulo obtaining +.>
Figure FDA00035499831500000612
For DSSS-GFSK, is +. >
Figure FDA00035499831500000613
Obtaining by modulo calculation
Figure FDA00035499831500000614
9. The method according to claim 8, wherein in the step S3, for the CPFSK/GFSK signal that is not spread, if a hard demodulation mode is adopted, the subscript with the largest matching modulus is selected first:
Figure FDA00035499831500000615
then, will
Figure FDA00035499831500000616
Inversely mapping the highest bit at 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 sequence with the length of K+2 bits inversely mapped back needs to discard the ISI bits before and after, and the middle K bits are taken as the demodulation result;
if soft demodulation is employed, the soft information of the kth bit among the K observation bits is written as:
Figure FDA0003549983150000071
wherein ,I0 {. The first class of modified Bessel functions of zero order; SNR of h ＝|h|/σ 2 For the signal-to-noise ratio of the receiving end, wherein |h| is a flat attenuation module value, sigma 2 Gaussian noise power for the receiver;
Figure FDA0003549983150000072
and />
Figure FDA0003549983150000073
The index of the matching branch is inversely mapped to a set of 1 and 0 for the kth bit.
10. The method according to claim 9, wherein in the step S3, for the spread DSSS-CPFSK/DSSS-GFSK signal, if a hard demodulation method is adopted, the information bits before spreading are written as:
Figure FDA0003549983150000074
If soft demodulation is employed, the soft information is written as:
Figure FDA0003549983150000075
/>
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