CN114640562A - CPFSK/GFSK signal noncoherent demodulation method - Google Patents

Abstract

The present invention provides a CPFSK/GFSK signal non-coherent demodulation method, which generates a single-symbol length matched filter bank and a phase correction factor according to sent CPFSK/GFSK signal parameters; GFSK signal, the received samples are matched one by one K symbols, and the matching result is modulo; if the received DSSS‑CPFSK/DSSS‑GFSK signal is processed by direct sequence spread spectrum, the signal after spread spectrum processing is regarded as the whole , match the length of the spread spectrum code of the received samples one by one, and calculate the modulo value of the matching result; finally, if the received CPFSK/GFSK signal is not spread spectrum, each group will be soft demodulated or hard demodulated according to the decoding requirements. Solve the K-bit information; if the received DSSS-CPFSK/DSSS-GFSK signal, then solve the corresponding unspread original bits.

Description

A CPFSK/GFSK Signal Incoherent Demodulation Method

technical field

The present invention relates to the technical field of Internet of Things communication, and more particularly, to a non-coherent demodulation method for CPFSK/GFSK signals.

Background technique

With the rapid development of wireless communication technology and communication network, the demand for communication between things is growing rapidly. In the fifth generation mobile communication technology (5th Generation, 5G), Massive Machine Type Communication (mMTC) is listed as one of the three major application scenarios. Among many IoT physical layer technologies for mMTC scenarios, Continuous Phase Shift Keying (CPFSK) is widely used due to its excellent characteristics of constant envelope, continuous phase and high spectral efficiency. Gaussian filter frequency shift keying adds a low-pass Gaussian filter as a symbol phase shaping function on the basis of CPFSK (Gaussian Frequency Shift Keying, GFSK) on the basis of continuous phase modulation. Higher, but the introduction of Gaussian filter shaping will bring additional symbol crosstalk (Inter-symbol interference), and the implementation is more complicated. Further, CPFSK/GFSK modulation can also be combined with Direct Sequence Spread Spectrum (DSSS) and channel coding technology to achieve coverage enhancement and rate adaptation, so as to meet the needs of long-distance IoT communications.

In the design of low-cost receivers, the CPFSK/GFSK signal demodulation method is usually implemented based on a non-coherent method, because this method has low requirements on synchronization accuracy and strong anti-channel fading ability, and is more suitable for low-cost implementation. The currently commonly used non-coherent demodulation scheme uses the change polarity of the phase between single symbols to judge the information carried by the transmitted symbols, that is, the differential demodulation algorithm. Although the implementation is simple, its bit error rate (Bit Error Rate, BER) performance is poor at low signal-to-noise ratio (Signal-to-Noise Radio, SNR), and it is difficult to meet the needs of wide coverage. Another non-coherent 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 less than 1, which does not meet the requirement of orthogonality between symbols , so the BER performance is also poor at 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 idea of Maximum Likelihood Sequence Detection (MLSD), such as the optimal non-coherent solution. However, the computational complexity and storage complexity of this algorithm are very high, and it is difficult to adapt to practical engineering applications. In addition, the traditional idea of despreading and despreading will introduce a large amount of performance loss in despreading and demodulating the DSSS-FSK signal of direct sequence spread spectrum.

The prior art discloses a patent for a CPFSK demodulation device and method with fast automatic frequency compensation. The patent first starts the CPFSK demodulation device; then, the radio frequency signal is processed by the CPFSK demodulation device to obtain an input signal; then , the input signal and the quadrature signal of the local oscillator are respectively transmitted to the CPFSK demodulation device to obtain the output signal; this patent can not only realize the capture and tracking of a wide range of Doppler frequency offsets, but also achieve a wide range of Doppler frequency offsets. Another feature is that the calculation and update time of each error voltage is short, and the algorithm convergence speed is fast; this method has many advantages such as simple architecture, low hardware resource consumption, and easy FPGA implementation. However, this patent seldom mentions that a matched filter bank with a length of one symbol and a phase correction factor can achieve better performance with relatively low complexity.

SUMMARY OF THE INVENTION

The present invention provides a CPFSK/GFSK signal non-coherent demodulation method, which only needs a matched filter bank with a symbol length and a phase correction factor, and can achieve better performance with relatively low complexity. The group can reuse the reference waveform used by the look-up table method in the transmit part, further reducing the storage complexity.

In order to achieve above-mentioned technical effect, technical scheme of the present invention is as follows:

A CPFSK/GFSK signal non-coherent demodulation method, comprising the following steps:

S1: Generate a single-symbol length matched filter bank and a phase correction factor according to the sent CPFSK/GFSK signal parameters;

S2: Matching received samples: if the received signal is an unspread CPFSK/GFSK signal, the received samples are matched by K symbols, and the matching result is modulo; if the received signal is DSSS-CPFSK/DSSS processed by direct sequence spread spectrum -GFSK signal, the signal after spread spectrum processing is regarded as the whole, and the length of the spread spectrum code is matched for the received samples one by one, and the modulo value of the matching result is calculated;

S3: Demodulate the matching result: if the unspread CPFSK/GFSK signal is received, each group will decode the K-bit information by soft demodulation or hard demodulation according to the decoding requirements; if the received DSSS- CPFSK/DSSS-GFSK signal, the corresponding unspread original bits are solved.

Further, the CPFSK/GFSK signal has a constant envelope, and its complex baseband signal model is:

Among them, α is the bit sequence to be modulated of length L and α _i ∈{-1,1} is the ith binary bipolar bit to be modulated; N is the single-chip sampling factor, n is the sampling subscript; h _m = _Δf / _Bw is the modulation factor, Δf is the frequency difference between two frequency points, _Bw is the chip rate/transmission bandwidth; q(n) is the accumulation of the single-symbol phase shaping function _h (n).

Further, for the full-response CPFSK signal that is not phase-shaped by the Gaussian filter, its shaping function h _c (n) is a rectangular filter with response length L _c =1, that is, the normalized symbol length, and its expression is:

Therefore, the expression for the k-th symbol of the CPFSK signal is:

where θ _k-1 is the accumulated phase of the first k-1 items, a _k n/N is the phase change factor of the k-th symbol, which changes linearly under the full response CPFSK signal; The shaped part responds to the GFSK signal, and its shaping function h _g (n) is a low-pass Gaussian filter with a response length L _g , and the expression is:

BT为3dB衰减的带宽- 时间因子，L_g截断3就建模GFSK信号的码间串扰，即单个GFSK符号主要与前后两个符号产生马间串扰，因此GFSK信号第k个符号的表达式为：The Gaussian filter bandwidth factor in the above formula

BT is the bandwidth-time factor of 3dB attenuation, and L _g is cut off by 3 to model the intersymbol interference of GFSK signals, that is, a single GFSK symbol mainly produces intersymbol interference with the two symbols before and after, so the expression of the kth symbol of GFSK signal is: :

where θ _k-1 is the accumulated phase of the first k-1 items, φ(n; BT; α _k-1 α _k α _k+1 ) is the phase change factor of the k-th symbol under the current time-bandwidth factor, which is subject to The ISI effects of the preceding and following symbols, which vary nonlinearly in the partial response GFSK signal model.

Further, in the step S1, according to the sent CPFSK/GFSK signal parameters, a matched filter bank with a single symbol length is generated as follows:

为CPFSK符号q∈{0,1}对应的参考复基带样本的逆采样顺序排列结果，{·}^H表示Hermitian转置，{·}^T表示矩阵转置；in,

is the inverse sampling order of the reference complex baseband samples corresponding to the CPFSK symbol q∈{0,1}, {·} ^H represents the Hermitian transpose, {·} ^T represents the matrix transpose;

The CPFSK symbol q is expressed as:

where n=0,1,...N-1, N is the upsampling factor, and h _m is the modulation factor of the CPFSK signal at the transmitting end.

Further, in the step S1, the phase correction factor of the single symbol length generated according to the sent CPFSK/GFSK signal parameters is expressed as:

表示当前符号q∈{0,1}对后续符号引入的相对附加相位。

represents the relative additional phase introduced by the current symbol q∈{0,1} to subsequent symbols.

Further, since the current symbol is affected by the crosstalk between the symbols before and after the symbol, the matched filter bank generated and stored needs to consider the impact of the symbols before and after, namely:

为符号l∈{0,1,...,7}对应的参考复基带样本的逆序，而l为当前比特q₁与前后两个比特q₀q₂组合对应的q₀q₁q₂右端最高位十进制映射，即：in

is the inverse order of the reference complex baseband samples corresponding to the symbol l∈{0,1,...,7}, and l is the right end of q ₀ q ₁ q ₂ corresponding to the combination of the current bit q ₁ and the previous two bits q ₀ q ₂ The highest-order decimal mapping, i.e.:

Then each sampling point of the symbol l is expressed as:

where n=0,1,...N-1, φ(n; BT; q ₀ q ₁ q ₂ ) is the phase change of the current symbol, which is affected by the preceding and following bits q ₀ and q ₂ , and the GFSK Gaussian shaping filter The influence of the 3dB attenuation bandwidth parameter BT;

The generated and stored phase correction factor is expressed as:

A relative additional phase is introduced for the GFSK symbols l∈{0,1,...,7}.

Further, in the step S2, the process of processing the non-spread CPFSK/GFSK signal includes:

其中

为接收当前分组的第K-k+1个符号的逆序排列的复基带信号样本点；Reverse order: Arrange the received samples r in reverse sampling order to obtain reverse order samples

in

is the complex baseband signal sample points arranged in reverse order for receiving the K-k+1 th symbol of the current packet;

Single-symbol matching: For the first symbol sample after reverse order (that is, the original K-th sample), the matching result is:

In the above formula, M refers to the modulation method: M='c' is CPFSK modulation, at this time the symbol shaping filter length L _M =1, and the matching result is the complex matching value of the symbol "0"/"1";M='g' is GPFSK modulation. At this time, the length of the symbol shaping filter is L _M =3, and the matching result is the matching value of "000" to "111" represented by the binary symbol. The result needs to be stored for subsequent iteration and merging;

的匹配结果，对于GFSK符号，得到

的匹配结果；Then, according to the above method, the second symbol after the reverse order, that is, the K-1th symbol in the sequence, is matched. For the CPFSK symbol, we get

The matching result of , for GFSK symbols, gives

match result;

Combination: For CPFSK symbols, two single-symbol matching results need to be passed as two-segment received symbols and four-symbol combinations of baseband reference waveforms "00", "10", "01", and "11" for matching results, while for GFSK signals , the influence of the two symbols before and after the matching symbol needs to be additionally considered, that is, the matching result of two single symbols needs to be extended to two received symbols and 16 kinds of symbol combinations "0000", "1000", ..., "1111", in which boldface In order to match the intersymbol interference symbols at both ends of the observation part;

进行复制，用于复制的矩阵为：Therefore, it is first necessary to match the results

Make a copy, the matrix used for copying is:

为

的单位阵，然后考虑CPFSK/GFSK 信号的相位连续性，除了需要对

进行复制，还需要进行相位旋转以适配前一个匹配符号引入的相位，对

复制矩阵写为：in

for

, and then consider the phase continuity of the CPFSK/GFSK signal, except that

For replication, phase rotation is also required to adapt to the phase introduced by the previous matching symbol.

The copy matrix is written as:

where blockdiag{·} is the block diagonalization operation, and the phase rotation matrix is written as:

为主对角线元素为

的方阵，

代表逆序后第二个匹配符号引入的附加相位，由此合并后的结果表示为：in

The main diagonal element is

the square matrix,

represents the additional phase introduced by the second matching symbol after reversal, so the combined result is expressed as:

因为

是第一个匹配结果；in

because

is the first matching result;

减小为

The only real complex multiplications in the above process are the single-symbol matching of each symbol and the additional phase correction during symbol merging, and the number of complex multiplications required is given by

reduced to

Iteration: If the above steps are iterated, the result of the matching and merging of the k-th symbol after the reverse order is:

为逆序后的第k个符号的单符号匹配结果，

为逆序后前k-1个符号的匹配合并后的结果，且：in,

is the single-symbol matching result of the k-th symbol after the reverse order,

is the result of the combination of the first k-1 symbols after the reverse order, and:

求模得到

对于GFSK，为

求模得到

Modulo: Finally, the result of K symbol matching and merging is obtained. For CPFSK, it is

get the modulo

For GFSK, it is

get the modulo

Further, in the step S2, the process of processing the spread spectrum CPFSK/GFSK signal includes:

其中

为接收当前分组的第L_s-k+1个码片符号的逆序排列的复基带信号样本点；Reverse order: sort the received samples r in reverse order to get the reverse order

in

is the complex baseband signal sample points arranged in reverse order of the L _s -k+1 th chip symbol of the current packet;

Single-symbol matching: Considering that the spreading sequence D _s is known at the receiving end, only two possible codeword combinations need to be considered for the received complex baseband samples of chip length L _s , that is, the spreading sequence mapped by bit "1" Spread spectrum sequence mapped with bit "0", so for CPFSK signal, consider the following set of spread spectrum mapping matrices:

为第i比特扩频码

的映射矩阵，如果

即映射的第i比特扩频码与原比特相同，则用于选取匹配滤波器组和相位修正因子的映射矩阵

否则，映射的第i比特扩频码与原比特相反，则

in,

Spreading code for the i-th bit

the mapping matrix, if

That is, the mapped ith bit spreading code is the same as the original bit, then the mapping matrix used to select the matched filter bank and the phase correction factor

Otherwise, the mapped ith bit spreading code is opposite to the original bit, then

For GFSK signals, consider the following set of mapping matrices:

为扩频序列第i比特的映射矩阵，需要同时考虑第i-1扩频比特，第i+1扩频比特对符号的影响；令

为第i-1、i、 i+1比特的十进制映射，则置1的下标为：

代表原始信息“1”和比特“0”到第i个码片的映射，其余下标置零；当前观测的扩频序列之外的码片默认为0，即

in,

For the mapping matrix of the i-th bit of the spreading sequence, it is necessary to consider the influence of the i-1-th spreading bit and the i+1-th spreading bit on the symbol at the same time; let

For the decimal mapping of the i-1, i, i+1 bits, the subscript set to 1 is:

Represents the mapping of the original information "1" and bit "0" to the i-th chip, and the rest of the subscripts are set to zero; the chips other than the currently observed spreading sequence are 0 by default, that is,

Single symbol matching: For the first and second symbol samples after the reverse order, the matching expression is:

是依据码片映射更新后的匹配滤波器组，匹配结果

代表未扩频比特“0”对应的匹配结果，

代表未扩频比特“1”对应的匹配结果；where i=1,2,

is the matched filter bank updated according to the chip map, and the matching result

represents the matching result corresponding to the unspread bit "0",

Represents the matching result corresponding to the unspread bit "1";

Merging: For DSSS-CPFSK symbols, the process of merging two single-symbol matching results is:

为经过扩频映射后的相位修正因子，考虑到 CPFSK/GFSK信号的相位连续性，需要经过相位修正后再进行同相叠加；in

For the phase correction factor after spread spectrum mapping, considering the phase continuity of the CPFSK/GFSK signal, it needs to be phase corrected and then superimposed in phase;

Iteration: The above steps are iterated, and the result of the matching and merging of the k-th chip after the reverse order is:

为逆序后前k-1个码片合并的结果；in

is the result of combining the first k-1 chips after the reverse order;

求模得到

对于DSSS-GFSK，为

求模得到

Modulo: Finally, the result of the complete L _s length chip matching and merging of a single DSSS-FSK signal is obtained. For DSSS-CPFSK, it is

get the modulo

For DSSS-GFSK, it is

get the modulo

Further, in the step S3, for the unspread CPFSK/GFSK signal, if the hard demodulation method is adopted, then first select the subscript with the largest matching modulus value:

按照右端最高位逆映射回二进制序列，对于CPFSK，映射的K比特长度的序列即为解调结果，对于GFSK，逆映射回的K+2比特长度的序列需要舍弃前后的ISI比特，取中间K比特为解调结果；followed by

Inversely map back to the binary sequence according to the highest bit on the right. For CPFSK, the mapped K-bit sequence is the demodulation result. For GFSK, the reverse-mapped K+2-bit sequence needs to discard the ISI bits before and after, and take the middle K Bit is the demodulation result;

If soft demodulation is used, the soft information of the kth bit in the K observed bits is written as:

和

为第k比特匹配支路下标逆映射为1和0的集合。Among them, I ₀ {·} is a zero-order modified Bessel function of the first kind; SNR _h = |h|/σ ² is the signal-to-noise ratio at the receiver, where |h| is the flat fading modulus value, and σ ² is the receiver Gaussian noise power;

and

Matching branch subscripts for the kth bit are inversely mapped to a set of 1s and 0s.

Further, in the step S3, for the DSSS-CPFSK/DSSS-GFSK signal after the spectrum spread, if the hard demodulation method is adopted, the information bits before the spectrum spread obtained by the solution are written as:

If soft demodulation is used, the soft information is written as:

Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

The method of the invention is suitable for demodulation of non-spread CPFSK/GFSK signal and DSSS-CPFSK/DSSS-GFSK signal after spread spectrum. Compared with the existing low-complexity and low-performance differential demodulation/envelope detection schemes, the demodulation performance is greatly improved without significantly increasing the complexity. Compared with the existing high-performance and high-complexity multi-symbol detection schemes, the computational complexity is greatly reduced at the cost of a small performance loss. The joint demodulation, modulation and spreading of the spread-spectrum DSSS-CPFSK/DSSS-GFSK signal can obtain more spreading gain under the condition of low complexity. The solutions described are all based on non-coherent implementations, have low requirements on synchronization accuracy, and are suitable for IoT applications with low cost and low power consumption for long-distance transmission.

Description of drawings

FIG. 1 shows a block diagram of CPFSK/GFSK signal matching calculation according to an embodiment of the present invention;

Fig. 2 shows another embodiment of the present invention for the DSSS-CPFSK/DSSS-GFSK signal matching calculation block diagram;

3 shows a schematic flowchart of CPFSK/GFSK demodulation according to an embodiment of the present invention;

Fig. 4 shows the CPFSK/GFSK demodulation performance comparison graph without channel coding under the AWGN channel proposed in Embodiment 1 of the present invention;

FIG. 5 is a graph showing the CPFSK/GFSK demodulation performance comparison under (2,1,3) convolutional coding and Viterbi soft decoding under the AWGN channel proposed in Embodiment 1 of the present invention;

FIG. 6 is a graph showing the comparison of the demodulation performance of DSSS-CPFSK without channel coding under the AWGN channel proposed in Embodiment 2 of the present invention.

Detailed ways

The accompanying drawings are for illustrative purposes only, and should not be construed as limitations on this patent;

In order to better illustrate this embodiment, some parts of the drawings are omitted, enlarged or reduced, which do not represent the size of the actual product;

It will be understood by those skilled in the art that some well-known structures and their descriptions may be omitted from the drawings.

The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

Example 1

As shown in Figure 3, a CPFSK/GFSK signal non-coherent demodulation method includes the following steps:

S1: Generate a single-symbol length matched filter bank and a phase correction factor according to the sent CPFSK/GFSK signal parameters;

S2: Matching received samples: if the received signal is an unspread CPFSK/GFSK signal, the received samples are matched by K symbols, and the matching result is modulo; if the received signal is DSSS-CPFSK/DSSS processed by direct sequence spread spectrum -GFSK signal, the signal after spread spectrum processing is regarded as the whole, and the length of the spread spectrum code is matched for the received samples one by one, and the modulo value of the matching result is calculated;

S3: Demodulate the matching result: if the unspread CPFSK/GFSK signal is received, each group will decode the K-bit information by soft demodulation or hard demodulation according to the decoding requirements; if the received DSSS- CPFSK/DSSS-GFSK signal, the corresponding unspread original bits are solved.

The CPFSK/GFSK signal has a constant envelope, and its complex baseband signal model is:

Among them, α is the bit sequence to be modulated of length L and α _i ∈{-1,1} is the ith binary bipolar bit to be modulated; N is the single-chip sampling factor, n is the sampling subscript; h _m = _Δf / _Bw is the modulation factor, Δf is the frequency difference between two frequency points, _Bw is the chip rate/transmission bandwidth; q(n) is the accumulation of the single-symbol phase shaping function _h (n).

For the full-response CPFSK signal without Gaussian filter phase shaping, its shaping function h _c (n) is a rectangular filter with response length L _c =1, that is, the normalized symbol length, and its expression is:

Therefore, the expression for the k-th symbol of the CPFSK signal is:

where θ _k-1 is the accumulated phase of the first k-1 items, a _k n/N is the phase change factor of the k-th symbol, which changes linearly under the full response CPFSK signal; The shaped part responds to the GFSK signal, and its shaping function h _g (n) is a low-pass Gaussian filter with a response length L _g , and the expression is:

BT为3dB衰减的带宽- 时间因子，L_g截断3就建模GFSK信号的码间串扰，即单个GFSK符号主要与前后两个符号产生马间串扰，因此GFSK信号第k个符号的表达式为：The Gaussian filter bandwidth factor in the above formula

BT is the bandwidth-time factor of 3dB attenuation, and L _g is cut off by 3 to model the intersymbol interference of GFSK signals, that is, a single GFSK symbol mainly produces intersymbol interference with the two symbols before and after, so the expression of the kth symbol of GFSK signal is: :

where θ _k-1 is the accumulated phase of the first k-1 items, φ(n; BT; α _k-1 α _k α _k+1 ) is the phase change factor of the k-th symbol under the current time-bandwidth factor, which is subject to The ISI effects of the preceding and following symbols, which vary nonlinearly in the partial response GFSK signal model.

In step S1, generating a matched filter bank with a single symbol length according to the sent CPFSK/GFSK signal parameters is:

为CPFSK符号q∈{0,1}对应的参考复基带样本的逆采样顺序排列结果，{·}^H表示Hermitian转置，{·}^T表示矩阵转置；in,

is the inverse sampling order of the reference complex baseband samples corresponding to the CPFSK symbol q∈{0,1}, {·} ^H represents the Hermitian transpose, {·} ^T represents the matrix transpose;

The CPFSK symbol q is expressed as:

where n=0,1,...N-1, N is the upsampling factor, and h _m is the modulation factor of the CPFSK signal at the transmitting end.

Further, in the step S1, the phase correction factor of the single symbol length generated according to the sent CPFSK/GFSK signal parameters is expressed as:

表示当前符号q∈{0,1}对后续符号引入的相对附加相位。

represents the relative additional phase introduced by the current symbol q∈{0,1} to subsequent symbols.

Since the current symbol is affected by the crosstalk between the symbols before and after the symbol, the generated and stored matched filter bank needs to consider the impact of the symbols before and after, namely:

为符号l∈{0,1,...,7}对应的参考复基带样本的逆序，而l为当前比特q₁与前后两个比特q₀q₂组合对应的q₀q₁q₂右端最高位十进制映射，即：in

is the inverse order of the reference complex baseband samples corresponding to the symbol l∈{0,1,...,7}, and l is the right end of q ₀ q ₁ q ₂ corresponding to the combination of the current bit q ₁ and the previous two bits q ₀ q ₂ The highest-order decimal mapping, i.e.:

Then each sampling point of the symbol l is expressed as:

where n=0,1,...N-1, φ(n; BT; q ₀ q ₁ q ₂ ) is the phase change of the current symbol, which is affected by the preceding and following bits q ₀ and q ₂ , and the GFSK Gaussian shaping filter The influence of the 3dB attenuation bandwidth parameter BT;

The generated and stored phase correction factor is expressed as:

A relative additional phase is introduced for the GFSK symbols l∈{0,1,...,7}.

In step S2, the process of processing the non-spread CPFSK/GFSK signal includes:

其中

为接收当前分组的第K-k+1个符号的逆序排列的复基带信号样本点；Reverse order: Arrange the received samples r in reverse sampling order to obtain reverse order samples

in

is the complex baseband signal sample points arranged in reverse order for receiving the K-k+1 th symbol of the current packet;

Single-symbol matching: For the first symbol sample after reverse order (that is, the original K-th sample), the matching result is:

In the above formula, M refers to the modulation method: M='c' is CPFSK modulation, at this time the symbol shaping filter length L _M =1, and the matching result is the complex matching value of the symbol "0"/"1";M='g' is GPFSK modulation. At this time, the length of the symbol shaping filter is L _M =3, and the matching result is the matching value of "000" to "111" represented by the binary symbol. The result needs to be stored for subsequent iteration and merging;

的匹配结果，对于GFSK符号，得到

的匹配结果；Then, according to the above method, the second symbol after the reverse order, that is, the K-1th symbol in the sequence, is matched. For the CPFSK symbol, we get

The matching result of , for GFSK symbols, gives

match result;

Combination: For CPFSK symbols, two single-symbol matching results need to be passed as two-segment received symbols and four-symbol combinations of baseband reference waveforms "00", "10", "01", and "11" for matching results, while for GFSK signals , the influence of the two symbols before and after the matching symbol needs to be additionally considered, that is, the matching result of two single symbols needs to be extended to two received symbols and 16 kinds of symbol combinations "0000", "1000", ..., "1111", in which boldface In order to match the intersymbol interference symbols at both ends of the observation part;

进行复制，用于复制的矩阵为：Therefore, it is first necessary to match the results

Make a copy, the matrix used for copying is:

为

的单位阵，然后考虑CPFSK/GFSK 信号的相位连续性，除了需要对

进行复制，还需要进行相位旋转以适配前一个匹配符号引入的相位，对

复制矩阵写为：in

for

, and then consider the phase continuity of the CPFSK/GFSK signal, except that

For replication, phase rotation is also required to adapt to the phase introduced by the previous matching symbol.

The copy matrix is written as:

where blockdiag{·} is the block diagonalization operation, and the phase rotation matrix is written as:

为主对角线元素为

的方阵，

代表逆序后第二个匹配符号引入的附加相位，由此合并后的结果表示为：in

The main diagonal element is

the square matrix,

represents the additional phase introduced by the second matching symbol after reversal, so the combined result is expressed as:

因为

是第一个匹配结果；in

because

is the first matching result;

减小为

The only real complex multiplications in the above process are the single-symbol matching of each symbol and the additional phase correction during symbol merging, and the number of complex multiplications required is given by

reduced to

Iteration: If the above steps are iterated, the result of the matching and merging of the k-th symbol after the reverse order is:

为逆序后的第k个符号的单符号匹配结果，

为逆序后前k-1个符号的匹配合并后的结果，且：in,

is the single-symbol matching result of the k-th symbol after the reverse order,

is the result of the combination of the first k-1 symbols after the reverse order, and:

求模得到

对于GFSK，为

求模得到

Modulo: Finally, the result of K symbol matching and merging is obtained. For CPFSK, it is

get the modulo

For GFSK, it is

get the modulo

In step S2, the process of processing the spread spectrum CPFSK/GFSK signal includes:

其中

为接收当前分组的第L_s-k+1个码片符号的逆序排列的复基带信号样本点；Reverse order: sort the received samples r in reverse order to get the reverse order

in

is the complex baseband signal sample points arranged in reverse order of the L _s -k+1 th chip symbol of the current packet;

Single-symbol matching: Considering that the spreading sequence D _s is known at the receiving end, only two possible codeword combinations need to be considered for the received complex baseband samples of chip length L _s , that is, the spreading sequence mapped by bit "1" Spread spectrum sequence mapped with bit "0", so for CPFSK signal, consider the following set of spread spectrum mapping matrices:

为第i比特扩频码

的映射矩阵，如果

即映射的第i比特扩频码与原比特相同，则用于选取匹配滤波器组和相位修正因子的映射矩阵

否则，映射的第i比特扩频码与原比特相反，则

in,

Spreading code for the i-th bit

the mapping matrix, if

That is, the mapped ith bit spreading code is the same as the original bit, then the mapping matrix used to select the matched filter bank and the phase correction factor

Otherwise, the mapped ith bit spreading code is opposite to the original bit, then

For GFSK signals, consider the following set of mapping matrices:

为扩频序列第i比特的映射矩阵，需要同时考虑第i-1扩频比特，第i+1扩频比特对符号的影响；令

为第i-1、i、 i+1比特的十进制映射，则置1的下标为：

代表原始信息“1”和比特“0”到第i个码片的映射，其余下标置零；当前观测的扩频序列之外的码片默认为0，即

in,

For the mapping matrix of the i-th bit of the spreading sequence, it is necessary to consider the influence of the i-1-th spreading bit and the i+1-th spreading bit on the symbol at the same time; let

For the decimal mapping of the i-1, i, i+1 bits, the subscript set to 1 is:

Represents the mapping of the original information "1" and bit "0" to the i-th chip, and the rest of the subscripts are set to zero; the chips other than the currently observed spreading sequence are 0 by default, that is,

Single symbol matching: For the first and second symbol samples after the reverse order, the matching expression is:

是依据码片映射更新后的匹配滤波器组，匹配结果

代表未扩频比特“0”对应的匹配结果，

代表未扩频比特“1”对应的匹配结果；where i=1,2,

is the matched filter bank updated according to the chip map, and the matching result

represents the matching result corresponding to the unspread bit "0",

Represents the matching result corresponding to the unspread bit "1";

Merging: For DSSS-CPFSK symbols, the process of merging two single-symbol matching results is:

为经过扩频映射后的相位修正因子，考虑到 CPFSK/GFSK信号的相位连续性，需要经过相位修正后再进行同相叠加；in

For the phase correction factor after spread spectrum mapping, considering the phase continuity of the CPFSK/GFSK signal, it needs to be phase corrected and then superimposed in phase;

Iteration: The above steps are iterated, and the result of the matching and merging of the k-th chip after the reverse order is:

为逆序后前k-1个码片合并的结果；in

is the result of combining the first k-1 chips after the reverse order;

求模得到

对于DSSS-GFSK，为

求模得到

Modulo: Finally, the result of the complete L _s length chip matching and merging of a single DSSS-FSK signal is obtained. For DSSS-CPFSK, it is

get the modulo

For DSSS-GFSK, it is

get the modulo

In step S3, for the unspread CPFSK/GFSK signal, if the hard demodulation method is adopted, first select the subscript with the largest matching modulus value:

按照右端最高位逆映射回二进制序列，对于CPFSK，映射的K比特长度的序列即为解调结果，对于GFSK，逆映射回的K+2比特长度的序列需要舍弃前后的ISI比特，取中间K比特为解调结果；followed by

Inversely map back to the binary sequence according to the highest bit on the right. For CPFSK, the mapped K-bit sequence is the demodulation result. For GFSK, the reverse-mapped K+2-bit sequence needs to discard the ISI bits before and after, and take the middle K Bit is the demodulation result;

If soft demodulation is used, the soft information of the kth bit in the K observed bits is written as:

和

为第k比特匹配支路下标逆映射为1和0的集合。Among them, I ₀ {·} is a zero-order modified Bessel function of the first kind; SNR _h = |h|/σ ² is the signal-to-noise ratio at the receiver, where |h| is the flat fading modulus value, and σ ² is the receiver Gaussian noise power;

and

Matching branch subscripts for the kth bit are inversely mapped to a set of 1s and 0s.

In step S3, for the DSSS-CPFSK/DSSS-GFSK signal after the spectrum spread, if the hard demodulation method is adopted, the information bits before the spectrum spread obtained by the solution are written as:

If soft demodulation is used, the soft information is written as:

Example 2

As shown in Figure 3, a method for non-coherent demodulation of CPFSK/GFSK signal, the method includes:

S1: Generate a single-symbol length matched filter bank and a phase correction factor according to the sent CPFSK/GFSK signal parameters;

与序列“00…0”～“11…1”这2^K种连续相位的基带波形组合进行匹配；S2: Matching the received samples: This step replaces the redundant symbol matching calculation with the matching result to pass the received samples with lower complexity

Match with the baseband waveform combinations of 2 ^K continuous phases in the sequence "00...0" ~ "11...1";

S3: Demodulate the matching result: Decode each group of K bits to obtain K bits of information in a soft demodulation or hard demodulation manner according to decoding requirements.

In this embodiment, the CPFSK/GFSK signal has the excellent characteristics of constant envelope and continuous phase, and its complex baseband signal model is:

Among them, α is the bit sequence to be modulated of length L and α _i ∈{-1,1} is the ith binary bipolar bit to be modulated; N is the single-chip sampling factor, n is the sampling index; h _n = _Δf / _Bw is the modulation factor, Δf is the frequency difference between two frequency points, _Bw is the chip rate/transmission bandwidth; q(n) is the accumulation of the single-symbol phase shaping function _h (n). For the full-response CPFSK signal without phase shaping by Gaussian filter, its shaping function h _c (n) is a rectangular filter with response length L _c =1 (normalized symbol length), and its expression is:

Therefore, the expression for the k-th symbol of the CPFSK signal is:

where θ _k-1 is the accumulated phase of the first k-1 items, and a _k n/N is the phase change factor of the k-th symbol, which changes linearly under the full-response CPFSK signal. For the partial response GFSK signal that is phase shaped by the Gaussian filter, the shaping function h _g (n) is a low-pass Gaussian filter with the response length L _g , and the expression is:

BT为3dB衰减的带宽- 时间因子。L_g通常截断3就可以建模GFSK信号的码间串扰 (inter-symbol-interference,ISI)，即单个GFSK符号主要与前后两个符号产生马间串扰，因此GFSK信号第k个符号的表达式为：The Gaussian filter bandwidth factor in the above formula

BT is the bandwidth-time factor of the 3dB attenuation. L _g is usually truncated to 3 to model the inter-symbol-interference (ISI) of GFSK signals, that is, a single GFSK symbol mainly generates inter-symbol interference with the two symbols before and after, so the expression of the k-th symbol of GFSK signal for:

where θ _k-1 is the accumulated phase of the first k-1 items, φ(n; BT; α _k-1 α _k α _k+1 ) is the phase change factor of the k-th symbol under the current time-bandwidth factor, which is subject to The ISI effects of the preceding and following symbols, which vary nonlinearly 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:

为CPFSK符号q∈{0,1}对应的参考复基带样本的逆排序序列。具体而言，依据 CPFSK的信号模型，符号q可以表示为：Among them, {·} ^H represents the Hermitian transpose, {·} ^T represents the matrix transpose,

is the inverse ordered sequence of reference complex baseband samples corresponding to CPFSK symbols q∈{0,1}. Specifically, according to the signal model of CPFSK, the symbol q can be expressed as:

Among them, h _m is the modulation factor of the CPFSK signal at the transmitting end. And the pre-generated and stored additional phase correction factor can be expressed as:

represents the relative additional phase introduced by the current matching symbol q∈{0,1} to subsequent matching symbols.

For partially responding 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 impact of the preceding and following symbols, namely:

where is the inverse order of the reference complex baseband samples corresponding to the symbols l∈{0,1,...,7}, and l is the q ₀ q ₁ q ₂ corresponding to the combination of the current bit q ₁ and the preceding and following two bits q ₀ q ₂ Right-hand most significant decimal mapping, that is:

Then each sampling point of the symbol l can be expressed as:

Among them, φ(n; BT; q ₀ q ₁ q ₂ ) is the phase change of the current symbol, which is affected by the preceding and following bits q ₀ and q ₂ , and the 3dB attenuation bandwidth parameter BT of the GFSK Gaussian shaping filter. The pre-generated and stored additional phase correction factors can be expressed as:

A relative additional phase is introduced for the GFSK symbols l∈{0,1,...,7}. The matching waveform can reuse the waveform stored in the Look-up-table (LUT) method of the baseband modulation part, which further saves storage space.

与序列“00…0”～“11…1”这2^K种连续相位的基带波形组合进行匹配。具体流程图如图1所示，上述步骤可以划分为逆序、单符号匹配、合并、迭代、取模；In step S2, for the unspread CPFSK/GFSK signal, the received signal is divided into a group of every K symbols for demodulation. This step replaces the redundant symbol matching calculation with the matching result transfer, and converts the received samples with lower complexity.

Match with the baseband waveform combination of 2 ^K continuous phases in the sequence "00...0" ~ "11...1". The specific flowchart is shown in Figure 1, and the above steps can be divided into reverse order, single-symbol matching, merging, iteration, and modulo;

其中

为接收当前分组的第K-k个符号的逆序排列的复基带信号样本点；Reverse order: sort the received samples r in reverse order to get the reverse order

in

is the complex baseband signal sample points arranged in reverse order for receiving the Kk th symbol of the current packet;

Single-symbol matching: For the first symbol sample after reverse order (that is, the original K-th sample), the matching result is:

In the above formula, M refers to the modulation method: M='c' is CPFSK modulation, at this time the symbol shaping filter length L _M =1, and the matching result is the complex matching value of the symbol "0"/"1";M='g' is GPFSK modulation. At this time, the length of the symbol shaping filter is L _M =3, and the matching result is the matching value of symbols "000" to "111" (binary representation), that is, considering the influence of the preceding and following symbols on the phase change of the intermediate symbols. The current operation result needs to be stored for subsequent iteration and merging.

的匹配结果，对于GFSK符号，得到

的匹配结果。Then, according to the above method, the reversed second symbol sample (that is, the original K-1th sample) is matched. For the CPFSK symbol, we get

The matching result of , for GFSK symbols, gives

match result.

Combination: For CPFSK symbols, two single-symbol matching results need to be extended to the results of matching two received symbols with four double-symbol combinations "00" "10" "01" "11". For the GFSK signal, the influence of the two symbols before and after needs to be additionally considered, that is, the matching result of two single symbols needs to be extended to two received symbols and 16 kinds of symbol combinations "0000", "1000", ..., "1111" ( The boldface is the intersymbol interference term).

进行复制，复制矩阵为：Therefore, it is first necessary to match the results

To make a copy, the copy matrix is:

为

的单位阵。然后考虑到CPFSK/GFSK 信号的相位连续性，除了需要对

进行复制，还需要进行相位旋转以适配前一个符号引入的相位，对

复制矩阵可以写为：in

for

unit array. Then considering the phase continuity of the CPFSK/GFSK signal, in addition to the need for

For replication, phase rotation is also required to adapt to the phase introduced by the previous symbol.

The copy matrix can be written as:

where blockdiag{·} is the block diagonalization operation. And the phase rotation matrix can be written as:

为主对角线元素为

的方阵。

代表逆序后第二个匹配符号引入的附加相位，由此合并后的结果可以表示为：in

The main diagonal element is

square matrix.

represents the additional phase introduced by the second matching symbol after reversal, so the combined result can be expressed as:

in

减小为

In the above process, only the single-symbol matching of each symbol and the additional phase correction during symbol merging are really used for complex multiplication. Therefore, compared with the traditional matching method, the number of complex multiplications required is given by

reduced to

Iteration: If the above steps are iterated, the result of the matching and merging of the k-th symbol after the reverse order is:

为逆序后的第k个符号单符号匹配结果，

为逆序后前k-1个符号的匹配合并后的结果，且：in,

is the single-symbol matching result of the k-th symbol after the reverse order,

is the result of the combination of the first k-1 symbols after the reverse order, and:

而直接与K个所有可能的符号组合做匹配需要的CM次数和CA次数均为

相较而言本方案复杂度可以大大降低。In summary, the number of complex multiplications (CM) and complex additions (CA) required for K symbol matching are both

The CM times and CA times required to directly match all K possible symbol combinations are

In comparison, the complexity of this scheme can be greatly reduced.

求模得到

对于GFSK，为

求模得到

取模所需的实数乘法(real multiplication,RM)次数为

实数加法(real addition,RA)次数为

Modulo: Finally, the result of K symbol matching and merging can be obtained. For CPFSK, it is

get the modulo

For GFSK, it is

get the modulo

The number of real multiplications (RM) required to take the modulo is

The number of real additions (RA) is

Specifically, in step S3, corresponding K-bit information needs to be demodulated for the final non-coherent matching and combining result. If the hard demodulation method is used, first select the subscript with the largest matching modulus value:

按照右端最高位逆映射回二进制序列。对于CPFSK，映射的K比特长度的序列即为解调结果。对于GFSK，映射的K+2比特长度的序列需要舍弃前后的ISI比特，取中间K比特为解调结果。where i represents the subscript of the matching modulo value. followed by

Inversely map back to the binary sequence according to the highest bit on the right. For CPFSK, the mapped sequence of K-bit length is the demodulation result. For GFSK, the mapped sequence with a length of K+2 bits needs to discard the ISI bits before and after, and take the middle K bits as the demodulation result.

If soft demodulation is adopted, the soft information of the kth bit among the K observed bits can be written as

和

为右端最高逆映射后第k 比特匹配支路下标为“1”和“0”的集合。Among them, I ₀ {·} is a zero-order modified Bessel function of the first kind; SNR _h = |h|/σ ² is the signal-to-noise ratio at the receiver, where |h| is the flat fading modulus value, and σ ² is the Gaussian noise power;

and

It is the set of subscripts "1" and "0" for the kth bit matching branch after the highest inverse mapping at the right end.

In order to verify the effectiveness of the designed incoherent demodulation method proposed in the embodiment of the present invention, further simulation experiments are performed, as follows:

Under the AWGN channel, for the commonly used CPFSK signal demodulation with h=0.5 and GFSK signal demodulation with h=0.5, BT=0.5, the curve of BER performance versus SNR of different demodulation schemes is plotted. Figure 4 is the performance curve under the unencoded condition, and Figure 5 is the performance curve under the (2, 1, 3) convolutional code encoding and soft Viterbi decoding. The solid line represents the GFSK demodulation performance and the dot-dash line represents the CPFSK demodulation performance. The corresponding scheme in this embodiment is marked with "Δ", the optimal multi-symbol detection scheme is marked with "□", and the differential detection scheme is marked with "○", The envelope detection scheme is marked with "+", and the theoretical performance of the orthogonal 2-FSK signal incoherent detection scheme under unencoded conditions is plotted with dotted lines, 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 performance of envelope detection and differential detection under uncoded conditions is worse than the theoretical bound of the quadrature 2-FSK signal incoherent detection scheme, and the present scheme and the optimal multi-symbol detection scheme are both Better than the theoretical performance bounds of incoherent detection schemes for quadrature 2-FSK signals. Compared with the best multi-symbol detection scheme in the unencoded condition, the performance loss for CPFSK demodulation is close to 2dB when the BER=10 ^-4 required for reliable IoT communication is achieved, and the performance loss for GFSK demodulation is close to 1dB. Under the coding condition, the performance loss of this scheme is only 0.5dB when BER=10 ^-4 , but it can greatly reduce the complexity of the receiver. Compared with envelope detection and differential detection with poor performance, the performance gain of this scheme is 3-6dB under the condition of uncoded BER=10 ^-4 , and the performance gain of this scheme is 3dB under the condition of coding.

次RM以及

次RA 解出K比特信息，最佳多符号检测需要

次RM以及

次RA才能解出K个观测符号的中间符号的信息，包络检测需要

次RM以及

次RA解出当前符号的信息，差分检测需要4N+2次RM以及2N+1次RA解出当前符号的信息。综上，平均每个符号的解调复杂度统计如下所示：In order to further illustrate the low complexity of the scheme, the complexity of different demodulation schemes is compared next, where one CM is equivalent to four RMs, and one CA is equivalent to two RAs. This program requires a total of

RM and

The second RA solves the K-bit information, and the optimal multi-symbol detection requires

RM and

The information of the middle symbols of the K observation symbols can be solved only after RA times, and the envelope detection needs

RM and

The information of the current symbol is solved by RA times, and the differential detection requires 4N+2 times of RM and 2N+1 times of RA to solve the information of the current symbol. In summary, the average demodulation complexity statistics per symbol are as follows:

Taking the observation length K=5 and the upsampling factor N=4, then for GFSK demodulation, the optimal multi-symbol detection requires 10496 times of RM and 5248 times of RA to solve the information of one symbol, and the solution of the present invention needs 382.4 times of RM and 191.2 times of RM. RA solves one symbol information, envelope detection requires 144 RM and 72 RA to solve one symbol information, and differential detection requires 18 RM and 9 RA to solve one symbol information. For CPFSK demodulation, the optimal multi-symbol detection requires 2624 times of RM and 1312 times of RA to solve the information of one symbol, the solution of the present invention needs 95.6 times of RM and 47.8 times of RA to solve the information of one symbol, and the envelope detection needs 36 times of RM And 18 times of RA to solve the information of one symbol, differential detection requires 18 times of RM and 9 times of RA to solve the information of one symbol. In contrast, the complexity of the scheme of the present invention is much lower than that of the optimal multi-symbol detection scheme, and higher than that of envelope detection and differential detection, but the performance gain compared to the receiver is still acceptable. In addition, the matched filter bank of this scheme can multiplex the reference waveform of single symbol length stored by the table look-up method in the baseband modulation part, which further reduces the space complexity of implementation.

Example 3

As shown in Figure 3, a method for non-coherent demodulation of CPFSK/GFSK signal, the method includes:

S1: Generate a single-symbol length matched filter bank and a phase correction factor according to the sent CPFSK/GFSK signal parameters;

S2: Matching received samples: This step treats the spread spectrum DSSS-FSK as a complete symbol, in which each received chip is single-chip matched with the matched filter bank, and then the phase-corrected matching results are superimposed, and Calculate the modulo value of the final result;

S3: Demodulate the matching result: Decode each group of K bits to obtain K bits of information in a soft demodulation or hard demodulation manner according to decoding requirements.

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 undergo direct sequence spread spectrum first. processing, the expression after the direct spread processing of the spreading sequence D _s is:

b[kL _s +i]=a[k]·D _s [i], 0≤i<L _s

where b[i]∈{-1,1} is the ith binary bipolar bit, and a[i]∈{-1,1} is the ith original information bit.

与“0”、“1”信息比特对应的参考符号进行匹配并且求模。具体流程图如图2所示，上述步骤可以划分为逆序、单符号匹配、合并、迭代、取模；The processing flow of step S1 in this embodiment is exactly the same as that of step S1 in embodiment 1. In step S2, for the DSSS-CPFSK/DSSS-GFSK signal spread by the spreading sequence D _s of length L _S , the spread DSSS-CPFSK/DSSS-GFSK is regarded as a complete symbol, in which each Each received chip is single-chip matched with a matched filter bank, then the phase-corrected matching results are superimposed, and the final result is modulo valued. The above procedure is equivalent to a single DSSS-CPFSK/DSSS-GFSK symbol that will be received

The reference symbols corresponding to the "0", "1" information bits are matched and modulo. The specific flowchart is shown in Figure 2, and the above steps can be divided into reverse order, single-symbol matching, merging, iteration, and modulo;

其中

为接收当前分组的第L_s-k+1个符号的逆序排列的复基带信号样本点。Reverse order: sort the received samples r in reverse order to get the reverse order

in

is the complex baseband signal sample points arranged in reverse order for the L _s -k+1 th symbol of the received current packet.

Single-symbol matching: Considering that the spreading sequence D _s is known, only two possible codeword combinations need to be considered for the received complex baseband samples of chip length L _s , namely the spreading sequence mapped by bit "1" and the bit "0" mapped spreading sequence. So for the CPFSK signal, consider the following set of spread spectrum mapping matrices:

为第i比特扩频码

的映射矩阵，如果S⁽ⁱ⁾＝1，即映射的第i比特扩频码与原比特相同，则用于选取匹配滤波器组和相位修正因子的映射矩阵

否则，映射的第i比特扩频码与原比特相反，则

in,

Spreading code for the i-th bit

The mapping matrix of , if S ⁽ⁱ⁾ = 1, that is, the i-th bit spreading code of the mapping is the same as the original bit, then the mapping matrix used to select the matched filter bank and the phase correction factor

Otherwise, the mapped ith bit spreading code is opposite to the original bit, then

For GFSK signals, consider the following set of mapping matrices:

为第i比特扩频码的映射矩阵，需要同时考虑第i-1扩频比特，第i+1扩频比特对符号的影响。令

为第i-1、i、 i+1比特的十进制映射，则置1的下标为：

代表原始信息“1”和比特“0”到第i个码片的映射。in,

For the mapping matrix of the spreading code of the i-th bit, it is necessary to consider the influence of the i-1-th spreading-spectrum bit and the i+1-th spreading-spectrum bit on the symbol at the same time. make

For the decimal mapping of the i-1, i, i+1 bits, the subscript set to 1 is:

Represents the mapping of original information "1" and bit "0" to the ith chip.

Single symbol matching: For the first and second symbol samples after the reverse order, the matching expression is:

是依据码片映射更新后的匹配滤波器组，匹配结果

代表未扩频比特“0”对应的匹配结果，

代表未扩频比特“1”对应的匹配结果。in

is the matched filter bank updated according to the chip map, and the matching result

represents the matching result corresponding to the unspread bit "0",

Represents the matching result corresponding to the unspread bit "1".

Merging: For DSSS-CPFSK symbols, the process of merging two single-symbol matching results is:

为经过扩频映射后的相位修正因子，考虑到 CPFSK/GFSK信号的相位连续性，需要经过相位修正后再进行同相叠加。in

For the phase correction factor after spread spectrum mapping, considering the phase continuity of the CPFSK/GFSK signal, it is necessary to perform in-phase superposition after phase correction.

Iteration: The above steps are iterated, and the result of the matching and merging of the k-th chip after the reverse order is:

为逆序后前k-1个码片合并的结果。in

is the result of combining the first k-1 chips after the reverse order.

求模得到

对于 DSSS-GFSK，为

求模得到

Modulo: Finally, the result of the complete L _s length chip matching and merging of a single DSSS-FSK signal can be obtained. For DSSS-CPFSK, it is

get the modulo

For DSSS-GFSK, it is

get the modulo

Specifically, in step S3, for the DSSS-CPFSK/DSSS-GFSK signal after the spectrum spread, if the hard demodulation method is adopted, the information bits before the spectrum spread can be written as:

If soft demodulation is adopted, the soft information can be written as:

In order to verify the effectiveness of the designed incoherent despreading and demodulation method proposed in the embodiment of the present invention, further simulation experiments are performed, as follows:

Under the AWGN channel, for the commonly used DSSS-CPFSK signal demodulation with h=0.5, the curve of BER performance versus SNR under uncoded conditions of different demodulation and despreading schemes is plotted, as shown in Figure 4. In this example, "+ ” mark, the combination of differential demodulation and soft decoding is marked with “0”, and different line shapes are used to distinguish the performance curves under different spreading code lengths L _s = {4, 8, 16, 32}, the abscissa represents SNR, the vertical axis The coordinates represent BER. It can be seen from the figure that in this embodiment, a spread spectrum gain of about 3dB can be obtained at BER=10 ⁻⁴ , while the traditional scheme of separating despreading and demodulation can only achieve a spread spectrum gain of 1;2dB. When the length of the spreading code is 4, this scheme has a performance gain of 3dB compared to the comparison scheme, and when the length of the spreading code is 32, this scheme has a performance gain of 6dB compared to the comparison scheme. And considering that the spreading codes at the transceiver end are known, the demodulation complexity of this scheme is similar to that of envelope detection, except for an additional phase correction step. The single-symbol matched filter bank used in this scheme can multiplex the baseband waveform stored by the look-up table method in the baseband modulation part, so the storage complexity can be further saved. In addition, the length and value of the spreading code in this scheme can be arbitrarily configured without requiring the receiving end to regenerate the matching reference waveform corresponding to the spreading sequence, which further improves flexibility.

The same or similar reference numbers correspond to the same or similar parts;

The positional relationship described in the accompanying drawings is only for exemplary illustration, and should not be construed as a limitation on this patent;

Obviously, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those of ordinary skill in the art, changes or modifications in other different forms can also be made on the basis of the above description. There is no need and cannot be exhaustive of all implementations here. Any modifications, equivalent replacements and improvements made within the spirit and principle of the present invention shall be included within 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 alpha_iE { -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 is_m＝Δ_f/B_wAs a modulation factor, Δ_fIs the frequency difference of two frequency points, B_wChip 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 filter_c(n) is the response length L_c1, a rectangular filter of normalized symbol length, whose expression is:

the expression for the kth symbol of the CPFSK signal is thus:

wherein θ_k-1Accumulated phase of the first k-1 term, a_kN/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 h_g(n) is the response length L_gThe 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, L_gThe 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 θ_k-1Is the accumulated phase of the first k-1 term, φ (n; BT; α)_k-1α_kα_k+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 0,1_mThe 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:

representing the relative additional phase introduced by the current symbol q e 0,1 for subsequent symbols.

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 L_MThe 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 is_MThe 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 packet_s-complex baseband signal sample points of reverse order of k +1 chip symbols;

single symbol matching: taking into account the spreading sequence D_sKnown at the receiving end and therefore only needs to be done for L_sThe 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 obtained_sThe 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; SNR_h＝|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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