CPM iterative equalization method based on UAMP algorithm

Abstract

The invention relates to the technical field of wireless communication, in particular to a CPM iterative equalization method based on a UAMP algorithm, which comprises the following steps: step A, inserting two tail symbols into a sending symbol sequence, placing tail data as CP at a frame header position, modulating the frame data into a baseband CPM signal, and finally loading the modulated signal to a carrier for transmission; step B, removing CP from the received baseband signal and then constructing a corresponding received signal matrix model, and performing unitary transformation on the matrix model; c, performing factorization on a joint posterior probability density function of a to-be-estimated variable in the system model after unitary transformation to obtain a corresponding factor graph model; step D, designing a CPM iterative equalization algorithm based on UAMP for the factor graph model in the step C, and obtaining an estimated value of the sent data; e, repeating the step D until the algorithm converges; according to the invention, CPM signal equalization with low complexity and high performance is realized.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a CPM iterative equalization method based on a UAMP algorithm. Background Art

[0002] Continuous phase modulation (CPM) plays an important role in the field of wireless communications. The advantages of CPM signals mainly include constant envelope and continuous phase change, which make it more robust to nonlinear amplifiers, thus making the power amplifier design more flexible. In addition, the spectral compactness of CPM signals means that it has higher spectrum utilization, which is especially important in environments where spectrum resources are scarce. Therefore, CPM has been widely used in mobile communications, satellite communications, aerospace, Internet of Things, and synaesthesia.

[0003] However, the excellent characteristics of CPM signals also bring great challenges to the design of receivers. The numerous modulation parameters and the memory characteristics of CPM signals require more complex processing technology for CPM signal receivers. Especially in multipath fading channels, CPM signals are subject to severe inter-symbol interference (ISI), which further increases the difficulty of processing CPM signals. Turbo equalization can effectively eliminate ISI and improve the equalization performance of signals through iteration between the equalizer and the decoder. Its structure includes two grid-based detectors, one of which is dedicated to equalization and the other is used for channel decoding, and external information is exchanged through the BCJR algorithm. Subsequently, some scholars combined the linear filter-based equalizer with the channel decoding technology to achieve performance similar to that of the grid-based algorithm, while greatly reducing the computational complexity. However, the original Turbo equalization method is only applicable to linear modulation signals and cannot be directly applied to nonlinear CPM signals. Therefore, many scholars are committed to Turbo equalization for CPM signals.

[0004] For the turbo equalization of CPM signals, some scholars have proposed a turbo linear equalizer (TLE) based on Laurent decomposition. However, the algorithm complexity is high and the turbo gain is not significant. In contrast, the dual turbo iterative equalizer based on the minimum mean square error (MMSE) and soft interference cancellation (SIC) algorithm integrates equalization, CPM demodulation and channel decoding. By changing the number of back-end iterations after each front-end iteration, the prior information of the next round of front-end iteration is improved, thereby improving the algorithm performance and accelerating the iterative convergence speed. Subsequently, this method was further extended to the frequency domain, achieving performance similar to that of time domain equalization while reducing the algorithm complexity. In addition, some scholars have adopted a method based on MMSE / SIC to eliminate the self-interference caused by Laurent decomposition. However, the above works are all based on the MMSE algorithm, which treats each transmission symbol as a Gaussian variable, resulting in serious performance loss of the equalizer. In order to avoid the defects related to the MMSE algorithm, some scholars adopted a non-coherent detection algorithm and used the survivor path processing (PSP) algorithm to reduce the memory length of the channel and CPM signal. Although this can reduce the complexity of the grid-based equalizer algorithm, its complexity is still a huge challenge compared with the MMSE-based algorithm.

[0005] In summary, the existing MMSE-based CPM equalization algorithm has serious performance loss, and the incoherent detection algorithm is too complex to be applied in practice. Therefore, it is very important to propose a CPM equalization algorithm with low complexity and high accuracy. Summary of the invention

[0006] The purpose of the present invention is to overcome the shortcomings of the prior art and avoid the high complexity of the incoherent detection algorithm which is difficult to apply in practice, and propose a CPM iterative equalization method based on the UAMP algorithm. The present invention realizes low-complexity and high-performance CPM signal equalization.

[0007] The object of the present invention is achieved by the following measures: A CPM iterative equalization method based on the UAMP algorithm comprises the following steps:

[0008] Step A: insert two tail symbols into the transmitted symbol sequence, place the tail data as CP at the frame header position, modulate the frame data into a baseband CPM signal, and finally load the modulated signal onto the carrier for transmission;

[0009] Step B, after removing the CP from the received baseband signal, construct a corresponding received signal matrix model, and perform unitary transformation on the matrix model;

[0010] Step C, factoring the joint posterior probability density function of the variables to be estimated in the system model after the unitary transformation to obtain a corresponding factor graph model;

[0011] Step D: for the factor graph model in step C, design a CPM iterative equalization algorithm based on UAMP and obtain an estimated value of the transmitted data;

[0012] Step E: Repeat step D until the algorithm converges.

[0013] Preferably, in step A, the length N of the inserted cyclic prefix CP is P Greater than the channel memory length L c , and insert two N-length K The end symbol of .

[0014] Preferably, the two lengths N are inserted into the transmitted symbol sequence. K The method of the tail symbol is:

[0015] Step A1: Divide the data symbol α with a transmission length of N in the j-th transmission data block into two segments: The superscript (j) indicates the jth data block;

[0016] Step A2: and The length of the subsequent insertions is N K The tail symbol and The length of the formation is The data block:

[0017] Step A3: Block the data As CP put In front, the length is The sending data block:

[0018]

[0019] The corresponding CPM baseband signal is expressed as:

[0020]

[0021] Where E s and T represent symbol energy and symbol duration respectively, represents the modulation phase, which is expressed as:

[0022]

[0023] Where h = Q / P represents the modulation index, Q and P are mutually prime, and g(t) is the phase shaping function that satisfies the following relationship:

[0024]

[0025] Where ω(t) represents a frequency pulse function with a duration of LT. Commonly used pulse functions include raised cosine pulses, rectangular pulses, and Gaussian pulses. At time t∈[nT,(n+1)T], the modulation phase expression can be further written as:

[0026]

[0027] in It represents the accumulated phase. When Q is an even number or an odd number, it has P or 2P possible values ​​respectively. Represents the instantaneous phase, which has M L possible values. n When there are 2P values, the phase trajectory of the CPM signal is time-varying. In order to obtain a time-invariant phase trajectory, the CPM signal phase can be converted into a tilted phase:

[0028]

[0029] The corresponding tilted CPM signal is:

[0030] y(t,α)=x(t,α)e jph(M-1)t / T

[0031] At this time q n No matter Q is an odd number or an even number, there are only P possible values ​​for it.

[0032] The CPM signal state at time n is defined as:

[0033] ∈ n = {q n ,a n-1 ,...,a n-L+1}

[0034] At this time, the CPM signal at the time [nT, (n+1)T] can be n and the current input symbol a n Mapping, the corresponding y(t,α) has a total of PM L The possible values ​​are recorded as follows:

[0035]

[0036] At the same time, you can also get the state of the next moment:

[0037] ∈ n+1 = {q n+1 ,a n ,...,a n-L+2}

[0038] q n+1 It can be obtained by the following recursive formula:

[0039]

[0040] in

[0041]

[0042] Represents the correction symbol, and its value set is {0,1,...,M-1}.

[0043] Preferably, in step B, under the interference of inter-symbol interference (ISI) and additive white Gaussian noise (AWGN), the model of the received signal is:

[0044]

[0045] where h m represents the correlation gain of the mth propagation path, v(t) represents a mean of 0 and a variance of s 2 Additive Gaussian white noise; for the received signal at time t = (kn + i) T s Discretize, where k and T s Respectively represent the number of sampling points and sampling period of each symbol, i∈{0,1,...,k-1}, the discretized received signal is expressed as:

[0046]

[0047] in:

[0048]

[0049] The superscripts and subscripts in symbols are as follows represents the i-th sampling point in the n-th symbol time, and the corresponding discretized tilted CPM signal is:

[0050]

[0051] in

[0052] After removing the CP, the received signal can be represented by the following matrix form:

[0053] r=Hx+v

[0054] The channel matrix H is the first column of Size The circulant matrix, and The channel matrix H can be decomposed by singular value decomposition SVD to H = UΛV, and the unitary transformation of the received signal can be obtained:

[0055] z=UH r=Φx+w

[0056] Where Φ=U H H=ΛV, Λ is the value of The diagonal matrix of H v and has the same mean and variance as v. Since H is a circulant matrix, it can be diagonalized using the discrete Fourier transform (DFT) matrix and its inverse matrix. In this case, we can set U = F H And V = F, where F is the size of The DFT matrix of Fh0 is shown in Figure 2. And Λ can be obtained by Λ=diag(Fh0).

[0057] Preferably, in step C, according to the matrix model after the unitary transformation of the CPM signal, under the given observation variable z, the joint posterior probability density function distribution of the original bit sequence b, the encoded data c, the mapped symbol α, the baseband CPM signal x, the tilted CPM signal y and the CPM state ∈ can be factorized as follows:

[0058]

[0059] in

[0060]

[0061] Represents a factor node and polymerization, It indicates the information transmitted by observation. represents the hard constraint relationship between the CPM signal and the tilted CPM signal, Represents the modulation relationship of the CPM signal, Indicates the CPM signal state transition relationship, represents the mapping constraint, f c (b,c) represents the encoding constraints, Represents the prior information of bits;

[0062] According to the factor decomposition results and the factor graph construction rules, the factor graph model corresponding to the CPM receiving signal matrix model under ISI and AWGN interference is obtained.

[0063] Preferably, the step D specifically comprises the following steps:

[0064] Step D1: Use the UAMP algorithm to calculate the right-hand output message of the equalizer on the factor graph of the joint posterior probability density function distribution.

[0065] Step D2: Using the BP rule, calculate the right output message of the CPM signal demodulator on the factor graph of the joint posterior probability density function distribution

[0066] Step D3: Use the BCJR algorithm to calculate the posterior probability of the decoder's original bit sequence b and the extrinsic information of the coded bits on the factor graph of the joint posterior probability density function distribution.

[0067] Step D4: Using the BP rule, calculate the left output of the demodulator, i.e., the input message of the equalizer, on the factor graph of the joint posterior probability density function distribution.

[0068] Preferably, the step D1 specifically includes the following:

[0069] Using the UAMP algorithm, the right-hand output message of the equalizer is calculated on the factor graph distributed by the joint posterior probability density function

[0070]

[0071] Preferably, the step D2 specifically includes the following:

[0072] Using the BP rule, the right-hand output message of the CPM signal demodulator is calculated on the factor graph of the joint posterior probability density function distribution

[0073]

[0074] Preferably, the step D3 specifically includes the following:

[0075] Using the BCJR algorithm, the posterior probability of the decoder's original bit sequence b and the extrinsic information of the coded bits are calculated on the factor graph of the joint posterior probability density function distribution.

[0076]

[0077] Preferably, the step D4 specifically includes the following:

[0078] Using the BP rule, the left output of the demodulator, i.e. the input message of the UAMP algorithm, is calculated on the factor graph of the joint posterior probability density function distribution.

[0079]

[0080] Beneficial effects of the present invention: The present invention constructs a cyclic channel matrix H by inserting CP at the transmitting end, and uses the DFT matrix and its inverse matrix to realize the diagonalization of the channel matrix H, and then uses the unitary transformation to process the received signal model. On this basis, a factor graph representation method is proposed, and the corresponding message passing algorithm is derived by combining the UAMP algorithm and the BP rule. Numerical results show that the algorithm significantly surpasses the existing iterative equalization algorithm in bit error rate performance while maintaining a low complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is a flow chart of the present invention;

[0082] Figure 2 Figure 1 is a diagram of the data frame structure sent by CPM in the presence of CP;

[0083] Figure 3 It is a schematic diagram of the factor graph model;

[0084] Figure 4 BER performance curves of different algorithms;

[0085] Figure 5 The graphs show the convergence curves of BER of different algorithms with the number of iterations. DETAILED DESCRIPTION

[0086] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0087] Example 1: Figure 1 As shown, a CPM iterative balancing method based on the UAMP algorithm includes the following steps:

[0088] Step A: insert two tail symbols into the transmitted symbol sequence, and place the tail data as CP at the frame header position, then modulate the frame data into a baseband CPM signal, and finally load the modulated signal onto the carrier for transmission;

[0089] Step B, after removing the CP from the received baseband signal, construct a corresponding received signal matrix model, and then perform a unitary transformation on the matrix model;

[0090] Step C, factoring the joint posterior probability density function of the variables to be estimated in the system model after the unitary transformation to obtain a corresponding factor graph model;

[0091] Step D: Design a CPM iterative equalization algorithm based on UAMP for the factor graph model in step C, and obtain an estimated value of the transmitted data;

[0092] Step E: Repeat step D until the algorithm converges.

[0093] In step A, for CPM signals, in addition to ensuring that the length N of the cyclic prefix (CP) is inserted P Greater than the channel memory length L c In addition, two additional N-length K The tail symbol is used to ensure the phase continuity of the CPM signal within and between transmitted data blocks. Specifically,

[0094] Step A1: Divide the data symbol α with a transmission length of N in the j-th transmission data block into two segments: The superscript (j) indicates the jth data block;

[0095] Step A2: and The length of the subsequent insertions is N K The tail symbol and This forms a length of The data block:

[0096] Step A3: Block the data As CP put In front, form Figure 2 Length shown is The sending data block:

[0097]

[0098] The corresponding CPM baseband signal can be expressed as:

[0099]

[0100] Where E s and T represent symbol energy and symbol duration respectively, represents the modulation phase, which is expressed as:

[0101]

[0102] Where h = Q / P (Q and P are mutually prime) represents the modulation index, and g(t) is the phase shaping function that satisfies the following relationship:

[0103]

[0104] Where ω(t) represents a frequency pulse function with a duration of LT. Commonly used pulse functions include raised cosine pulses, rectangular pulses, and Gaussian pulses. At time t∈[nT,(n+1)T], the modulation phase expression can be further written as:

[0105]

[0106] in It represents the accumulated phase. When Q is an even number or an odd number, it has P or 2P possible values ​​respectively. Represents the instantaneous phase, which has M L possible values. n When there are 2P values, the phase trajectory of the CPM signal is time-varying. In order to obtain a time-invariant phase trajectory, the CPM signal phase can be converted into a tilted phase:

[0107]

[0108] The corresponding tilted CPM signal is:

[0109] y(t,α)=x(t,α)e jph(M-1)t / T

[0110] At this time q n No matter Q is an odd number or an even number, there are only P possible values ​​for it.

[0111] The CPM signal state at time n is defined as:

[0112] ∈ n = {q n ,a n-1 ,...,a n-L+1}

[0113] At this time, the CPM signal at the time [nT, (n+1)T] can be n and the current input symbol a n Mapping, the corresponding y(t,α) has a total of PM L The possible values ​​are recorded as follows:

[0114]

[0115] At the same time, you can also get the status of the next moment

[0116] ∈ n+1 = {q n+1 ,a n ,...,a n-L+2}

[0117] q n+1 It can be obtained by the following recursive formula:

[0118]

[0119] in

[0120]

[0121] Represents the correction symbol, and its value set is {0,1,...,M-1}.

[0122] In step B, under the condition of ISI and AWGN interference, the model of the received signal can be written as:

[0123]

[0124] where h m represents the correlation gain of the mth propagation path, v(t) represents a mean of 0 and a variance of s 2 Additive Gaussian white noise. For the received signal at time t = (kn + i)T s Discretize, where k and T s Respectively represent the number of sampling points and sampling period of each symbol, i∈{0,1,...,k-1}, then the discretized received signal can be expressed as:

[0125]

[0126] in:

[0127]

[0128] The superscripts and subscripts in symbols are as follows represents the i-th sampling point in the n-th symbol time. The corresponding discretized tilted CPM signal can be written as:

[0129]

[0130] in

[0131] After removing the CP, the received signal can be represented by the following matrix form:

[0132] r=Hx+v

[0133] The channel matrix H is the first column of Size The circulant matrix, and The channel matrix H can be decomposed by singular value decomposition (SVD) to H = UΛV, so the unitary transformation of the received signal can be obtained:

[0134] z=U H r=Φx+w

[0135] Where Φ=U H H=ΛV, Λ is the value of The diagonal matrix of H v and has the same mean and variance as v. Since H is a circulant matrix, it can be diagonalized using the discrete Fourier transform (DFT) matrix and its inverse matrix. In this case, we can set U = F H And V = F, where F is the size of The DFT matrix of Fh0 is shown in Figure 2. And Λ can be obtained by Λ=diag(Fh0).

[0136] In step C, according to the matrix model after unitary transformation of the CPM signal, given the observation variable z, the joint posterior probability density function distribution of the original bit sequence b, the encoded data c, the mapped symbol α, the baseband CPM signal x, the tilted CPM signal y and the CPM state ∈ can be factorized as follows:

[0137]

[0138] in

[0139]

[0140] Represents a factor node and polymerization, It indicates the information transmitted by observation. represents the hard constraint relationship between the CPM signal and the tilted CPM signal, Represents the modulation relationship of the CPM signal, Indicates the CPM signal state transition relationship, represents the mapping constraint, f c (b,c) represents the encoding constraints, Represents the prior information of bits.

[0141] like Figure 3 As shown, according to the factor graph model construction rules, the factor graph model corresponding to the CPM receiving signal matrix model under ISI and AWGN interference is obtained.

[0142] Based on the above, step D specifically includes the following 4 steps:

[0143] Step D1: Use the UAMP algorithm to calculate the right-hand output message of the equalizer on the factor graph of the joint posterior probability density function distribution.

[0144] Step D2: Using the BP rule, calculate the right output message of the CPM signal demodulator on the factor graph of the joint posterior probability density function distribution

[0145] Step D3: Use the BCJR algorithm to calculate the posterior probability of the decoder's original bit sequence b and the extrinsic information of the coded bits on the factor graph of the joint posterior probability density function distribution.

[0146] Step D4: Using the BP rule, calculate the left output of the demodulator, i.e., the input message of the equalizer, on the factor graph of the joint posterior probability density function distribution.

[0147] Step D1 specifically includes:

[0148] Using the UAMP algorithm, the right-hand output message of the equalizer is calculated on the factor graph distributed by the joint posterior probability density function First, according to the UAMP algorithm, the input parameters include: the received signal z after unitary transformation, the channel matrix H, and the noise variance s 2 , the expectation of the last estimated value of the estimated symbol and variance t x ; UAMP algorithm initialization parameters include: equalizer output expectation q = 0 and variance τ q =1, intermediate variable s=0, The prior probability And define: λ=diag(ΛΛ H 1). First, calculate the confidence of symbol x based on the result of the previous iteration (initialization data is used for the first iteration) The mean Obtained by the following formula:

[0149]

[0150] Variance t x Obtained by the following formula:

[0151]

[0152] In the above steps Represents the normalized probability:

[0153]

[0154] in:

[0155]

[0156] in express The prior probability of is updated by step C4 (initialization data is used for the first time). Then the following UAMP algorithm iteration process is performed:

[0157] τ p =t x λ

[0158]

[0159] τ s =1. / (τ p +s 2 1)

[0160] s=τ s ×(zp)

[0161]

[0162] Finally, we get the output message of UAMP algorithm

[0163] Step D2 specifically includes:

[0164] Using the BP rule, the right-hand output message of the CPM signal demodulator is calculated on the factor graph of the joint posterior probability density function distribution First, the right message in the demodulator It can be calculated as:

[0165]

[0166] In order to facilitate derivation, all variable nodes y n Passed to factor node The message is recorded as The corresponding reverse message is recorded as At this time, the downlink message of the CPM signal demodulator can be calculated as:

[0167]

[0168] Its initial value is:

[0169]

[0170] Where p(∈ -1 ) represents ∈ -1 The prior distribution of the states, which is usually known. The path metric representing CPM can be calculated using the following formula:

[0171]

[0172] Indicates symbol a n The prior information is based on the external information output by the decoder in step D3. Update. In addition It represents the state transition relationship, and its value is either 0 or 1. This relationship is implicit in the final expression. Similarly, the uplink message of the CPM signal demodulator can be calculated as:

[0173]

[0174] Its initial value is:

[0175]

[0176] The final right-hand output of the demodulator can be calculated as:

[0177]

[0178] Step D3 specifically includes:

[0179] Using the BCJR algorithm, the posterior probability of the decoder's original bit sequence b and the extrinsic information of the coded bits are calculated on the factor graph of the joint posterior probability density function distribution. It can be obtained by the following formula:

[0180]

[0181] Will be sent to the BCJR decoder, and then the external information will be updated according to the output of the decoder and the posterior probability of b.

[0182] Step D4 specifically includes:

[0183] Using the BP rule, the left output of the demodulator, i.e. the input message of the equalizer, is calculated on the factor graph of the joint posterior probability density function distribution. First, the left message of the demodulator It can be calculated as:

[0184]

[0185] in:

[0186]

[0187] at this time It can be calculated as:

[0188]

[0189] according to You can get the left output message of the demodulator That is, the input message of the equalizer is:

[0190]

[0191] A comparison between the transmission scheme of the present invention and other existing transmission schemes is given below to make the advantages and features of the present invention more obvious.

[0192] Setting of simulation parameters: The modulation order of CPM is set to M=4, the correlation length is L=2, the modulation index is h=1 / 3, and the frequency pulse uses a raised cosine shaped pulse. Two different channels are selected: the TU-6 channel (channel 1) and the Proakis'C channel (channel 2) with more severe fading. It is assumed that each frame experiences independent multipath fading, and the channel response remains constant within a frame. In addition, it is assumed that the receiver is perfectly synchronized. The normalized energy of channel 1 is: [0.189, 0.379, 0.255, 0.090, 0.055, 0.032], and the corresponding path delay is: [0, T s ,2T s ,8T s ,12T s ,25T s ], the length of CP in this channel is set to N P =13. The normalized energy of channel 2 is: [0.227, 0.460, 0.688, 0.460, 0.227], and the corresponding path delay is: [0, T s ,2T s ,3T s ,4T s ], the length of CP in this channel is set to N P =2. The number of sampling points in each symbol period is set to k = 2. The channel coding uses a recursive system convolutional code with a generating polynomial of [5,7]8, a code rate of 1 / 2, and pseudo-random interleaving. The length of the transmitted data N is set to 508, and the length of the tail symbol data is N K =2. Therefore, the sequence length after inserting the tail symbol data is

[0193] Figure 4 The bit error rate (BER) performance curves of different algorithms are shown in Figure 2, where the number of iterations is 20. The simulation results show that the proposed algorithm is better than the comparison algorithm under different channel models. In particular, when the BER is 10 -5 The performance of the proposed algorithm in channel 1 and channel 2 is improved by about 1.5dB and 1.7dB respectively compared with the traditional MMSE / SIC-based algorithm. Table 1 shows the complexity comparison of different algorithms, where n is the number of iterations, L f is the filter length of the TDE equalizer. It can be seen from the table that the complexity of the proposed algorithm is only comparable to that of the MMSE / SIC-FDE algorithm.

[0194] Table 1

[0195]

[0196] Figure 5 The BER of different algorithms converges with the number of iterations. b / N0 is set to 4dB and 6.5dB respectively. The simulation results show that under channel 1, the convergence speed of the proposed algorithm is the same as that of the algorithm based on MMSE / SIC, and all algorithms reach convergence after 6 iterations. However, under channel 2 with more severe conditions, the proposed algorithm reaches convergence after 7 iterations, while the algorithm based on MMSE / SIC requires more iterations, and the BER becomes stable after about 10 iterations.

[0197] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A CPM iterative equalization method based on the UAMP algorithm, characterized in that: The steps include: Step A: insert two tail symbols into the transmitted symbol sequence, place the tail data as CP at the frame header position, modulate the frame data into a baseband CPM signal, and finally load the modulated signal onto the carrier for transmission; Step B, after removing the CP from the received baseband signal, construct a corresponding received signal matrix model, and perform unitary transformation on the matrix model; Step C, factoring the joint posterior probability density function of the variables to be estimated in the system model after the unitary transformation to obtain a corresponding factor graph model; Step D: for the factor graph model in step C, design a CPM iterative equalization algorithm based on UAMP and obtain an estimated value of the transmitted data; Step E: Repeat step D until the algorithm converges.

2. The CPM iterative equalization method based on the UAMP algorithm according to claim 1, characterized in that: In step A, the length N of the cyclic prefix CP is inserted P Greater than the channel memory length L c , and insert two N-length K The end symbol of .

3. The CPM iterative equalization method based on the UAMP algorithm according to claim 2, characterized in that: The two lengths N are inserted into the transmitted symbol sequence. K The method of the tail symbol is: Step A1: Divide the data symbol α with a transmission length of N in the j-th transmission data block into two segments: The superscript (j) indicates the jth data block; Step A2: and The length of the subsequent insertions is N K The tail symbol and The length of the formation is The data block: Step A3: Block the data As CP put In front, the length is The sending data block:

4. The CPM iterative equalization method based on the UAMP algorithm according to claim 1, characterized in that: In step B, the model of the received signal is: where h m represents the correlation gain of the mth propagation path, v(t) represents a mean of 0 and a variance of s 2 Additive Gaussian white noise; for the received signal at time t = (kn + i) T s Discretize, where k and T s Respectively represent the number of sampling points and sampling period of each symbol, i∈{0,1,...,k-1}, the discretized received signal is expressed as: in: The superscripts and subscripts in symbols are as follows represents the i-th sampling point in the n-th symbol time, and the corresponding discretized tilted CPM signal is: in After removing the CP, the received signal can be represented by the following matrix form: r=Hx+v The channel matrix H is the first column of Size The circulant matrix, and The channel matrix H can be decomposed by singular value decomposition SVD to H = UΛV, and the unitary transformation of the received signal can be obtained: z=U H r=Φx+w Where Φ=U H H=ΛV, Λ is the value of The diagonal matrix of H v and has the same mean and variance as v.

5. The CPM iterative equalization method based on the UAMP algorithm according to claim 1, characterized in that: In step C, according to the matrix model after the unitary transformation of the CPM signal, under the given observation variable z, the joint posterior probability density function distribution of the original bit sequence b, the encoded data c, the mapped symbol α, the baseband CPM signal x, the tilted CPM signal y and the CPM state ∈ can be factorized as follows: in Represents a factor node and polymerization, It indicates the information transmitted by observation. represents the hard constraint relationship between the CPM signal and the tilted CPM signal, Represents the modulation relationship of the CPM signal, Indicates the CPM signal state transition relationship, represents the mapping constraint, f c (b,c) represents the encoding constraints, Represents the prior information of bits; According to the factor decomposition results and the factor graph construction rules, the factor graph model corresponding to the CPM receiving signal matrix model under ISI and AWGN interference is obtained.

6. The CPM iterative equalization method based on the UAMP algorithm according to claim 1, characterized in that: The step D specifically comprises the following steps: Step D1: Use the UAMP algorithm to calculate the right-hand output message of the equalizer on the factor graph of the joint posterior probability density function distribution. Step D2: Using the BP rule, calculate the right output message of the CPM signal demodulator on the factor graph of the joint posterior probability density function distribution Step D3: Use the BCJR algorithm to calculate the posterior probability of the decoder's original bit sequence b and the extrinsic information of the coded bits on the factor graph of the joint posterior probability density function distribution. Step D4: Using the BP rule, calculate the left output of the demodulator, i.e., the input message of the equalizer, on the factor graph of the joint posterior probability density function distribution.

7. The CPM iterative equalization method based on the UAMP algorithm according to claim 1, characterized in that: The step D1 specifically includes the following: Using the UAMP algorithm, the right-hand output message of the equalizer is calculated on the factor graph distributed by the joint posterior probability density function 8. The CPM iterative equalization method based on the UAMP algorithm according to claim 5, characterized in that: The step D2 specifically includes the following: Using the BP rule, the right-hand output message of the CPM signal demodulator is calculated on the factor graph of the joint posterior probability density function distribution 9. The CPM iterative equalization method based on the UAMP algorithm according to claim 5, characterized in that: The step D3 specifically includes the following: Using the BCJR algorithm, the posterior probability of the decoder's original bit sequence b and the extrinsic information of the coded bits are calculated on the factor graph of the joint posterior probability density function distribution.

10. The CPM iterative equalization method based on the UAMP algorithm according to claim 5, characterized in that: The step D4 specifically includes the following: Using the BP rule, the left output of the demodulator, i.e. the input message of the UAMP algorithm, is calculated on the factor graph of the joint posterior probability density function distribution.

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