Active user detection and data decoding method of asynchronous massive machine type communication system

Abstract

The invention belongs to the technical field of information and communication, and relates to an active user detection and data decoding method of an asynchronous massive machine type communication system. Aiming at the problem that the detection and estimation performance is reduced due to unknown user time delay in asynchronous transmission, the method comprises the following steps: initial estimation and preprocessing: detecting initial active users and transmission time delay thereof through correlation peaks, and whitening received signals; the iterative joint detection and channel estimation module is used for iteratively updating channel information and data symbol information for multiple rounds based on a factor graph and a message passing algorithm; the data decoding module is used for decoding data based on a soft decision device; the detection and decoding performance is improved by transmitting external information among the modules; and the time delay parameter updating adopts a greedy search algorithm to obtain the optimal time delay. According to the method, the active user detection rate, the channel estimation precision and the data decoding accuracy under the condition that the receiving and transmitting ends are completely asynchronous are improved.

Description

Technical Field

[0001] The present invention belongs to the field of information and communication technology, and relates to an active user detection and data decoding method for an asynchronous massive machine type communication system. Background Art

[0002] Massive Machine-Type Communications (mMTC) is one of the three primary use cases identified by the Third Generation Partnership Project (3GPP) for 5G networks. In mMTC, access points (APs) need to provide connectivity for a large number of low-power, low-cost devices. However, their uplink activity is sporadic: they remain in sleep mode for extended periods to conserve energy. Only when triggered by external events do a small number of devices activate and send short data packets to the AP. Because data packets from different devices arrive at the AP at different times, the AP must be able to dynamically detect active devices, estimate their channels, and recover the data they are transmitting.

[0003] In existing mobile communication systems, the commonly used random access method is grant-based slotted ALOHA. Specifically, when a user needs to establish a connection with a base station, the user randomly selects a preamble sequence from a pool of orthogonal preamble sequences and sends it to the base station. Once the base station successfully detects the preamble sequence, the user can then send data to the base station. However, due to the limited number of orthogonal preamble sequences in the sequence pool, in massive machine-type communication scenarios, there is a high probability that multiple active devices will select the same sequence, leading to access conflicts and failures. Furthermore, the complex signaling exchanges in grant-based random access methods make them unsuitable for massive machine-type communication scenarios. In the paper C. Wei, H. Liu, Z. Zhang, J. Dang, and L. Wu, “Approximate messagepassing-based joint user activity and data detection for noma,” IEEE Commun. Lett., vol. 21, no. 3, pp. 640–643, 2017, the authors proposed a grant-free random access scheme based on approximate message passing (AMP) and expectation maximization (EM). AMP is used to calculate the posterior mean and variance of transmitted symbols, and EM is used to estimate user activity parameters. Compared to grant-based random access, this scheme significantly reduces the complexity of signaling exchanges. In the literature B. Wang, L Dai, Y. Zhang, T. Mir, and J. Li, “Dynamic compressive sensing-based multi-user detection for uplink grant-free noma,” IEEE Commun. Lett., vol. 20, no. 11, pp. 2320-2323, 2016, the authors proposed a multi-active device detection algorithm based on dynamic compressive sensing, which can simultaneously detect active devices and their data in multiple consecutive time slots. Recently, in the literature RB Di Renna and RC de Lamare. “Joint channel estimation. activity detection and data decoding based on dynamic message-scheduling strategies for mmtc,” IEEE Trans. Commun., vol. 70, no. 4, pp. 24642479, 2022, the authors proposed an AMP-based joint active device detection, channel estimation and data decoding method.However, existing unlicensed random access methods all assume that devices and APs transmit data in a fully or partially synchronized manner. That is, the transmission time delay is fully or partially known on the AP side, and active devices have compensated for the time delay in advance when sending data to avoid the impact of different delays on the transmitted data. This assumption is too idealistic. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem of degradation of active user detection and data decoding performance due to unknown user transmission delay in an asynchronous massive machine type communication system.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical means:

[0006] The present invention provides a novel receiver suitable for asynchronous massive machine type communication system, comprising N R A receiving antenna and does the following:

[0007] Based on the sliding listening window technology to process the received signal, within any sliding window, the nth R The oversampled discrete signal of the receiving antenna is expressed as:

[0008]

[0009] For all N R The signals of the receiving antennas are jointly modeled to obtain the system receiving matrix:

[0010]

[0011] Joint estimation and detection of active users, channels, and data under fully asynchronous conditions are achieved by solving a joint model.

[0012] Parameter meaning explanation:

[0013] Among them, K is the number of users in the sliding window, α k ∈{0, 1} is the user activity indicator coefficient, For users k to n R The channel gain of the receiving antennas, Indicates that the delay τ k The preamble sequence and data signal vector are as follows: is Gaussian noise, is the Toeplitz matrix whose elements are the discrete sample values ​​of the convolution z(t) of the pulse shaping filter q(t) and the matched filter m(t) The matrix structure is:

[0014]

[0015] F is a Toeplitz matrix with the same structure as Z, whose elements are composed of discrete sample values ​​of the matched filter m(t);

[0016] where X(τ)=[x1(τ1),…,x K (τ K )] is the delay-dependent user signal matrix, G represents the equivalent channel matrix, and W is the noise matrix.

[0017] The present invention also provides an active user detection and data decoding method for an asynchronous massive machine type communication system, comprising the following steps:

[0018] Step 1: Initial estimation and preprocessing: At the receiving end, correlation peak detection is performed on the received signal and all preamble sequences in the preamble sequence pool to preliminarily estimate the set of active users contained in the sliding window and their transmission delays. The received signal is whitened so that the noise covariance matrix after oversampling is a diagonal matrix.

[0019] Step 2: Joint active user detection, channel estimation, and data symbol detection module A:

[0020] Based on the message passing algorithm, the following parameters are updated through multiple rounds of iterations:

[0021] Step 2.1: Calculate Factor Node To the variable node The average message and variance By entering the variable node The posterior mean of the Gaussian distribution is obtained by multiplying the information of and variance and the residual and inverse residual variance

[0022] Step 2.2: Calculate Factor Node To the variable node The average message and variance and update its posterior estimate

[0023] Step 2.3: Calculate Factor Node To variable node b nk The average message With variance v γ，nk , and update its posterior estimate v b,nk , further, calculate the factor node p(b nk |·) to variable node x ik The average message With variance v m，ik, and update its posterior estimate v m，ik ;

[0024] Step 2.4: Based on the estimated channel gain power and the preset threshold η th The comparison result is used to update the user activity indicator coefficient

[0025] Step 2.5: When the iterative convergence condition is met, that is, If the value is less than the set threshold, the process ends; otherwise, go to step 2.1.

[0026] Step 3, data symbol decoding module B:

[0027] Based on the output of module A, soft input and soft output decoding is performed on the data symbols of each user, the extrinsic information of the data symbols is calculated, and the posterior mean and variance of the data symbols are updated using the constellation point information;

[0028] External information transfer between modules: The external information of module A is used as the prior information of module B, and the external information of module B is fed back to module A to optimize subsequent iterations;

[0029] Step 4: Update the delay parameters: Use a greedy search algorithm to update the transmission delay in each round of global iteration;

[0030] Step 5, global iteration control: In each round of global iteration, module A, module B, and delay update are executed in sequence. If the maximum number of iterations is not reached, steps 2 to 4 are repeated; otherwise, the entire process ends.

[0031] In the above scheme, step 1 is specifically as follows:

[0032] Step 1.1: At the receiving end, perform correlation peak detection on the received signal and all preamble sequences in the preamble sequence pool, and preliminarily estimate the number of active users and their transmission delays within the sliding window to obtain:

[0033] Active user collection:

[0034]

[0035] Delay vector:

[0036]

[0037] Among them, N W Indicates the width of the sliding window, M OSF is the oversampling multiple, K represents the number of users in the sliding window, Indicates the estimated delay of the kth active user The signal below;

[0038] Step 1.2: Perform whitening on the received signal so that the covariance matrix of the oversampled noise is a diagonal matrix.

[0039] In the above scheme, step 2.1 includes the following steps:

[0040] In the u I In each iteration, the following operations are performed:

[0041] Step 2.1.1: For each receiving antenna n R And each data symbol index n, from factor node p Pass to variable node The message can be approximated as a Gaussian distribution with a mean of and variance They are

[0042]

[0043] in, For variable node b nk uth I The posterior mean of the iterations, For variable node b nk uth I The posterior variance of the iteration, For variable nodes uth I The posterior mean of the iterations, For variable nodes uth I The posterior variance of the iteration, For u I -1 iteration residual;

[0044] Step 2.1.2: Compute variable nodes The posterior mean of and variance

[0045]

[0046] Step 2.1.3: Calculate the residual and inverse residual variance

[0047]

[0048] In the above scheme, step 2.2 includes the following steps:

[0049] Step 2.2.1: From the factor node Pass to variable node The message can be approximated as a Gaussian distribution with a mean of and variance They are

[0050]

[0051]

[0052] Step 2.2.2: In the u I Posterior mean during +1 iteration and variance They are

[0053]

[0054] in, ρ is the sparsity, and

[0055]

[0056] Where λ is the path loss, represents a complex Gaussian distribution.

[0057] In the above scheme, step 2.3 includes the following steps:

[0058] In the u I In each iteration, the following operations are performed:

[0059] Step 2.3.1: For each user k and data symbol index n, from the factor node Passed to variable node b nk The message can be approximated as a Gaussian distribution with a mean of and variance They are

[0060]

[0061] Step 2.3.2: For each user k and data symbol index n, from the factor node p(b nk |·) is passed to variable node b nk The message data symbol can be approximated as a Gaussian distribution, with a mean of and variance They are

[0062]

[0063] Among them, z ni represents the elements of the Z matrix, Variable node x ik In the u I The estimated value of the iteration, Represents the variable node x ik In the u IThe variance of the iterations, Indicates the uth I -1 iteration residual;

[0064] Step 2.3.3: Calculate the variable node b through the product operation nk In the u I Posterior mean of +1 iteration and variance They are

[0065]

[0066] Step 2.3.4: In the u I In the iterative process, the factor node p(b nk |·) is passed to the variable node x ik The message can be approximated as a Gaussian distribution with a mean of and variance They are

[0067]

[0068] Step 2.3.5: x ik In the u I Posterior mean during +1 iteration and variance They are

[0069]

[0070] In the above scheme, step 2.5 is specifically as follows:

[0071] If the power of the kth row of matrix G is greater than the set threshold η th , then the kth user is in active state, that is:

[0072]

[0073] in, represents the estimated active state of the k-th user.

[0074] In the above solution, step 3 is specifically as follows:

[0075] For each user k, perform the following operations:

[0076] Step 3.1: Calculate the extrinsic information of the first bit of the data symbol:

[0077]

[0078] Where i represents the data symbol index, Indicates that the kth user is in the uth OThe delay estimate in the delay update iteration, represents the set of constellation points where the lth bit is 1, represents the set of constellation points where the lth bit is 0, For a given x ik Observed The conditional probability, P(x ik ) represents x ik The prior probability of Represents the prior information of module B;

[0079] Step 3.2: Use the external information of module A as the prior information of module B:

[0080]

[0081] Among them, x ik (l) represents the lth bit of the symbol of the kth user at the i-th time, Represents the external information output by module A, Represents the prior information of module B;

[0082] Step 3.3: Output the result according to the soft decoder Calculate the external information of module B:

[0083]

[0084] Step 3.4: Feed the external information of module B back to module A as prior information:

[0085]

[0086] In the above solution, step 4 is specifically as follows:

[0087] Update delay estimates using a greedy search algorithm include:

[0088] Step 4.1: For the i-th element exist Search within the range, ε is the preset search radius;

[0089] Step 4.2: Select the delay estimate that maximizes the following objective function:

[0090]

[0091] Where Z represents the Toeplitz matrix formed by the convolution of the pulse shaping filter and the matched filter,

[0092] Indicates that at the uth o The estimated value of X(τ) at the iteration, Indicates that at the uth O The variance of X(τ) at iterations, Indicates that at the uth O Iteration The variance of Indicates that at the uth O The x of the iteration k (τ k ), Indicates that at the uth O The x of the iteration k (τ k )’s variance.

[0093] Because the present invention adopts the above technical means, it has the following beneficial effects:

[0094] The present invention adopts asynchronous transmission to reduce the signaling overhead required for synchronization between the device and the AP, simplifying the design of the transmitter. On this basis, a joint active user detection, channel estimation and data decoding algorithm with delay calibration function is proposed. The algorithm is based on the EM method: in the expectation step of EM, a joint active user detection, channel estimation and data symbol detection algorithm based on message passing is used to obtain the posterior probability information of the channel and data symbols; in the maximization step of EM, a delay calibration algorithm based on a greedy search algorithm is used to update the time delay. The overall solution proposed by the present invention solves the technical problem of insufficient active user detection and data decoding performance in asynchronous massive machine type communication systems. Numerical results demonstrate the effectiveness of the proposed algorithm in terms of normalized mean square error of channel estimation and data symbol estimation, data bit error rate and false detection probability. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 : System model diagram.

[0096] Figure 2 : Factor graph.

[0097] Figure 3 : Simulation results under different signal-to-noise ratio (SNR) conditions.

[0098] Figure 4 : Simulation results under different numbers of active users. DETAILED DESCRIPTION

[0099] The following is a detailed description of the embodiments of the present invention. Although the present invention will be described and illustrated in conjunction with certain specific embodiments, it should be noted that the present invention is not limited to these embodiments. On the contrary, modifications or equivalent substitutions of the present invention are intended to fall within the scope of the claims of the present invention.

[0100] In addition, in order to better illustrate the present invention, numerous specific details are given in the following detailed description. It will be understood by those skilled in the art that the present invention can also be implemented without these specific details.

[0101] Example 1

[0102] The present invention proposes a novel receiver suitable for asynchronous massive machine type communication systems, aiming to achieve joint estimation and detection of active users, channels and data at the AP end under fully asynchronous conditions.

[0103] System model such as Figure 1 As shown, assuming that AP has N R receiving antennas, serving multiple single-antenna users, where q(t) is the pulse shaping filter, m(t) is the matching filter, and M OSF is the oversampling multiple. Define N PL is the number of available preamble sequences, each preamble sequence is N in length p During the uplink access process, each active user randomly selects a preamble sequence from the preamble sequence pool and sends N D data to the AP, then the AP is on the nth R The signal received by the receiving antenna is:

[0104]

[0105] in, For active user k to AP end n R The channel gain of the receiving antennas; z(t) is the convolution of q(t) and m(t); x k The preamble and data signal sent by the kth active user; τ k is the transmission delay from the kth active user to the AP; It is environmental noise.

[0106] Considering the sliding listening window technology, After sampling any sliding window, we get

[0107]

[0108] Where i and j represent symbol indices, K is the number of users in the sliding window; α k is the user activity indicator coefficient, which is 1 when the user is active, otherwise it is 0; N w is the width of the sliding window;

[0109]

[0110]

[0111] TS is the duration of a symbol. The matrix form of the above formula can be written as:

[0112]

[0113] in, is Gaussian noise; is a Toeplitz matrix, whose structure is:

[0114]

[0115] Since z(t) is symmetric about t=0, Z is a symmetric matrix. It is a Toeplitz matrix structure such as Z composed of m(t).

[0116] Consider all N R receiving antennas, we get:

[0117]

[0118] in,

[0119] Example 2

[0120] In this specific embodiment, considering the ZC sequence as the leading sequence, the nth element in the sequence is exp(-jπvn(n+1) / N P ), n=0, 1, ..., N P -1, v = 1, ..., N P -1, the parameter settings of the specific method are shown in the following table:

[0121] parameter symbol Value Number of receiving antennas <![CDATA[N R ]]> 64 Number of service users 300 Preamble length <![CDATA[N P ]]> 67 Data length <![CDATA[N D ]]> 128 Sliding window length <![CDATA[N W ]]> 245 Number of available preamble sequences <![CDATA[N PL ]]> 64 False alarm probability <![CDATA[P FA ]]> <![CDATA[10 -2 ]]> Pulse shaping filters q(t) Root Raised Cosine Filter Digital modulation QPSK Encoding / decoding method LDPC Coding rate 0.5 Code length 256 bits

[0122] Table 1 Main simulation parameters

[0123] To facilitate those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in the form of an overall step description. According to the above parameter settings, the specific steps of the simulation are as follows: Step 1 to Step 23:

[0124] Step 1: At the receiving end, perform correlation peak detection on the received signal and all the preamble sequences in the preamble sequence pool to preliminarily estimate the number of active users included in the sliding window. and its delay

[0125] Step 2: Whiten the received signal so that the covariance matrix of the oversampled noise is a diagonal matrix.

[0126] Step 3: Define A=BG. Get as Figure 2 The factor graph shown. According to the sum-product algorithm, in the uth I In the iterative process, the factor node Pass to variable node The message can be approximated as a Gaussian distribution, with mean and variance respectively.

[0127]

[0128]

[0129] Step 4: Enter the variable node The posterior mean and variance of the Gaussian distribution are obtained by multiplying the information of

[0130]

[0131] Step 5: Residual and inverse residual variance Calculated as

[0132]

[0133] Step 6: From the factor node Pass to variable node The message can be approximated as a Gaussian distribution, with mean and variance respectively.

[0134]

[0135] Step 7 In the u i The posterior mean and variance in the +1 iteration process are

[0136]

[0137] where ρ is the sparsity, and

[0138]

[0139] Step 8. Similarly, in the uth i In the iterative process, the factor node Passed to variable node b nk The message can be approximated as a Gaussian distribution, with mean and variance respectively.

[0140]

[0141] Step 9: In the u1th iteration, from the factor node p(b nk |·) is passed to variable node b nkThe message can be approximated as a Gaussian distribution, with mean and variance respectively.

[0142]

[0143] Step 10, enter the variable node b nk The information of , and the product, the posterior mean and variance of the Gaussian distribution are

[0144]

[0145] Step 11: Residual and inverse residual variance Calculated as

[0146]

[0147] Step 12: In the u1th iteration, from the factor node p(b nk |·) is passed to the variable node x ik The message can be approximated as a Gaussian distribution, with mean and variance respectively.

[0148]

[0149] Step 13, x ik In the u I The posterior mean and variance in the +1 iteration process are

[0150]

[0151] Step 14: If the power of the kth row of the matrix G is greater than the set threshold η th , then the kth user is in active state, that is:

[0152]

[0153] Step 15: If If the value is less than the set threshold, the process ends; otherwise, go to step 3.

[0154] Step 16: Calculate the log-likelihood ratio of the first bit of the data symbol:

[0155]

[0156] in, Represents τ k In the u O The estimated value during the iteration process.

[0157] Step 17: The external information of module A (i.e., steps 3 to 15) is used as the prior information of module B (i.e., the soft decoder), i.e.

[0158] Step 18: Output the result according to the soft decoder Calculate the external information of module B, that is

[0159] Step 19: The external information of module B is regarded as the prior information of module A, that is,

[0160] Step 20, x ik In the u I The posterior mean and variance in the +1 iteration process are modified as follows:

[0161]

[0162] Among them, x S,j represents the symbol of the j-th constellation point, Indicates the constellation points.

[0163] Step 21: If k=K, then end; otherwise, go to step 16.

[0164] Step 22: Update the delay using the expectation maximization algorithm Update sequentially from the first element to the last one, where the i-th element exist The search is performed within the range, and ε is a small positive real number to reduce the search complexity, so that:

[0165]

[0166] maximum.

[0167] Step 23: If the maximum number of iterations is exceeded, the process ends; otherwise, go to step 3.

[0168] Due to the lack of a completely asynchronous random access algorithm, Figure 3 and Figure 4 The performance comparison between the proposed algorithm and the authorization-based asynchronous random access algorithm UAD-DC proposed in the literature Z.Shao, X.Yuan, RCde Lamare, and Y.Zhang, “User activity detection with delay-calibration for asynchronous massive random access,” 2024 is shown. Since the UAD-DC algorithm only considers the channel estimation problem, the least squares algorithm is used in the simulation to further estimate the data information. Figure 3 The number of active users K real =75; Figure 4In the example, the signal-to-noise ratio (SNR) is 20 dB. It can be seen that the proposed algorithm has better performance.

Claims

1. A novel receiver suitable for asynchronous massive machine type communication systems, characterized in that: Including N R A receiving antenna and does the following: Based on the sliding listening window technology to process the received signal, within any sliding window, the nth R The oversampled discrete signal of the receiving antenna is expressed as: For all N R The signals of the receiving antennas are jointly modeled to obtain the system receiving matrix: Joint estimation and detection of active users, channels, and data under fully asynchronous conditions are achieved by solving a joint model. Parameter meaning explanation: Among them, K is the number of users in the sliding window, α k ∈{0, 1} is the user activity indicator coefficient, For users k to n R The channel gain of the receiving antennas, Indicates that the delay τ k The preamble sequence and data signal vector are as follows: is Gaussian noise, is the Toeplitz matrix whose elements are the discrete sample values ​​of the convolution z(t) of the pulse shaping filter q(t) and the matched filter m(t) The matrix structure is: F is a Toeplitz matrix with the same structure as Z, whose elements are composed of discrete sample values ​​of the matched filter m(t); where X(τ)=[x1(τ1),…,x K (τ K )] is the delay-dependent user signal matrix, G represents the equivalent channel matrix, and W is the noise matrix.

2. A method for active user detection and data decoding in an asynchronous massive machine type communication system, characterized in that: The following steps are involved: Step 1: Initial estimation and preprocessing: At the receiving end, correlation peak detection is performed on the received signal and all preamble sequences in the preamble sequence pool to preliminarily estimate the set of active users included in the sliding window and their transmission delays. Performing whitening processing on the received signal so that the noise covariance matrix after oversampling is a diagonal matrix; Step 2: Joint active user detection, channel estimation, and data symbol detection module A: Based on the message passing algorithm, the following parameters are updated through multiple rounds of iterations: Step 2.1: Calculate Factor Node To the variable node The average message and variance By entering the variable node The posterior mean of the Gaussian distribution is obtained by multiplying the information of and variance and the residual and inverse residual variance Step 2.2: Calculate Factor Node To the variable node News, mean and variance and update its posterior estimate Step 2.3: Calculate Factor Node To variable node b nk The average message With variance v γ，nk , and update its posterior estimate v b,nk , further, calculate the factor node p(b nk |·) to variable node x ik News, mean With variance v m,ik , and update its posterior estimate v m，ik ; Step 2.4: Based on the estimated channel gain power and the preset threshold η th The comparison result is used to update the user activity indicator coefficient Step 2.5: When the iterative convergence condition is met, that is, If the value is less than the set threshold, the process ends; otherwise, go to step 2.

1. Step 3, data symbol decoding module B: Based on the output of module A, soft input and soft output decoding is performed on the data symbols of each user, the extrinsic information of the data symbols is calculated, and the posterior mean and variance of the data symbols are updated using the constellation point information; External information transfer between modules: The external information of module A is used as the prior information of module B, and the external information of module B is fed back to module A to optimize subsequent iterations; Step 4: Update the delay parameters: Use a greedy search algorithm to update the transmission delay in each round of global iteration; Step 5, global iteration control: In each round of global iteration, module A, module B, and delay update are executed in sequence. If the maximum number of iterations is not reached, steps 2 to 4 are repeated; otherwise, the entire process ends.

3. The method according to claim 2, characterized in that Step 1 is as follows: Step 1.1: At the receiving end, perform correlation peak detection on the received signal and all preamble sequences in the preamble sequence pool, and preliminarily estimate the number of active users and their transmission delays within the sliding window to obtain: Active user collection: Delay vector: Among them, N W Indicates the width of the sliding window, M OSF is the oversampling multiple, K represents the number of users in the sliding window, Indicates the estimated delay of the kth active user The signal below; Step 1.2: Perform whitening on the received signal so that the covariance matrix of the oversampled noise is a diagonal matrix.

4. The method according to claim 3, characterized in that Step 2.1 includes the following steps: In the u I In each iteration, the following operations are performed: Step 2.1.1: For each receiving antenna n R And each data symbol index n, from factor node p Pass to variable node The message can be approximated as a Gaussian distribution with a mean of and variance They are in, For variable node b nk uth I The posterior mean of the iterations, For variable node b nk uth I The posterior variance of the iteration, For variable nodes uth I The posterior mean of the iterations, For variable nodes uth I The posterior variance of the iteration, For u I -1 iteration residual; Step 2.1.2: Compute variable nodes The posterior mean of and variance Step 2.1.3: Calculate residuals and inverse residual variance 5. The method according to claim 4, characterized in that Step 2.2 includes the following steps: Step 2.2.1: From the factor node Pass to variable node The message can be approximated as a Gaussian distribution with a mean of and variance They are express conjugation of; Step 2.2.2: In the u I Posterior mean during +1 iteration and variance They are where ρ is the sparsity, and Where λ is the path loss, represents a complex Gaussian distribution.

6. The method according to claim 5, characterized in that Step 2.3 includes the following steps: In the u I In each iteration, the following operations are performed: Step 2.3.1: For each user k and data symbol index n, from the factor node Passed to variable node b nk The message can be approximated as a Gaussian distribution with a mean of and variance They are Step 2.3.2: For each user k and data symbol index n, from the factor node p(b nk |·) is passed to variable node b nk The message data symbol can be approximated as a Gaussian distribution, with a mean of and variance They are Among them, z ni represents the elements of the Z matrix, Variable node x ik In the u I The estimated value of the iteration, Represents the variable node x ik In the u I The variance of the iterations, Indicates the uth I -1 iteration residual; Step 2.3.3: Calculate the variable node b through the product operation nk In the u I Posterior mean of +1 iteration and variance They are Step 2.3.4: In the u I In the iterative process, the factor node p(b nk |·) is passed to the variable node x ik The message can be approximated as a Gaussian distribution with a mean of and variance They are Step 2.3.5: x ik In the u I Posterior mean during +1 iteration and variance They are 7. The method according to claim 6, characterized in that Step 2.5 is as follows: If the power of the kth row of matrix G is greater than the set threshold η th , then the kth user is in active state, that is: in, represents the estimated active state of the k-th user.

8. The method according to claim 7, characterized in that Step 3 is as follows: For each user k, perform the following operations: Step 3.1: Calculate the extrinsic information of the first bit of the data symbol: Where i represents the data symbol index, represents the delay estimate of the kth user in the u0th delay update iteration, represents the set of constellation points where the lth bit is 1, represents the set of constellation points where the lth bit is 0, For a given x ik Observed The conditional probability, P(x ik ) represents x ik The prior probability of Represents the prior information of module B; Step 3.2: Use the external information of module A as the prior information of module B: Among them, x ik (l) represents the lth bit of the symbol of the kth user at the i-th time, Represents the external information output by module A, Represents the prior information of module B; Step 3.3: Output the result according to the soft decoder Calculate the external information of module B: Step 3.4: Feed the external information of module B back to module A as prior information:

9. The method according to claim 8, characterized in that Step 4 is as follows: Update delay estimates using a greedy search algorithm include: Step 4.1: For the i-th element exist Search within the range, ε is the preset search radius; Step 4.2: Select the delay estimate that maximizes the following objective function: Where Z represents the Toeplitz matrix formed by the convolution of the pulse shaping filter and the matched filter, represents the estimated value of X(τ) at the u0th iteration, represents the variance of X(τ) at the u0th iteration, Indicates the u0th iteration The variance of represents x at the u0th iteration k (τ k ), represents x at the u0th iteration k (τ k )’s variance.

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