A random access method based on binary subspace chirp codes and generalized approximate message passing over fast fading channels

Abstract

A random access method based on binary subspace chirp codes and generalized approximate message passing on a fast fading channel is applicable to fast fading channel scenarios. The method comprises: firstly, setting the symmetric matrix and vector constituting the binary chirp part to 0 to obtain a new codeword construction formula; then, based on the principle that the subspace has no intersection except the zero vector, selecting matrices constituting the subspace; substituting the matrices constituting the subspace into the new codeword construction formula to obtain a new codebook; then, allocating the new codebook to users as a transmitted signal; then, transmitting the received signal through the fast fading channel; and executing a generalized approximate message passing algorithm to estimate active users; iterating at the receiving end; and finally, judging the termination of iteration based on the active user set and the number of iterations to obtain an estimated active user set. The present invention reduces computational complexity while also reducing the missed detection rate.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a random access method based on binary subspace chirp codes and generalized approximate message transmission on a fast fading channel. Background Art

[0002] Massive machine-type communication (mMTC) networks need to address the problem of sporadic and short packet transmissions from a large number of users to access points (APs). Random access (RA) is an effective technique for reducing signaling overhead in mMTC networks and enhancing network access capabilities. In RA, each user is assigned a unique non-orthogonal signature code whose length is less than the number of potential users. Due to the non-orthogonality of signature codes, interference between users is inevitable. To reduce this interference, a large body of research has been conducted on low-correlation signature codes and active user identification (AUI) methods for quasi-static channels. Furthermore, frequency hopping is often used in secure mMTC systems to mitigate attacks such as radio frequency jamming. This causes each symbol in the signature sequence to be transmitted on a different frequency and experience different channel fading. Therefore, research on RA over rapidly varying channels is needed. Compared to quasi-static channels, where the channel remains unchanged throughout the signature sequence transmission phase, the rapid temporal variations of different symbols in rapidly varying channels further degrade the low-correlation characteristics of the signature sequence at the receiver. Consequently, signature codes designed for quasi-static channels are not applicable to rapidly varying channels.

[0003] In 2021, Roope Vehkalahti et al. pointed out for the first time in “Signature code design for fast fading channels” (in Proc. of IEEE ISIT, Melbourne, Australia, July 2021, pp. 2936-2941) that the codebook design criteria for quasi-static fading channels are not applicable to fast fading channels; then, a definition of fading correlation and a design criterion based on fading correlation were given (generally, the smaller the codeword fading correlation, the better the performance). In addition, in 2023, Jyotish Robin et al. used an on-off keying Bernoulli sequence as a signature code in “Active user identification in fast fading massive random access channels” (in Proc. of IEEE ITW, Saint-Malo, France, 23-26 April 2023, pp. 232-237), but used a binary sequence of Bernoulli distribution as a signature code, which has a large fading correlation and performs poorly on fast fading channels.

[0004] Roope Vehkalahti et al. also proposed using the absolute value matched filtering (AV-MF) algorithm for active user detection in "Signature code design for fast fading channels" (in Proc. of IEEE ISIT, Melbourne, Australia, July 2021, pp. 2936-2941). Assume that the number of active users is K, and for a codebook x with a code length of L and a number of codewords of N, the absolute value of the received signal is expressed as For n = {1, 2, ..., N}, calculate The n decisions corresponding to the top K maximum values ​​are considered active users. In 2010, Dino Sejdinovic et al., in "Note on noisy group testing: Asymptotic bounds and belief propagation reconstruction" (in Proc. of Allerton Conf, Monticello, IL, USA, 29 Sep.-01 Oct. 2010, pp. 998-1003), first formulated the AUI problem as a group testing (GT) problem and used the belief propagation (BP) algorithm to solve the equivalent GT problem. However, this approach did not consider the actual fast fading channels. Furthermore, this algorithm first required a binary hard decision based on the received signal energy to convert it into a GT problem. This process results in information loss, limiting its performance.

[0005] In 2023, J. Robin and E. Erkip considered the implementation of the BP algorithm based on the GT equivalent in the actual fast time-varying channel in "Active user identification in fast fading massive random access channels," (in Proc. of IEEE ITW., Saint-Malo, France, 23-26 April 2023, pp. 232-237). For the BP algorithm, the received signal is equivalent to represents the user index set of the t-th channel transmitting non-zero elements, is the number of active users on the tth channel. Therefore, u t =|y t | 2 obeys exponential distribution, First, the received signal is subjected to binary hard decision. in is a threshold parameter. Therefore The problem is transformed into z=(z1,…,z L ) is the problem of recovering β. That is, to find the posterior probability p(β n Specifically, in the factor graph, N users are used as variable nodes {β n}, L channels as check nodes {z t}, Denote as the set of all check nodes connected to the nth variable node, Represents the set of all variable nodes connected to the t-th check node. First, the probability of the variable node being passed to the check node is initialized to p(β n )=λ=K / N, the second step is to check the node zt to the variable node β n Delivering Messages Step 3: Variable node β n To check node z t The information conveyed is: where p(β n )=λδ(β n -1)+(1-λ)δ(β n ). Iterate the second and third steps above until convergence to obtain the posterior probability p(β n |z), thereby obtaining the index set of active users. However, when using the BP algorithm for AUI, the algorithm has high computational complexity when updating the verification node (in actual calculation, only the nodes that make The maximum corresponding The Hamming weight of is no greater than several items of v0, and the complexity of each iteration is ), when the number of users is large, this solution takes a long time to run and has low efficiency. Summary of the Invention

[0006] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a random access method based on binary subspace chirp codes and generalized approximate message passing on fast fading channels, construct a new codebook to reduce fading correlation, and perform active user detection based on the codebook through a generalized approximate message passing algorithm. Since the designed signature code has a small fading correlation, its excellent performance on fast fading channels is guaranteed, laying the foundation for achieving highly reliable and secure large-scale machine-type communications. The received signal vector is directly processed, avoiding the information loss caused by hard decision in the traditional BP method, thereby improving the detection performance.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] A random access method based on binary subspace chirp codes and generalized approximate message passing over a fast fading channel comprises the following steps:

[0009] Step 1: Set the symmetric matrices and vectors that make up the binary chirp (BC) part of the binary subspace chirp (BSSC) codeword construction formula to 0 to obtain a new codeword construction formula.

[0010] Step 2: Based on the principle that the subspaces in the new codeword construction formula obtained in step 1 have no intersection except for the zero vector, select the matrix constituting the subspace from the Binary Subspace Chirps (BSSC) codeword construction formula;

[0011] Step 3: Substitute the matrix constituting the subspace selected in step 2 into the new codeword construction formula obtained in step 1 to obtain a new codebook;

[0012] Step 4: Set the maximum number of iterations, then assign the new codebook obtained in Step 3 to the user as the transmitted signal. The transmitted signal is transmitted over a fast fading channel to obtain the received signal. The generalized approximate message passing algorithm is then applied to the received signal to estimate the active users, and iterations are performed at the receiving end.

[0013] Step 5: Based on the active user set estimated in step 4 and the maximum number of iterations, determine the iteration stop condition and finally obtain the estimated active user set.

[0014] The binary subspace chirp (BSSC) codeword construction formula in step 1 is:

[0015]

[0016] The Binary Subspace Chirps (BSSC) codeword construction formula is an L=2 m dimensional, consisting of rank 0≤r≤m, binary chirp (BC) part and switching pattern; for a∈H, if in Then the subspace H is an m×r matrix subspace of Represents a binary field, set and The jth column is the i-th column of the m×m identity matrix j List; Collection of express, The number of The BC part is composed of the r×r symmetric matrix S r and Indicates; switch mode is indicated by Indicates that

[0017] The new codeword construction formula in step 1 is:

[0018]

[0019] The step 2 specifically includes: Select the matrix The matrix selected at the xth iteration Recorded as And satisfy its subspace and the previous iteration Division by zero vector 0 m There is no intersection between the subspaces outside the set, and all matrices that meet the conditions are Add to collection In the matrix The matrix set consisting of the subspace of

[0020] The step 3 specifically includes: and the matrix that constitutes the subspace Substitute into the new codeword construction formula In , construct a new codebook.

[0021] The step 4 comprises:

[0022] Step 4.1: Assign the new codebook obtained in step 3 to the user as the transmitted signal. There are K active users, and the signal y received on the tth channel is t Expressed as Among them, the index of K active users is recorded as Use β=(β1,β2,...,β N ) indicates active state, if Then β n =1; each user is assigned a codeword of length L, and each codeword is represented by Where P is the normalization factor that can make the energy of each codeword equal to 1; at the receiving end, represent the signals transmitted by N users on the t-th channel and the channel fading vector respectively; The signal-to-noise ratio (SNR) is defined as represents the element-wise Hadamard product of two vectors;

[0023] Step 4.2: Equivalently transform the channel in step 4.1 to v = Aβ, and the number of active users of the t-th channel after fast fading is expressed as v = (v1,…,v L ) indicates that A is the unnormalized equivalent codebook matrix, let u=(u1,…,u L ),u t =|y t | 2 , t=1,2,...,L is the vector of received signal energy, so for the input active user set β and the output vector u of received signal energy, there is the following input-output relationship, u=f nl(v=Aβ), this nonlinear relationship is determined by the transition probability express;

[0024] Step 4.3: Set the number of iterations e = 0, the maximum number of iterations e max =50, set the prior mean of the active user set β in step 4.2 and variance Where n∈{1,2,...,N}, λ=K / N, and iterate steps 4.4 to 4.7, with e=e+1 for each iteration;

[0025] Step 4.4: Output linear step: Calculate the number of active users vector v = (v1,…,v L )’s variance and mean:

[0026]

[0027] Where t∈{1,2,...,L}, then the active user vector v=(v1,…,v L ) in which the elements obey distributed;

[0028] Step 4.5: Output nonlinear step: For any t∈{1,2,...,L}, according to the distribution obtained in step 4.4 and the transition probability in step 4.2 Calculate v t The posterior mean and variance of , the posterior mean is expressed as:

[0029]

[0030] The variance is expressed as:

[0031]

[0032] Among them, p(v t =g) can be obtained from the Gaussian distribution, that is:

[0033] where g=0,1,…,v t,max , ζ is to make The normalization factor of , further calculates the redundancy and the inverse of its variance:

[0034]

[0035] Step 4.6: Input linear step: For any n∈{1,2,...,N}, the redundant information obtained in step 4.5 Calculating β n The variance and mean of , the variance is expressed as:

[0036]

[0037] The mean is expressed as:

[0038]

[0039] Among them, n∈{1,2,...,N}, the elements in the active user set β obey distributed;

[0040] Step 4.7: Input nonlinear step: For any n∈{1,2,...,N}, according to the distribution obtained in step 4.6 Calculate the posterior mean and variance of the active user set β. The mean is expressed as:

[0041]

[0042] The variance is expressed as:

[0043]

[0044] When the number of iterations e in step 5 is equal to the maximum number of iterations e max Or calculated based on the active user set β The iteration stops when , and the estimated value obtained after convergence Arrange in descending order, take the first K as 1, and put the corresponding n as active users into the active user set.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. This invention constructs a new codebook based on binary subspace chirps (BSSC) codewords and employs a generalized approximate message passing algorithm suitable for fast-fading channel scenarios, resulting in smaller fading correlation. Compared with existing Bernoulli sequences, the new codebook has a larger Hamming distance, effectively reducing fading correlation and exhibiting better performance in fast-fading channels.

[0047] 2. The method proposed in the present invention estimates active users by directly receiving signals and executing a generalized approximate message passing algorithm. It does not require judgment on the received signals, but directly processes the received signals, avoiding the existing BP algorithm that performs binary hard judgment on the received signals and causes information loss.

[0048] 3. The disadvantage of high complexity when updating the verification node is that the complexity of the generalized approximate message passing algorithm is Compared with BP algorithm It improves efficiency, greatly reduces complexity, saves running time and reduces missed detection rate.

[0049] In summary, this invention reduces both computational complexity and missed detection rates. Furthermore, the proposed codeword exhibits minimal fading correlation, ensuring excellent performance over fast-fading channels and laying the foundation for highly reliable and secure large-scale machine-type communications. The generalized approximate message passing algorithm enables active user detection, contributing to the realization of low-latency, highly reliable, and secure large-scale machine-type communications. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Schematic diagram of the transmitting and receiving ends of signal transmission of the present invention.

[0051] Figure 2 Schematic diagram of equivalent channel input and output for active user detection according to the present invention.

[0052] Figure 3 Comparison of missed detection rates between the present invention and the prior art using different codewords and different detection methods in scenario 1.

[0053] Figure 4 The figure is a comparison chart of missed detection rates between the present invention and the prior art using different codewords and different detection methods in scenario 2. DETAILED DESCRIPTION

[0054] The present invention will be described in detail below with reference to the accompanying drawings.

[0055] A random access method based on binary subspace chirp codes and generalized approximate message passing over a fast fading channel comprises the following steps:

[0056] Step 1: Set the symmetric matrices and vectors that make up the binary chirp (BC) part of the binary subspace chirp (BSSC) codeword construction formula to 0, so that all elements that constitute the codeword are real numbers, and obtain a new codeword construction formula;

[0057] Step 2: Based on the principle that the subspaces in the new codeword construction formula obtained in Step 1 have no intersection except for the zero vector, the matrix constituting the subspace is selected from the Binary Subspace Chirps (BSSC) codeword construction formula. This constructs a codeword with a larger Hamming distance and smaller fading correlation, resulting in better performance in fast fading channels.

[0058] Step 3: Substitute the matrix constituting the subspace selected in step 2 into the new codeword construction formula obtained in step 1 to obtain a new codebook;

[0059] Step 4: Set the maximum number of iterations, then assign the new codebook obtained in step 3 to the user as the transmitted signal. The transmitted signal is transmitted through a fast fading channel to obtain the received signal. The generalized approximate message passing algorithm is then executed on the received signal to estimate the active users, and it is iterated at the receiving end. Since the elements in the input β and the output u are independent, this algorithm can be used to solve the sparse signal recovery problem where the input and output elements are independently distributed. Moreover, this algorithm does not require judgment on the received signal, but directly processes the received signal, avoiding the shortcomings of the BP algorithm, improving efficiency, greatly reducing complexity, saving running time, and reducing the missed detection rate.

[0060] Step 5: Based on the active user set estimated in step 4 and the maximum number of iterations, determine the iteration stop condition and finally obtain the estimated active user set.

[0061] The binary subspace chirp (BSSC) codeword construction formula in step 1 is:

[0062]

[0063] The Binary Subspace Chirps (BSSC) codeword construction formula is an L=2 m dimensional, consisting of rank 0≤r≤m, binary chirp (BC) part and switching pattern; for a∈H, if in Then the subspace H is an m×r matrix subspace of Represents a binary field, set and The jth column is the i-th column of the m×m identity matrix j List; Collection of express, The number of The BC part is composed of the r×r symmetric matrix S r and Indicates; switch mode is indicated by Indicates that

[0064] The new codeword construction formula in step 1 is:

[0065]

[0066] The step 2 specifically includes: Select the matrix The matrix selected at the xth iteration Recorded as And satisfy its subspace and the previous iteration Division by zero vector 0 m There is no intersection between the subspaces outside the set, and all matrices that meet the conditions are Add to collection In the matrix The matrix set consisting of the subspace of

[0067] The step 3 specifically includes: and the matrix that constitutes the subspace Substitute into the new codeword construction formula In the code, a new codebook is constructed. The constructed code is of code length 2 m , weight 2 r The constant weight code, the minimum Hamming distance between code words is 2 r+1 -2, fading correlation value is 2 -r2 , the number of codewords reaches or approaches the maximum value of the constant weight code under the corresponding parameters.

[0068] The step 4 comprises:

[0069] Step 4.1: The structure of the transceiver of the present invention is as follows Figure 1 As shown, the new codebook obtained in step 3 is assigned to the user as the transmission signal. There are K active users, and the signal y received on the tth channel is t Expressed as Among them, the index of K active users is recorded as Use β=(β1,β2,...,β N ) indicates active state, if Then β n =1; each user is assigned a codeword of length L, and each codeword is represented by Where P is the normalization factor that can make the energy of each codeword equal to 1; at the receiving end, represent the signals transmitted by N users on the t-th channel and the channel fading vector respectively; The signal-to-noise ratio (SNR) is defined as represents the element-wise Hadamard product of two vectors;

[0070] Step 4.2: The equivalent channel input and output diagram of the present invention is as follows Figure 2 As shown, the channel in step 4.1 is equivalent to v = Aβ, and the number of active users of the t-th channel after fast fading is expressed as v = (v1,…,v L ) indicates that A is the unnormalized equivalent codebook matrix, let u=(u1,…,u L ),u t =|y t |2 , t=1,2,...,L is the vector of received signal energy, so for the input active user set β and the output vector u of received signal energy, there is the following input-output relationship, u=f nl (v=Aβ), this nonlinear relationship is determined by the transition probability express;

[0071] Step 4.3: Set the number of iterations e = 0, the maximum number of iterations e max =50, set the prior mean of the active user set β in step 4.2 and variance Where n∈{1,2,...,N}, λ=K / N, and iterate steps 4.4 to 4.7, with e=e+1 for each iteration;

[0072] Step 4.4: Output linear step: Calculate the number of active users vector v = (v1,…,v L )’s variance and mean:

[0073]

[0074] Where t∈{1,2,...,L}, then the active user vector v=(v1,…,v L ) in which the elements obey distributed;

[0075] Step 4.5: Output nonlinear step: For any t∈{1,2,...,L}, according to the distribution obtained in step 4.4 and the transition probability in step 4.2 Calculate v t The posterior mean and variance of , the posterior mean is expressed as:

[0076]

[0077] The variance is expressed as:

[0078]

[0079] Among them, p(v t =g) can be obtained from the Gaussian distribution, that is:

[0080] where g=0,1,…,v t,max , ζ is to make The normalization factor of , further calculates the redundancy and the inverse of its variance:

[0081]

[0082] Step 4.6: Input linear step: For any n∈{1,2,...,N}, the redundant information obtained in step 4.5 Calculating β n The variance and mean of , the variance is expressed as:

[0083]

[0084] The mean is expressed as:

[0085]

[0086] Among them, n∈{1,2,...,N}, the elements in the active user set β obey distributed;

[0087] Step 4.7: Input nonlinear step: For any n∈{1,2,...,N}, according to the distribution obtained in step 4.6 Calculate the posterior mean and variance of the active user set β. The mean is expressed as:

[0088]

[0089] The variance is expressed as:

[0090]

[0091] When the number of iterations e in step 5 is equal to the maximum number of iterations e max Or calculated based on the active user set β The iteration stops when , and the estimated value obtained after convergence Arrange in descending order, take the first K as 1, and put the corresponding n as active users into the active user set.

[0092] Simulation experiment

[0093] Attachment Figure 3 and attached Figure 4 The simulation results are presented to demonstrate the performance of the proposed signature code and AUI method. Scenario 1 involves 100 users transmitting signature codes through 64 channels, and scenario 2 involves 200 users transmitting signature codes through 128 channels.

[0094] Simulation conditions and simulation content:

[0095] The present invention obtains simulation data and draws simulation diagrams through the Matlab platform.

[0096] The signal-to-noise ratio (SNR) of the proposed solution is fixed at 20dB. Furthermore, the simulation parameters for the proposed solution are set as follows: The best simulation results are achieved when the threshold parameter ε in the existing BP algorithm is 0.1, and v0 is set to 2 during approximate calculations (in this case, the proposed GAMP algorithm still has lower complexity than the existing BP algorithm). Simulations found that the best simulation results are achieved when the Bernoulli parameter (the probability that an element in the codeword is 1) is 0.1. Detection is performed using the existing BP algorithm, the proposed GAMP algorithm, and the existing absolute value matched filtering (AV-MF) method. Simulations are performed on the BSSC (64, 100, 6, 2) and Bern (64, 100, 0.1) codewords with m = 6, codeword number N = 100, and codeword length L = 64, and on the BSSC (128, 200, 6, 2) and Bern (128, 200, 0.1) codewords with m = 7, codeword number N = 200, and codeword length L = 128. The simulations show the missed detection rates using the three detection methods.

[0097] First, the fading correlation of BSSC(64,100,6,2) and BSSC(128,200,6,2) is calculated, which are both 0.5. The fading correlations of Bern(64,100,0.1) and Bern(128,200,0.1) are 1.94 and 1.32 respectively. Figure 3 A performance comparison for scenario 1 is presented. As expected, the newly proposed BSSC-based signature code performs better than the Bernoulli-distributed codeword. Furthermore, the GAMP algorithm proposed in this invention exhibits superior performance compared to the existing BP algorithm. Furthermore, when Bern (64, 100, 0.1) is used, the GAMP algorithm proposed in this invention achieves a significant gain over the existing BP algorithm, whereas when BSSC (64, 100, 6, 2) is used, the GAMP algorithm proposed in this invention achieves a smaller gain over the existing BP algorithm. Because the Bern codebook is not a constant-weight code, taking v0 = 2 for the approximate calculation of all check node updates significantly impacts the performance of the existing BP algorithm. However, taking v0 = 2 has a smaller impact on the proposed constant-weight BSSC codebook. Therefore, when using the BSSC-based codebook, the GAMP algorithm proposed in this invention achieves a less significant gain over the existing BP algorithm. Figure 4 The performance in the second scenario is given, and similar conclusions can be drawn.

[0098] Note that to simplify computation, the existing BP algorithm uses v0 = 2. First, in this case, based on runtime tests, the complexity of the existing BP algorithm is higher than that of the GAMP algorithm proposed in this paper. When v0 is larger and the check nodes are adaptive, the performance comparison results between the GAMP algorithm proposed in this paper and the existing BP algorithm may differ. However, under limited computing resources, GAMP will demonstrate better performance than BP.

Claims

1. A random access method based on binary subspace chirp codes and generalized approximate message passing over fast fading channels, characterized by: The following steps are involved: Step 1: Set the symmetric matrices and vectors that make up the binary chirp (BC) part of the binary subspace chirp (BSSC) codeword construction formula to 0 to obtain a new codeword construction formula. Step 2: Based on the principle that the subspaces in the new codeword construction formula obtained in step 1 have no intersection except for the zero vector, select the matrix constituting the subspace from the Binary Subspace Chirps (BSSC) codeword construction formula; Step 3: Substitute the matrix constituting the subspace selected in step 2 into the new codeword construction formula obtained in step 1 to obtain a new codebook; Step 4: Set the maximum number of iterations. Then, assign the new codebook obtained in Step 3 to the user as the transmitted signal. The transmitted signal is transmitted over a fast fading channel to obtain the received signal. The generalized approximate message passing algorithm is then applied to the received signal to estimate the active users. The algorithm then iterates at the receiving end. The specific steps are as follows: Step 4.1: Assign the new codebook obtained in step 3 to the user as the transmitted signal. There are K active users, and the signal y received on the tth channel is t Expressed as Among them, the index of K active users is recorded as Use β=(β1,β2,...,β N ) indicates active state, if Then β n =1; each user is assigned a codeword of length L, and each codeword is represented by Where P is the normalization factor that can make the energy of each codeword equal to 1; at the receiving end, represent the signals transmitted by N users on the t-th channel and the channel fading vector respectively; The signal-to-noise ratio (SNR) is defined as β°h t represents the element-wise Hadamard product of two vectors; Step 4.2: Equivalently transform the channel in step 4.1 to v = Aβ, and the number of active users of the t-th channel after fast fading is expressed as v = (v1,…,v L ) indicates that A is the unnormalized equivalent codebook matrix, let u=(u1,…,u L ),u t =|y t | 2 , t=1,2,...,L is the vector of received signal energy, so for the input active user set β and the output vector u of received signal energy, there is the following input-output relationship, u=f nl (v=Aβ), this nonlinear relationship is determined by the transition probability express; Step 4.3: Set the number of iterations e = 0, the maximum number of iterations e max =50, set the prior mean of the active user set β in step 4.2 and variance Where n∈{1,2,...,N}, λ=K / N, and iterate steps 4.4 to 4.7, with e=e+1 for each iteration; Step 4.4: Output linear step: Calculate the number of active users vector v = (v1,…,v L )’s variance and mean: Where t∈{1,2,...,L}, then the active user vector v=(v1,…,v L ) in which the elements obey distributed; Step 4.5: Output nonlinear step: For any t∈{1,2,...,L}, according to the distribution obtained in step 4.4 and the transition probability in step 4.2 Calculate v t The posterior mean and variance of , the posterior mean is expressed as: The variance is expressed as: Among them, p(v t =g) can be obtained from the Gaussian distribution, that is: where g=0,1,…,v t,max , ζ is to make The normalization factor of , further calculates the redundancy and the inverse of its variance: Step 4.6: Input linear step: For any n∈{1,2,...,N}, the redundant information obtained in step 4.5 Calculating β n The variance and mean of , the variance is expressed as: The mean is expressed as: Among them, n∈{1,2,...,N}, the elements in the active user set β obey distributed; Step 4.7: Input nonlinear step: For any n∈{1,2,...,N}, according to the distribution obtained in step 4.6 Calculate the posterior mean and variance of the active user set β. The mean is expressed as: The variance is expressed as: Step 5: Based on the active user set β estimated in step 4 and the maximum number of iterations e, determine the iteration stopping condition. max Or calculated based on the active user set β The iteration stops when , and the estimated value obtained after convergence Arrange in descending order, take the first K as 1, and put the corresponding n as active users into the active user set, and finally get the estimated active user set.

2. The random access method based on binary subspace chirp codes and generalized approximate message passing over a fast fading channel according to claim 1, characterized in that: The binary subspace chirp (BSSC) codeword construction formula in step 1 is: The Binary Subspace Chirps (BSSC) codeword construction formula is an L=2 m dimensional, consisting of rank 0≤r≤m, binary chirp (BC) part and switching pattern; for a∈H, if in Then the subspace H is an m×r matrix subspace of Represents a binary field, set and The jth column is the i-th column of the m×m identity matrix j List; Collection of express, The number of The BC part is composed of the r×r symmetric matrix S r and Indicates; switch mode is indicated by Indicates that The new codeword construction formula in step 1 is:

3. The random access method based on binary subspace chirp codes and generalized approximate message passing over a fast fading channel according to claim 1, characterized in that: The step 2 specifically includes: Select the matrix The matrix selected at the xth iteration Recorded as And satisfy its subspace and the previous iteration Division by zero vector 0 m There is no intersection between the subspaces outside the set, and all matrices that meet the conditions are Add to collection In the matrix The matrix set consisting of the subspace of 4. The random access method based on binary subspace chirp codes and generalized approximate message passing over a fast fading channel according to claim 1, characterized in that: The step 3 specifically includes: and the matrix that constitutes the subspace Substitute into the new codeword construction formula In , construct a new codebook.

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