Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning

Abstract

The invention discloses a Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning, and belongs to the technical field of wireless communication. The method comprises the following steps: modeling an unknown quantity in a channel estimation problem as a random variable, and constructing a Bayesian probability graph model; structural Gaussian mixture prior distribution is introduced for channel elements, and Gaussian mixture prior is converted into a product form through Bernoulli discrete variables; and deducing conditional posteriori distribution of all variables, performing high-dimensional sampling by using a plurality of parallel Gibbs samplers, collecting convergence samples, and averaging to obtain a channel estimation value. According to the method, the sparse Bayesian learning and the Markov chain Monte Carlo method are combined, the problems that a traditional compressed sensing algorithm is insufficient in dependence on prior information and prone to falling into local optimum are solved, the channel estimation precision is remarkably improved, meanwhile, the calculation complexity is reduced through parallel sampling, and the method is suitable for a super-large-scale MIMO system.

Description

Technical Field

[0001] The invention relates to a Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning, belongs to the technical field of wireless communication, and is suitable for obtaining channel state information of a very large-scale multiple-input multiple-output (MIMO) system. Background Art

[0002] In recent years, large-scale multiple-input multiple-output (MIMO) technology has greatly improved spectrum efficiency and energy efficiency by deploying a large number of antennas in base stations. However, in frequency division duplex systems, due to the lack of channel reciprocity, the acquisition of downlink channel state information faces high training and feedback costs.

[0003] Compressed sensing technology based on channel sparsity can effectively reduce channel estimation overhead, but the regularization method of traditional compressed sensing is susceptible to structural errors, and the traditional greedy algorithm relies on accurate prior information and is difficult to obtain the global optimal solution. Sparse Bayesian learning improves sparsity modeling and inference capabilities by parameterizing prior models, but the performance of commonly used deterministic approximation methods (such as variational inference) degrades when the model deviates from the assumptions, resulting in increased estimation errors.

[0004] In contrast, Markov Chain Monte Carlo (MCMC), as a random approximation method, can approximate complex probability distributions with asymptotic accuracy, providing a powerful inference framework for high-dimensional channel estimation problems. By constructing a Markov chain and sampling from the target distribution, MCMC overcomes the high-dimensional problem that is difficult to handle with traditional methods and avoids falling into local optimality. In addition, MCMC supports parallel computing, further enhancing its application potential in ultra-large-scale MIMO systems. By combining efficient sampling strategies, MCMC technology shows superior performance in complex sparse channel inference, providing a practical solution for achieving efficient channel estimation. Summary of the invention

[0005] Technical problem: In response to the above-mentioned deficiencies in the prior art, the present invention provides a Markov Chain Monte Carlo channel estimation method based on sparse Bayesian learning, which uses Markov Chain Monte Carlo technology to perform sparse Bayesian learning inference, improves the accuracy of channel estimation, reduces the estimation overhead, and ensures reasonable estimation efficiency.

[0006] Technical solution: A Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning of the present invention comprises the following steps:

[0007] S1. Model all unknown quantities in the channel estimation problem as random variables and construct a Bayesian probability graph model. For the channel elements to be estimated, introduce a structured mixed Gaussian prior distribution, and transform the mixed Gaussian prior from a sum form to a product form by introducing Bernoulli discrete random variables. At the same time, introduce corresponding conjugate priors for all other random variables.

[0008] S2. Based on the Gibbs sampling principle, derive the conditional posterior distribution of all random variables in the Bayesian probability graphical model;

[0009] S3, running multiple parallel Gibbs samplers to perform serial sampling of the conditional posterior distribution of all random variables in dimensional order; after a preset burn-in period, collecting samples of each sampler convergence;

[0010] S4. Obtain an estimated value of the channel matrix element by averaging the random variable samples of the channel element collected by each sampler.

[0011] Preferably, the step S1 specifically includes:

[0012] S101. Model all unknown quantities as random variables and construct a Bayesian probability graph model;

[0013] S102: for the channel element H to be estimated k (n,m), introducing structured mixed Gaussian prior distribution

[0014]

[0015] where α c is a mixed Gaussian precision vector describing the joint sparsity among users, α k is a mixed Gaussian precision vector describing the sparsity of the user itself; H k (n,m) represents the channel element in the nth row and mth column of the kth user equipment channel matrix, ρ n represents the mixing coefficient of the mixed Gaussian prior, which ranges from [0,1]. K, N, and M represent the number of users, the number of columns in the channel matrix, and the number of rows in the channel matrix, respectively. N C Represents complex Gaussian distribution; describes the inherent sparsity and partial shared sparsity of the user equipment channel by introducing a mixed Gaussian prior distribution;

[0016] S103. Introducing Bernoulli discrete variable w n , whose expression is The mixed Gaussian prior is transformed from sum form to product form using the introduced discrete variables

[0017]

[0018] where αc,n is the noise precision variable describing the joint sparsity of the nth row of the inter-user channel matrix, α k,n is the noise precision variable describing the sparsity of the nth row of the user's own channel matrix;

[0019] S104, mixing coefficient ρ for mixed Gaussian prior n Introducing the beta prior, its expression is:

[0020] ρ n ~Beta(λ0,λ1)

[0021] Where λ0 and λ1 are the hyperparameters of the beta prior;

[0022] S105, precision element α for mixed Gaussian c,n and α k,n Introducing gamma prior, its expressions are:

[0023] α c,n ~Gamma(a c ,b c )

[0024] α k,n ~Gamma(a0,b0)

[0025] where a c With b c is α c,n Hyperparameters of the random variable gamma prior, a0 and b0 are α k,n Hyperparameters of the random variable gamma prior;

[0026] S106. Gamma prior is introduced for the unknown noise precision random variable, and its expression is:

[0027] β k ~Gamma(θ0,θ1)

[0028] Where θ0 and θ1 are random variables β k Hyperparameters of the gamma prior;

[0029] S107. Based on the probability graph model and the introduced prior, the joint probability distribution of the model is derived, and its expression is:

[0030]

[0031] Where Y represents the matrix composed of all user received signal matrices, and H represents the matrix composed of all user channel matrices.

[0032] Preferably, the conditional posterior probabilities of all random variables introduced in step S1 are derived, that is, the derivation of step S2, specifically including:

[0033] S201. Derivation of the mixing coefficient variable ρ in the Gaussian mixture prior n The conditional posterior probability distribution of is expressed as:

[0034] p(ρ n |-)∝Beta(λ0+w n ,λ1-w n +1)

[0035] S202, deriving noise accuracy variable α c,n The conditional posterior probability distribution of is expressed as:

[0036]

[0037] S203, deriving noise accuracy variable α k,n The conditional posterior probability distribution of is expressed as:

[0038]

[0039] S204. Derivation of the conditional posterior probability distribution of the discrete Bernoulli variable, which is expressed as:

[0040]

[0041] To simplify the representation, A and B are introduced to represent the complex formula in the brackets of the Bernoulli distribution, where

[0042]

[0043] S205, derive the conditional posterior probability distribution of the noise precision variable, which is expressed as:

[0044]

[0045] Where T represents the pilot length, X represents the pilot matrix, and Y k represents the received signal matrix of the kth user equipment;

[0046] S206, derive the conditional posterior probability distribution of the channel element variable, which is expressed as:

[0047]

[0048] To simplify the representation, C and D are introduced to represent the complex formula in brackets of the gamma distribution: Where X(i,n) represents the element in the i-th row and n-th column of the pilot matrix;

[0049] in represents the element of the i-th row and m-th column of the signal matrix received by the k-th user equipment. The definition of E(i) is given by the following formula:

[0050] Preferably, the step S3 specifically includes:

[0051] S301, for all dimensions K, N, M, a single Gibbs sampler samples the conditional posterior derived in step S2 in the order of the dimensions;

[0052] S302, after a certain number of sampling iterations and a preset burn-in period, collect the converged samples

[0053]

[0054] Where N burn-in represents the number of iterations of the Gibbs sampling burn-in period, N collect Indicates the number of samples collected after the burn-in period, N burn-in +N collect Represents the total number of iterations of Gibbs sampling;

[0055] S303, running multiple parallel Gibbs samplers, and collecting converged samples of each sampler.

[0056] The present invention also provides a communication device, comprising a memory and a processor, wherein the memory stores a computer program, and wherein the processor implements the steps of the above method when executing the computer program.

[0057] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above method are implemented.

[0058] The present invention also provides a computer program product, comprising a computer program, which implements the steps of the above method when executed by a processor.

[0059] Beneficial effects: Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0060] In frequency division duplex systems, downlink channel estimation faces high training overhead and feedback cost. Traditional compressed sensing methods rely on prior assumptions and are susceptible to structural errors, while variational inference methods of sparse Bayesian learning perform poorly when the model is mismatched. This paper combines the precise inference capability of Markov chain Monte Carlo (MCMC) with the flexible modeling of sparse Bayesian learning to achieve efficient and high-precision channel estimation through parallel Gibbs sampling.

[0061] Specifically, the present invention closely combines the Gibbs sampling method in Markov chain Monte Carlo with sparse Bayesian learning. On the one hand, by introducing a mixed Gaussian prior under the sparse Bayesian framework, the sparsity of the user channel itself and the partial common sparsity between users are described, which improves the estimation accuracy compared to the traditional structured Gaussian prior; on the other hand, the precise inference of Gibbs sampling is used to perform Bayesian inference in the entire sparse Bayesian probability framework, which significantly improves the accuracy of sparse channel estimation compared to the traditional compressed sensing algorithm and the sparse Bayesian learning algorithm based on approximate inference. At the same time, the parallelism of Markov chain Monte Carlo is used to generate enough samples through a large number of parallel samplers, which reduces the computational complexity compared to the approximate inference method.

[0062] Simulation results show that the NMSE performance of the proposed method is close to the theoretical lower bound and is superior to traditional compressed sensing and variational inference methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a flow chart of a Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning according to an embodiment of the present invention;

[0064] Figure 2 A sparse Bayesian probability graph model of a Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning in an embodiment of the present invention;

[0065] Figure 3 It is a comparison chart of the normalized mean square error (NMSE) performance between the method of the present invention and the comparative method. DETAILED DESCRIPTION

[0066] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0067] 1. System Model Used in This Example

[0068] This paper considers a frequency division duplex multi-user MIMO system with one base station and K user equipments. The base station is equipped with N antennas, while each user equipment is equipped with M antennas. During the considered frequency division duplex downlink training phase, the base station broadcasts a pilot sequence of length T to each user equipment. Subsequently, the user equipment sends feedback of the received signal to the base station, and then the downlink channel estimation of all user equipments is completed at the base station. The received signal can be expressed as:

[0069]

[0070] is the downlink channel matrix, is the pilot matrix, is a noise matrix whose elements are independent and identically distributed complex Gaussian random variables with mean zero and variance Due to the limited local scatterers in the physical propagation environment, the channel is approximately sparse when observed in the angle domain. This means that the channel matrix contains only a small number of significant components, while the rest are close to zero. It is assumed that the antennas installed at the base station and user equipment adopt uniform linear arrays. Using the angle domain representation, the channel matrix can be expressed as:

[0071]

[0072] in and Denote the discrete Fourier transform (DFT) matrices of the angle domain transformation of the user equipment and base station, respectively. is the angle domain channel matrix. Let Indicates H k The support set supp(h) = {i:h(i) ≠ 0}, because the index set of h consists of non-zero indices, where h(i) represents the i-th entry of h. From the above, we can summarize the two main characteristics of the considered multi-user massive MIMO system as follows:

[0073] Sparsity within user equipment: For the kth user equipment (k=1,…,K), H k All M columns have the same sparsity pattern:

[0074]

[0075] Partial sharing sparsity: For K user devices, {H k}Shared public support:

[0076]

[0077] 2. Specific steps of this embodiment

[0078] like Figure 2 As shown, the embodiment of the present invention provides a sparse Bayesian probability graph model of a Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning, which includes all unknown random variables in the system model and their relationships. Figure 1 As shown, an embodiment of the present invention provides a flow chart of a Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning,

[0079] S1. Model all unknown quantities in the channel estimation problem as random variables and construct a Bayesian probability graph model. For the channel elements to be estimated, introduce a structured mixed Gaussian prior distribution, and transform the mixed Gaussian prior from a sum form to a product form by introducing Bernoulli discrete random variables. At the same time, introduce corresponding conjugate priors for all other random variables.

[0080] S2. Based on the Gibbs sampling principle, derive the conditional posterior distribution of all random variables in the Bayesian probability graphical model;

[0081] S3, running multiple parallel Gibbs samplers to perform serial sampling of the conditional posterior distribution of all random variables in dimensional order; after a preset burn-in period, collecting samples of each sampler convergence;

[0082] S4. Obtain an estimated value of the channel matrix element by averaging the random variable samples of the channel element collected by each sampler.

[0083] The step S1 specifically includes:

[0084] S101. Model all unknown quantities as random variables and construct a Bayesian probability graph model;

[0085] S102: for the channel element H to be estimated k (n,m), introducing structured mixed Gaussian prior distribution

[0086]

[0087] where α c is a mixed Gaussian precision vector describing the joint sparsity among users, α k is a mixed Gaussian precision vector describing the sparsity of the user itself; H k (n,m) represents the channel element in the nth row and mth column of the kth user equipment channel matrix, ρ n represents the mixing coefficient of the mixed Gaussian prior, which ranges from [0,1]. K, N, and M represent the number of users, the number of columns of the channel matrix, and the number of rows of the channel matrix, respectively. By introducing the mixed Gaussian prior distribution, the sparsity of the user equipment channel itself and the partial shared sparsity are described.

[0088] S103. Introducing Bernoulli discrete variable w n , whose expression is The mixed Gaussian prior is transformed from sum form to product form using the introduced discrete variables

[0089]

[0090] where α c,nis the noise precision variable describing the joint sparsity of the nth row of the inter-user channel matrix, α k,n is the noise precision variable describing the sparsity of the nth row of the user's own channel matrix;

[0091] S104, mixing coefficient ρ for mixed Gaussian prior n Introducing the beta prior, its expression is:

[0092] ρ n ~Beta(λ0,λ1)

[0093] Where λ0 and λ1 are the hyperparameters of the beta prior;

[0094] S105, precision element α for mixed Gaussian c,n and α k,n Introducing gamma prior, its expressions are:

[0095] α c,n ~Gamma(a c ,b c )

[0096] α k,n ~Gamma(a0,b0)

[0097] where a c With b c is α c,n Hyperparameters of the random variable gamma prior, a0 and b0 are α k,n Hyperparameters of the random variable gamma prior;

[0098] S106. Gamma prior is introduced for the unknown noise precision random variable, and its expression is:

[0099] β k ~Gamma(θ0,θ1)

[0100] Where θ0 and θ1 are random variables β k Hyperparameters of the gamma prior;

[0101] S107. Based on the probability graph model and the introduced prior, the joint probability distribution of the model is derived, and its expression is:

[0102] Where Y represents the matrix composed of all user received signal matrices, and H represents the matrix composed of all user channel matrices. The conditional posterior probabilities of all random variables introduced in step S1 are derived, that is, the derivation of step S2, specifically including:

[0103] S201. Derivation of the mixing coefficient variable ρ in the Gaussian mixture prior nThe conditional posterior probability distribution of is expressed as:

[0104] p(ρ n |-)∝Beta(λ0+w n ,λ1-w n +1)

[0105] S202, deriving noise accuracy variable α c,n The conditional posterior probability distribution of is expressed as:

[0106]

[0107] S203, deriving noise accuracy variable α k,n The conditional posterior probability distribution of is expressed as:

[0108]

[0109] S204. Derivation of the conditional posterior probability distribution of the discrete Bernoulli variable, which is expressed as:

[0110]

[0111] To simplify the representation, A and B are introduced to represent the complex formula in the brackets of the Bernoulli distribution, where

[0112]

[0113] S205, derive the conditional posterior probability distribution of the noise precision variable, which is expressed as:

[0114]

[0115] Where T represents the pilot length, X represents the pilot matrix, and Y k represents the received signal matrix of the kth user equipment;

[0116] S206, derive the conditional posterior probability distribution of the channel element variable, which is expressed as:

[0117]

[0118] To simplify the representation, C and D are introduced to represent the complex formula in brackets of the gamma distribution: Where X(i,n) represents the element in the i-th row and n-th column of the pilot matrix;

[0119] in represents the element of the i-th row and m-th column of the signal matrix received by the k-th user equipment. The definition of E(i) is given by the following formula:

[0120] The step S3 specifically includes:

[0121] S301. For all dimensions K, N, and M, a single Gibbs sampler samples the above-derived conditional posterior in the order of the dimensions;

[0122] S302, after a certain number of sampling iterations and a preset burn-in period, collect the converged samples:

[0123]

[0124] Where N burn-in represents the number of iterations of the Gibbs sampling burn-in period, N collect Indicates the number of samples collected after the burn-in period, N burn-in +N collect Represents the total number of iterations of Gibbs sampling;

[0125] S303, initialize multiple parallel Gibbs samplers, perform Gibbs sampling iterations, and after traversing and sampling the conditional posteriori of random variables of all dimensions each time, determine whether the number of iterations reaches the burn-in period. If the burn-in period has not been reached, continue iterative sampling. If the burn-in period has been reached, collect all samples currently sampled, and continue sampling until the maximum number of iterations is reached.

[0126] S4. All collected H k The (n,m) sample is averaged as its estimate.

[0127] 3. Implementation Effect

[0128] In order to enable those skilled in the art to better understand the solution of the present invention, the following provides a comparison of the results of the Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning in this embodiment and a comparative method.

[0129] The simulation scenario considered is described as follows:

[0130] In a massive MIMO system, the base station is equipped with 64 antennas and there are 8 user devices, each equipped with 2 antennas. The signal-to-noise ratio (SNR) is defined as Where P represents the total transmit power, σ 2 is the variance of the noise. Assume For k=1,...,K, the channels are normalized to Based on the theory of compressed sensing, the pilot matrix X should satisfy the restricted isometry property, that is, the absolute inner product between any two columns in X should be as small as possible. Therefore, X is generated by truncating the discrete Fourier transform matrix to ensure the orthogonality between columns. The a priori hyperparameters are set to the following values: a0 = b0 = a c =b c =λ0=λ1=θ0=θ1=10-3 In the proposed method, 10 parallel samplers are used, each sampler iterates 300 times, and finally 32 samples are taken, with a total of 320 samples for estimation. The normalized mean square error (NMSE) is selected as the performance indicator and is defined as follows:

[0131]

[0132] Figure 3 A comparison chart of the NMSE performance of the present invention and the comparison method in the simulation scenario is shown, and the comparison method includes the orthogonal matching pursuit channel estimation method in the document "J.Lee, G.-T.Gil, and YHLee, "Channel estimation via orthogonal matching pursuit for hybrid MIMO systems in millimeter wave communications," IEEE Trans. Commun., vol. 64, no. 6, pp. 2370-2386, Jun. 2016." (hereinafter referred to as estimation scheme 1), the fast iterative shrinkage threshold algorithm in the document "Y.Huang, L.Wan, S.Zhou, Z.Wang, and J.Huang, "Comparison of sparse recovery algorithms for channel estimation in underwater acoustic OFDM with data-driven sparsity learning," Phys. Commun., vol. 13, pp. 156-167, Dec. 2014." (hereinafter referred to as estimation scheme 2), and the fast iterative shrinkage threshold algorithm in the document "JPVila and P.Schniter, "Expectation-maximization Gaussian-mixture approximate message passing,”IEEE Trans.Signal Process.,vol.61,no.19,pp.4658–4672,Oct.2013.” in the expectation-maximization Gaussian mixture approximate message passing (hereinafter referred to as estimation scheme 3), the special case of the present invention under Gaussian prior (hereinafter referred to as estimation scheme 4), and the theoretically optimal ideal linear mean square error estimation lower bound. It can be seen that under different SNR values, the present invention has improved performance compared with the various comparison methods, achieving an estimation performance close to the optimal lower bound, and at the same time using parallelism to generate enough samples, the algorithm complexity is smaller than that of estimation scheme 3.

[0133] The present invention also provides a communication device, comprising a memory and a processor, wherein the memory stores a computer program, and wherein the processor implements the steps of the above method when executing the computer program.

[0134] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above method are implemented.

[0135] The present invention also provides a computer program product, comprising a computer program, which implements the steps of the above method when executed by a processor.

[0136] What is described above in conjunction with the accompanying drawings is only a preferred embodiment of the present invention and cannot be used to limit the scope of rights included in the present invention. It should be understood that any equivalent changes made without departing from the spirit of the present invention are within the scope of protection covered by the claims of the present invention.

Claims

1. A Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning, characterized in that: The following steps are involved: S1. Model all unknown quantities in the channel estimation problem as random variables and construct a Bayesian probability graph model. For the channel elements to be estimated, introduce a structured mixed Gaussian prior distribution, and transform the mixed Gaussian prior from a sum form to a product form by introducing Bernoulli discrete random variables. Introduce corresponding conjugate priors for all other random variables. S2. Based on the Gibbs sampling principle, derive the conditional posterior distribution of all random variables in the Bayesian probability graphical model; S3, run multiple parallel Gibbs samplers to perform serial sampling of the conditional posterior distribution of all random variables in dimensional order; After a preset burn-in period, samples are collected for each sampler to converge; S4. Obtain an estimated value of the channel matrix by averaging the channel element samples of each sampler.

2. The Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning according to claim 1, characterized in that: In step S1: The structured Gaussian mixture prior distribution is defined as: Among them, α c is a mixed Gaussian precision vector describing the joint sparsity among users, α k is a mixed Gaussian precision vector describing the sparsity of the user itself; H k (n,m) represents the channel element in the nth row and mth column of the kth user equipment channel matrix, ρ n represents the mixing coefficient of the mixed Gaussian prior, which ranges from [0,1]. K, N, and M represent the number of users, the number of columns in the channel matrix, and the number of rows in the channel matrix, respectively. N C Represents complex Gaussian distribution; describes the inherent sparsity and partial shared sparsity of the user equipment channel by introducing a mixed Gaussian prior distribution; Introducing Bernoulli discrete variable w n , whose expression is Convert the mixed Gaussian prior into a product form Among them, α c,n is the noise precision variable describing the joint sparsity of the nth row of the inter-user channel matrix, α k,n It is the noise accuracy variable that describes the sparsity of the nth row of the user's own channel matrix.

3. The Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning according to claim 1, characterized in that: The step S1 further comprises: The mixing coefficient ρ of the mixed Gaussian prior n Introducing the beta prior, its expression is: r n ~Beta(λ0,λ1) Where λ0 and λ1 are the hyperparameters of the beta prior; The precision element α of the Gaussian mixture c,n and α k,n Introducing gamma prior, its expressions are: α c,n ~Gamma(a c ,b c ) α k,n ~Gamma(a0,b0) where a c With b c is α c,n Hyperparameters of the random variable gamma prior, a0 and b0 are α k,n Hyperparameters of the random variable gamma prior; The gamma prior is introduced for the unknown noise precision random variable, and its expression is: b k ~Gamma(θ0,θ1) Among them, θ0 and θ1 are random variables β k Hyperparameters of the gamma prior.

4. The Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning according to claim 3, characterized in that: The conditional posterior distribution in step S2 includes: Mixing coefficient variable ρ n The conditional posterior of is a Beta distribution, expressed as: p(r n |-)∝Beta(λ0+w n ,λ1-w n +1) Noise accuracy variable α c,n The conditional posterior of is a gamma distribution, expressed as: Noise accuracy variable α k,n The conditional posterior of is a gamma distribution, expressed as: Bernoulli variable w n The conditional posterior of is a Bernoulli distribution, expressed as: in, Noise accuracy variable β k The conditional posterior probability distribution of is a gamma distribution, expressed as: Where T represents the pilot length, X represents the pilot matrix, and Y k represents the received signal matrix of the kth user equipment; Channel element variable H k The conditional posterior of (n,m) is a complex Gaussian distribution, expressed as: Where X(i,n) represents the element in the i-th row and n-th column of the pilot matrix; in represents the element of the i-th row and m-th column of the signal matrix received by the k-th user equipment. The definition of E(i) is given by the following formula:

5. The Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning according to claim 4, characterized in that: The S3 includes: initializing multiple parallel Gibbs samplers, performing Gibbs sampling iterations, and after each traversal and sampling of the conditional posteriori of random variables of all dimensions, determining whether the number of iterations has reached the burn-in period, if not, continuing iterative sampling, and if reaching the burn-in period, collecting all samples currently sampled, and continuing sampling until the maximum number of iterations is reached.

6. A communication device, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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