Markov chain monte carlo channel estimation method based on sparse bayesian learning

Abstract

The application 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 unknown quantities in a channel estimation problem as random variables, and constructing a Bayesian probabilistic graph model; introducing a structured mixture Gaussian prior distribution for channel elements, and converting the mixture Gaussian prior into a product form through a Bernoulli discrete variable; deriving conditional posterior distributions of all variables, performing high-dimensional sampling through multiple parallel Gibbs samplers, and obtaining a channel estimation value by averaging converged samples. The application solves the problems of traditional compressed sensing algorithms, such as insufficient dependence on prior information and easy falling into local optimization, by combining sparse Bayesian learning and Markov chain Monte Carlo method, significantly improves channel estimation accuracy, and is suitable for super-large-scale MIMO systems by reducing computational complexity through parallel sampling.

Description

TECHNICAL FIELD

[0001] The present application relates to a Markov Chain Monte Carlo channel estimation method based on sparse Bayesian learning, belonging to the technical field of wireless communication, and suitable for channel state information acquisition of super large-scale Multiple-Input Multiple-Output (MIMO) system. BACKGROUND

[0002] In recent years, super large-scale Multiple-Input Multiple-Output (MIMO) technology has greatly improved the spectral efficiency and energy efficiency by deploying a large number of antennas at the base station. 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] Based on the channel sparsity of the compression sensing technology, the channel estimation overhead can be effectively reduced, but the regularization method of traditional compression sensing is easily affected by structural errors, and the traditional greedy algorithm relies on accurate prior information and is difficult to obtain a global optimal solution. Sparse Bayesian learning improves the sparse modeling and inference ability by parameterizing the prior model, but the commonly used deterministic approximation method (such as variational inference) has decreased performance when the model deviates from the hypothesis, resulting in increased estimation error.

[0004] In contrast, Markov Chain Monte Carlo (MCMC) as a stochastic approximation method can approximate complex probability distributions with asymptotic precision, providing a powerful inference framework for high-dimensional channel estimation problems. MCMC overcomes the high-dimensional problem that traditional methods are difficult to handle by constructing Markov chains and sampling from target distributions, and can avoid being trapped in local optima. In addition, MCMC supports parallel computing, further improving its application potential in super large-scale MIMO systems. By combining efficient sampling strategies, MCMC technology has shown superior performance in complex sparse channel inference, providing a practical solution for efficient channel estimation. SUMMARY

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

[0006] Technical scheme: The Markov Chain Monte Carlo channel estimation method based on sparse Bayesian learning of the present application comprises the following steps:

[0007] S1. Model all unknown quantities in the channel estimation problem as random variables and construct a Bayesian probability graphical 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. Run multiple parallel Gibbs samplers to serially sample the conditional posterior distributions of all random variables in dimensionally ordered order; after a preset burn-in period, collect the samples at which each sampler converges;

[0010] S4. Obtain an estimated value of the channel matrix element by averaging the channel element random variable samples 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 graphical 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 a complex Gaussian distribution; by introducing a mixed Gaussian prior distribution, it describes the inherent sparsity and partially shared sparsity of the user equipment channel;

[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, and k,n is the noise precision variable describing the sparsity of the nth row of the self-user channel matrix;

[0019] S104, the mixing coefficient of the mixed Gaussian prior is n Beta prior is introduced, and its expression is:

[0020] ρ n ~ Beta ( λ0, λ1)

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

[0022] S105, the precision element of the mixed Gaussian is c,n And k,n Gamma prior is introduced, and its expression is:

[0023] α c,n ~ Gamma ( a c , b c )

[0024] α k,n ~ Gamma ( a0, b0)

[0025] Where a c and b c are the hyperparameters of the gamma prior of the random variable α c,n , and a0 and b0 are the hyperparameters of the gamma prior of the random variable α k,n ;

[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 the hyperparameters of the gamma prior of the random variable β k ;

[0029] S107, according to 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, all random variables introduced in step S1 derive their conditional posterior probability, i.e. the derivation of step S2, which specifically includes:

[0033] S201, derive the conditional posterior probability distribution of the mixing coefficient variable p in the Gaussian mixture prior n p(ρ | X, Y) ∝ Beta(λ0+ w n , λ1- w n +1)

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

[0035] S202, derive the conditional posterior probability distribution of the noise precision variable a c,n p(a | X, Y) ∝ Gamma(λ0+ w k,n , λ1- w k +1)

[0036]

[0037] S203, derive the conditional posterior probability distribution of the noise precision variable a k,n p(a | X, Y) ∝ Gamma(λ0+ w k,n , λ1- w k +1)

[0038]

[0039] S204, derive the conditional posterior probability distribution of the introduced discrete Bernoulli variable, whose expression is

[0040]

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

[0042]

[0043] S205, derive the conditional posterior probability distribution of the noise precision variable a, whose expression is

[0044]

[0045] where T represents the pilot length, X represents the pilot matrix, 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, whose expression is

[0047]

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

[0049] where denotes the element of the received signal matrix of the kth user equipment in the i th row and the m th column, and the definition of E(i) is given by the following formula:

[0050] Preferably, the step S3 specifically comprises:

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

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

[0053]

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

[0055] S303, run multiple parallel Gibbs samplers and collect the samples that have converged for each sampler.

[0056] The application 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 method when executing the computer program.

[0057] The application also provides a computer readable storage medium, which stores a computer program, and wherein the processor implements the steps of the method when executing the computer program.

[0058] The application also provides a computer program product comprising a computer program, and wherein the processor implements the steps of the method when executing the computer program.

[0059] Advantages: Compared with the prior art, the technical scheme provided by the application has the following advantages:

[0060] In a frequency division duplex system, downlink channel estimation faces high training overhead and feedback cost. Traditional compressed sensing methods rely on prior assumptions and are easily affected by structural errors, and the variational inference method of sparse Bayesian learning has poor performance when the model is mismatched. The application combines the accurate inference ability of Markov Chain Monte Carlo (MCMC) and the flexible modeling of sparse Bayesian learning, and realizes efficient and high-precision channel estimation through parallel Gibbs sampling.

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

[0062] Simulation results show that the NMSE performance of the application is close to the theoretical lower bound, and is better than the traditional compressed sensing and variational inference method. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 A flow chart of the Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning of the embodiment of the application;

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

[0065] Figure 3 A normalized mean square error (NMSE) performance comparison chart of the method of the application and the comparative method. DETAILED DESCRIPTION

[0066] The application will be further described below in combination with the drawings and embodiments.

[0067] I. System model used in this embodiment

[0068] This paper considers a frequency division duplex multi-user MIMO system with one base station and K user devices. The base station is equipped with N antennas, and each user device is equipped with M antennas. In the considered frequency division duplex downlink training phase, the base station broadcasts a pilot sequence of length T to each user device. Then, the user device sends the feedback of the received signal to the base station, and then the estimation of the downlink channel of all user devices is completed at the base station end. The received signal can be represented 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 zero mean and variance Due to the limited number of 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. Assume that the antennas installed at the base station and user equipment employ a uniform linear array. Using the angle domain representation, the channel matrix can be expressed as:

[0071]

[0072] where and denote the discrete Fourier transform (DFT) matrices for the angle domain transformation at the user equipment and base station ends, respectively, is the angle domain channel matrix. Let denote the m-th column of H k . The support set supp(h) = {i: h(i)≠0} consists of the index set of h with h(i) denoting the i-th entry of h. From the above we can summarize the two main features of the considered multi-user massive MIMO system as follows:

[0073] User equipment internal sparsity: for the k-th user equipment (k = 1, …, K), all M columns of H k have the same sparsity pattern:

[0074]

[0075] Partial shared sparsity: for the K user equipments, {H k} share a partial common support:

[0076]

[0077] Second, the specific steps of the embodiment

[0078] As shown in Figure 2 , the present embodiment provides a sparse Bayesian probabilistic graphical model based on a Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning, which contains all unknown random variables in the system model and their mutual relationships. As shown in Figure 1 , the present embodiment provides a flowchart 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 graphical 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. Run multiple parallel Gibbs samplers to serially sample the conditional posterior distributions of all random variables in dimensionally ordered order; after a preset burn-in period, collect the samples at which each sampler converges;

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

[0083] The step S1 specifically includes:

[0084] S101. Model all unknown quantities as random variables and construct a Bayesian probability graphical 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 The mixing coefficient of the mixed Gaussian prior is in the range [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. By introducing the mixed Gaussian prior distribution, the inherent sparsity and partially shared sparsity of the user equipment channel 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, and k,n is the noise precision variable describing the sparsity of the nth row of the self-user channel matrix;

[0091] S104, the mixing coefficient of the mixed Gaussian prior n Beta prior is introduced, and its expression is:

[0092] ρ n ~ Beta (λ0, λ1)

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

[0094] S105, the precision element of the mixed Gaussian c,n and α k,n Gamma prior is introduced, and its expression is:

[0095] α c,n ~ Gamma (a c , b c )

[0096] α k,n ~ Gamma (a0, b0)

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

[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 hyperparameters of the gamma prior of the random variable β k ;

[0101] S107, according to 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 a matrix composed of all user received signal matrices, and H represents a matrix composed of all user channel matrices. The conditional posterior probability of all random variables introduced in step S1 is derived, that is, the derivation of step S2, which specifically includes:

[0103] S201, the conditional posterior probability distribution of the mixing coefficient variable ρ n in the Gaussian mixture prior is derived, and its expression is:

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

[0105] S202. Derivation of 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 Bernoulli distribution, where

[0112]

[0113] S205. Derivation of 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 the 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 in the i-th row and m-th column of the received signal matrix of 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, M, a single Gibbs sampler samples the above derived conditional posterior in the order of dimensions;

[0122] S302, sample for a certain number of iterations, after exceeding the preset pre-burning period, collect the samples that have converged:

[0123]

[0124] where N burn-in represents the number of iterations of the Gibbs sampling pre-burning period, N collect represents the number of samples collected after the pre-burning period, N burn-in +N collect represents the total number of iterations of the Gibbs sampling;

[0125] S303, initialize multiple parallel Gibbs samplers, and perform Gibbs sampling iterations, and each time the conditional posterior of the random variable of all dimensions is sampled, it is judged whether the number of iterations reaches the pre-burning period, if not, continue to iterate and sample, if the pre-burning period is reached, collect all samples at this time, and continue to sample until the maximum number of iterations is reached.

[0126] S4, average all collected H k (n,m) samples to estimate.

[0127] III. Implementation effect

[0128] In order to enable those skilled in the art to better understand the present application scheme, the following gives the result comparison of the Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning and the comparative method in the embodiment.

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

[0130] In a large-scale MIMO system, the base station is equipped with 64 antennas, and there are 8 user devices, each user device is 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. It is assumed that For k = 1,...,K, the channel is normalized as 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 a truncated discrete Fourier transform matrix to ensure the orthogonality between columns. The hyperparameters of the prior are set to the following values: a0 = b0 = a c = b c = λ0 = λ1 = θ0 = θ1 = 10 -3The present application uses 10 parallel samplers in the proposed method, each of which iterates 300 times, and finally takes 32 samples, a total of 320 samples for estimation. The normalized mean square error (NMSE) is selected as the performance indicator, defined as follows:

[0131]

[0132] Figure 3 The NMSE performance comparison figure of the present application and the comparative methods in the simulation scenario is shown, the comparative methods include the orthogonal matching pursuit channel estimation method in the literature "J. Lee, G.-T. Gil, and Y. H. Lee, "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 literature "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), the expectation-maximization Gaussian-mixture approximate message passing in the literature "J. P. Vila and P. Schniter, "Expectation-maximization Gaussian-mixture approximate message passing," IEEE Trans. Signal Process., vol. 61, no. 19, pp. 4658-4672, Oct. 2013." (hereinafter referred to as estimation scheme 3), the special case of the present application under Gaussian prior (hereinafter referred to as estimation scheme 4), and the theoretical optimal ideal linear mean square error estimation lower bound. It can be seen that the present application has performance improvement compared with each of the comparative methods under different SNR values, reaching the estimation performance close to the optimal lower bound, while utilizing parallelism to generate sufficient samples, and the algorithm complexity is smaller than that of estimation scheme 3.

[0133] The application further 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 method when executing the computer program.

[0134] The application further provides a computer readable storage medium, which stores a computer program, and wherein the computer program is executed by a processor to implement the steps of the method.

[0135] The application further provides a computer program product, which comprises a computer program, and wherein the computer program is executed by a processor to implement the steps of the method.

[0136] The above description is only a preferred embodiment of the application, and cannot be used to limit the scope of the application, and it should be understood that any equivalent changes made without departing from the spirit of the application shall fall within the scope of protection of the claims of the application.

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 graphical 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 dimension order; After a preset burn-in period, samples are collected for each sampler to converge; S4, obtaining an estimated value of the channel matrix by averaging the channel element samples of each sampler; In the 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 a complex Gaussian distribution; by introducing a mixed Gaussian prior distribution, it describes the inherent sparsity and partially shared sparsity of the user equipment channel; 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 is the noise precision variable that describes the sparsity of the nth row of the user's own channel matrix; The step S1 further includes: 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 gamma prior of the random variable; 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; The conditional posterior distribution in step S2 includes: Mixing coefficient variable ρ n The conditional posterior of is Beta distributed, 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 Bernoulli distribution, which is expressed as: in, Noise accuracy variable β k The conditional posterior probability distribution of is gamma distribution, which is expressed as: Among them, 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 in the i-th row and m-th column of the received signal matrix of the k-th user equipment. The definition of E(i) is given by the following formula:

2. The Markov chain Monte Carlo channel estimation method based on sparse Bayesian learning according to claim 1, 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, judging whether the number of iterations has reached the burn-in period; if not, continuing iterative sampling; if reaching the burn-in period, collecting all samples currently sampled, and continuing sampling until the maximum number of iterations is reached.

3. A communication device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 2 are implemented.

4. 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 2 are implemented.

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