A channel estimation method based on sparse Bayesian learning

Abstract

The present application relates to the technical field of wireless communication, especially to a channel estimation method based on sparse Bayesian learning, comprising the following steps: step A, using the sparse characteristics of the millimeter wave channel to model the channel, and constructing the corresponding RIS assisted MIMO communication system model; step B, first constructing two-layer sparse prior information of the channel, then factorizing the joint posterior probability density function of the parameters, and finally drawing the corresponding factor graph model according to the factorization; step C, for the factor graph model in step B, combining the unitary transformation approximate message passing, and using the sparse Bayesian algorithm framework to perform channel estimation; step D, repeating step C until the algorithm converges; the method in the present application has low complexity, reduces the pilot overhead of the system, and has high algorithm universality.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a channel estimation method based on sparse Bayesian learning. Background Technology

[0002] Mobile communication networks are a key infrastructure supporting the digital transformation and upgrading of various industries, driving efficiency and power changes. Intelligent and comprehensive digital information infrastructure serves as the information artery and new digital foundation supporting economic and social development. However, highly complex networks, high-cost hardware, and increasing energy consumption are key challenges facing future mobile communications. Reconfigurable intelligent surfaces (RIS), characterized by low cost, low energy consumption, programmability, and ease of deployment, offer the potential to break through the constraints of traditional wireless communication by constructing intelligent and controllable wireless environments, bringing a completely new paradigm to future mobile communication networks and possessing broad technological and industrial prospects.

[0003] In RIS-assisted wireless communication systems, in addition to the line-of-sight channel between the base station and the terminal, there are also cascaded channels between the base station and the RIS, and between the RIS and the terminal. Acquiring cascaded Channel State Information (CSI) is one of the fundamental problems that needs to be solved in passive RIS systems. Accurate CSI is indispensable for enhancing RIS performance and achieving intelligent control of the electromagnetic environment. However, the increased channel estimation dimensionality due to the increased number of RIS units undoubtedly presents a significant challenge to channel estimation. Furthermore, RIS-assisted communication has been extended to millimeter-wave environments, and many researchers aim to design more accurate channel estimation algorithms by leveraging the sparse structure unique to millimeter-wave channels in the angular domain. Researchers have proposed a three-stage channel estimation algorithm for RIS-assisted millimeter-wave uplink communication systems to reduce system pilot overhead, but this algorithm requires the RIS phase shift matrix to use a Bernoulli random matrix. In downlink millimeter-wave communication systems, some scholars have estimated the cascaded channel between the RIS-base station and the RIS-user using matrix decomposition and matrix completion methods, but this requires the correlation matrix to be sparse or low-rank. Utilizing slowly varying channel information and the sparsity of the channel, some researchers have designed a channel estimation algorithm combining message passing. Some scholars have proposed a three-stage channel estimation algorithm for RIS-assisted multi-user communication systems, aiming to design appropriate pilot signals to obtain accurate channel information. Other scholars have proposed a channel estimation method by utilizing the sparsity of the channel and combining it with a tensor decomposition model.

[0004] In summary, the computational complexity of the aforementioned methods is proportional to the square or cube of the number of RIS units, or they have specific requirements regarding the sparsity or low rank of the matrices involved. This undoubtedly hinders the widespread adoption of these channel estimation methods. Therefore, designing channel estimation algorithms with lower complexity and higher versatility is of great significance for the further application of RIS in next-generation wireless communication systems. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art, avoid the obstacles and high complexity of traditional algorithms, and provide a degree channel estimation method based on sparse Bayesian learning. The method in this invention has low complexity, reduces the pilot overhead of the system, and has high algorithm versatility.

[0006] The objective of this invention is achieved through the following measures: a channel estimation method based on sparse Bayesian learning, comprising the following steps:

[0007] Step A: Utilize the sparsity characteristics of millimeter-wave channels to perform channel modeling and construct the corresponding Intelligent Reflecting Surface (RIS)-assisted Multiple-Input Multiple-Output (MIMO) communication system model.

[0008] Step B: First, construct two layers of sparse prior information for the channel, then factorize the joint posterior probability density function of the parameters, and finally draw the corresponding factor graph model based on the factorization.

[0009] Step C: For the factor graph model in Step B, channel estimation is performed using the sparse Bayesian algorithm framework, combined with the unitary transform approximate message passing.

[0010] Step D, repeat step C, until the algorithm converges.

[0011] Preferably, in step A, consider a RIS-assisted uplink millimeter-wave communication system, wherein a RIS plane equipped with N reflector elements is arranged between a base station with M antennas and K users; the channel between the base station and the RIS is... The channel between RIS and the user is Assuming the base station antenna uses a uniform linear array, and the RIS uses... A uniform planar antenna array, in which ,but Specifically, it is expressed as follows:

[0012] ,

[0013] in, Indicates average path loss. For the number of paths, This represents the gain on the p-th path. For the angle of arrival, and To leave the angle, and These represent the response vectors of the base station and the RIS, respectively.

[0014] ,

[0015] and , and Let wavelength and antenna spacing represent the wavelength and antenna spacing, respectively. Then, the channel can be represented in the angular domain as follows:

[0016] ,

[0017] in, Represents the discrete Fourier transform matrix. Let represent a sparse matrix containing P non-zero elements. Similarly, the channel between the k-th user and the RIS can be represented as:

[0018] ,

[0019] And it can be represented in the angle domain as:

[0020] ,

[0021] This will be expanded to matrix form, i.e.:

[0022] ,

[0023] in, Considering that RIS has L phase configuration states, the received signal at the base station during the coherence time is represented as:

[0024] ,

[0025] in, Represents the phase shift matrix The OK, This indicates a mean of 0 and a noise precision of [value missing]. Additive white Gaussian noise, after removing the pilot signal and quantizing, yields:

[0026] ,

[0027] in ,Will Denoted in matrix form, Transpose it to get:

[0028] ,

[0029] in, .

[0030] Preferably, in step B, for sparse channel parameters in the angle domain... and Assume that both follow a Gaussian distribution, i.e.:

[0031] ,

[0032] And variance and All follow a Gamma distribution:

[0033]

[0034] in, It corresponds to the hyperparameter in the probability density function, and is related to the phase shift matrix. Perform SVD decomposition, i.e. Therefore, we can obtain After sorting, we get

[0035] ,

[0036] in, In the receiving matrix Given the channel and Angular domain sparse matrix and variance matrix and intermediate variables , and and noise accuracy The joint posterior probability density function is factored as follows:

[0037] ,

[0038] Then, based on the results of factorization, the corresponding factor graph model can be drawn.

[0039] Preferably, step C specifically includes the following steps:

[0040] Step C1: In Part I of the factor graph model, the unitary transform-based approximate message passing (UAMP) algorithm framework is used to process the input message. and output messages Update;

[0041] Step C2: In Part II of the factor graph model, based on the relationships between variables and the various rules of message passing, first update the reverse message. and Update positive messages again Then, based on the symmetry of the variables in the factor graph model, the corresponding backpropagation message is calculated. and positive message dissemination ;

[0042] Step C3: In Part III of the factor graph model, the sparse Bayesian learning algorithm framework is used to estimate the sparse variables, first updating the reverse message. Then update the positive message. Next, based on the symmetry of the variables in the factor graph model, the backpropagation messages are updated. Then update the positive message. Finally, the approximate marginal posterior of the sparse variable to be estimated is calculated from the obtained information, and the estimated value is obtained.

[0043] Preferably, step C1 specifically includes:

[0044] In Part I of the factor graph model, the UAMP algorithm framework is used to process the input message. and output messages Update:

[0045] ,

[0046] in, This represents the mean and variance of the variables in the above message.

[0047] Preferably, step C2 specifically includes:

[0048] In Part II of the factor graph model, based on the relationships between variables and the various rules of message passing, the reverse message is updated first. :

[0049] ,

[0050] in, This indicates the mean and variance of the variables in the above message; then update the positive message. :

[0051] ,

[0052] in, This represents the mean and variance of the variables in the above message; then, based on the symmetry of the variables in the factor graph model, the corresponding backpropagation message is calculated. , :

[0053] ,

[0054] in, This represents the mean and variance of the variables in the above message; forward propagation message. :

[0055] ,

[0056] in, This represents the mean and variance of the variables in the above message.

[0057] Preferably, step C3 specifically includes:

[0058] In Part III of the factor graph model, a sparse Bayesian learning algorithm framework is used to estimate sparse variables, first by updating the reverse message. :

[0059] ,

[0060] in, express The estimated value This indicates the mean and variance of the variables in the above message; then the positive message is updated. :

[0061] ,

[0062] in, This represents the mean and variance of the variables in the above message; next, based on the symmetry of the variables in the factor graph model, the backpropagation message is updated. , :

[0063] ,

[0064] in, This indicates the mean and variance of the variables in the above message; then the positive message is updated. :

[0065] ,

[0066] in, This represents the mean and variance of the variables in the above message; finally, the approximate marginal posterior of the sparse variable to be estimated is calculated from the obtained message, and the estimated value is obtained:

[0067] ,

[0068] in, This represents the mean and variance of the variables in the above message.

[0069] The beneficial effects of this invention are as follows: This invention targets RIS-assisted millimeter-wave MIMO communication systems. Considering the sparse characteristics of millimeter-wave channels in the angular domain, it transforms the channel estimation problem into a structured sparse signal recovery problem. Combining a sparse Bayesian learning framework, a message-passing iterative estimation algorithm is designed. Since the proposed sparse Bayesian-based message-passing algorithm can more accurately estimate the sparse prior information of the channel, it achieves better estimation performance. Simultaneously, the algorithm has lower computational complexity, significantly reducing the system's pilot overhead, and has no special requirements for the correlation matrix, resulting in higher algorithm versatility. Numerical results show that compared with existing algorithms, this algorithm has significant performance advantages, is closer to the performance lower bound obtained based on least squares, and has lower algorithm complexity. Attached Figure Description

[0070] Figure 1 This is a flowchart of the present invention;

[0071] Figure 2 This is a schematic diagram of a factor graph model;

[0072] Figure 3 A schematic diagram showing the simulation comparison of the estimation performance of different algorithms under different SNRs for different numbers of RIS training configurations;

[0073] Figure 4 A schematic diagram showing the simulation comparison of the estimation performance of different algorithms under different numbers of RIS training configurations when SNR=20dB;

[0074] Figure 5 This is a system structure diagram of the present invention. Detailed Implementation

[0075] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] Example 1: As Figures 1-5 As shown, a channel estimation method based on sparse Bayesian learning includes the following steps:

[0077] Step A: Utilize the sparsity characteristics of millimeter-wave channels to perform channel modeling and construct the corresponding Intelligent Reflecting Surface (RIS)-assisted Multiple-Input Multiple-Output (MIMO) communication system model.

[0078] Step B: First, construct two layers of sparse prior information for the channel, then factorize the joint posterior probability density function of the parameters, and finally draw the corresponding factor graph model based on the factorization.

[0079] Step C: For the factor graph model in Step B, channel estimation is performed using the sparse Bayesian algorithm framework, combined with the unitary transform approximate message passing.

[0080] Step D, repeat step C, until the algorithm converges.

[0081] In step A, consider a RIS-assisted uplink millimeter-wave communication system, in which a RIS plane equipped with N reflector elements is arranged between a base station with M antennas and K users; the channel between the base station and the RIS is... The channel between RIS and the user is Assuming the base station antenna uses a uniform linear array, and the RIS uses... A uniform planar antenna array, in which ,but Specifically, it is expressed as follows:

[0082] ,

[0083] in, Indicates average path loss. For the number of paths, This represents the gain on the p-th path. For the angle of arrival, and To leave the angle, These represent the response vectors of the base station and the RIS, respectively.

[0084] ,

[0085] and , and Let wavelength and antenna spacing represent the wavelength and antenna spacing, respectively. Then, the channel can be represented in the angular domain as follows:

[0086] ,

[0087] in, Represents the discrete Fourier transform matrix. Let represent a sparse matrix containing P non-zero elements. Similarly, the channel between the k-th user and the RIS can be represented as:

[0088] ,

[0089] And it can be represented in the angle domain as:

[0090] ,

[0091] in For inclusion A sparse vector with n non-zero elements will be expanded into matrix form, i.e.:

[0092]

[0093] in, Considering that RIS has L phase configuration states, the received signal at the base station during the coherence time is represented as:

[0094] ,

[0095] in, Represents the phase shift matrix The OK, This indicates a mean of 0 and a noise precision of [value missing]. Additive white Gaussian noise, after removing the pilot signal and quantizing, yields:

[0096] ,

[0097] in, ,Will Denoted in matrix form, Transpose it to get:

[0098] ,

[0099] in, .

[0100] In step B, the sparse Bayesian learning method is combined with the sparse channel parameters in the angle domain. and Assume that both follow a Gaussian distribution, i.e.:

[0101] ,

[0102] And variance All follow a Gamma distribution:

[0103] ,

[0104] in, It corresponds to the hyperparameter in the probability density function, and is related to the phase shift matrix. Perform SVD decomposition, i.e. Therefore, we can obtain After sorting, we get

[0105] ,

[0106] in, In the receiving matrix Given the channel and Angular domain sparse matrix and variance matrix and intermediate variables , and and noise accuracy The joint posterior probability density function is factored as follows:

[0107] ,

[0108] in, The prior distribution representing the noise accuracy, i.e. , express Prior information, namely , express and The relationship, that is , express , and Deterministic relations, i.e. , and Both indicate a deterministic relationship, that is , express Prior information, namely , express Prior information, namely , and Both indicate a deterministic relationship, that is , express Prior information, namely , express Prior information, namely .

[0109] Then, as Figure 2 Based on the results of factorization, the corresponding factor graph model can be drawn.

[0110] Step C specifically includes the following steps:

[0111] Step C1: In Part I of the factor graph model, the unitary transform-based approximate message passing (UAMP) algorithm framework is used to process the input message. and output messages Update;

[0112] Step C2: In Part II of the factor graph model, based on the relationships between variables and the various rules of message passing, first update the reverse message. Update positive messages again Then, based on the symmetry of the variables in the factor graph model, the corresponding backpropagation message is calculated. and positive message dissemination ;

[0113] Step C3: In Part III of the factor graph model, the sparse Bayesian learning algorithm framework is used to estimate the sparse variables, first updating the reverse message. Then update the positive message. Next, based on the symmetry of the variables in the factor graph model, the backpropagation messages are updated. Then update the positive message. Finally, the approximate marginal posterior of the sparse variable to be estimated is calculated from the obtained information, and the estimated value is obtained.

[0114] Step C1 specifically includes:

[0115] In Part I of the factor graph model, the UAMP algorithm framework is used to process the input message. and output messages Update:

[0116] ,

[0117] in, This represents the mean and variance of the variables in the above message, where, and It can be obtained from the UAMP algorithm framework.

[0118] Step C2 specifically includes:

[0119] In Part II of the factor graph model, based on the relationships between variables and the various rules of message passing, the reverse message is updated first. :

[0120] ,

[0121] in, ,but The confidence level can be expressed as:

[0122] ,

[0123] in, If it was obtained from the previous iteration, then

[0124] ,

[0125] The reverse message can be calculated using the belief propagation rule. :

[0126] ,

[0127] in, .

[0128] in, This indicates the mean and variance of the variables in the above message; then update the positive message. :

[0129] ,

[0130] in, , and express The mean and variance are both obtained from the previous iteration. Using confidence propagation, we can obtain:

[0131] ,

[0132] in, , Then there is

[0133] ,

[0134] in, , yes The matrix extended from it, , This represents the mean and variance of the variables in the above message; then, based on the symmetry of the variables in the factor graph model, the corresponding backpropagation message is calculated. :

[0135] ,

[0136] in, This represents the mean and variance of the variables in the above message; forward propagation message. :

[0137] ,

[0138] in, This represents the mean and variance of the variables in the above message.

[0139] Step C3 specifically includes:

[0140] In Part III of the factor graph model, a sparse Bayesian learning algorithm framework is used to estimate sparse variables, first by updating the reverse message. :

[0141] ,

[0142] so, The confidence level can be expressed as:

[0143] ,

[0144] Therefore, we can conclude that:

[0145] ,

[0146] in and It was obtained from the previous iteration, and

[0147] ,

[0148] Therefore, there is

[0149] ,

[0150] Using the UAMP algorithm, we can obtain:

[0151] ,

[0152] in, express The estimated value This indicates the mean and variance of the variables in the above message; then the positive message is updated. :

[0153] ,

[0154] in, , and express and The vector form, and In sparse Bayesian learning, variational inference can be used to compute:

[0155] .

[0156] in, This represents the mean and variance of the variables in the above message; where As a product of multiple Gaussian messages, It is also Gaussian, that is ,in,

[0157] ,

[0158] Based on the above process, we can conclude that:

[0159] .

[0160] Next, based on the symmetry of the variables in the factor graph model, the backpropagation messages are updated. , and :

[0161] ,

[0162] in, This indicates the mean and variance of the variables in the above message; then the positive message is updated. :

[0163] ,

[0164] in, This represents the mean and variance of the variables in the above message; finally, the approximate marginal posterior of the sparse variable to be estimated is calculated from the obtained message, and the estimated value is obtained:

[0165] ,

[0166] in, This represents the mean and variance of the variables in the above message.

[0167] The following comparison between the transmission scheme of the present invention and other existing transmission schemes will make the advantages and features of the present invention more apparent.

[0168] Simulation Parameter Settings: In this section, we provide numerical experiments to demonstrate the advantages of the proposed sparse Bayesian learning-based channel estimation method. The selected comparison algorithms are a matrix calibration (MCB)-based channel estimation algorithm and a least squares-based channel estimation algorithm (lower bound of estimation performance). Scale ambiguity in the estimation is eliminated during the calculation of the normalized mean square error (NMSE). and , RIS phase matrix It is considered a partial DFT matrix, i.e., the phase matrix. It is part of the DFT matrix, assuming the Rician channel includes LOS paths and multiple NLOS paths, and the Rician factor is set to 13.2 dB, millimeter-wave channel. and The number of paths are set as follows: and The AoA and AoD parameters are determined by... The average distribution is generated. A threshold is set. and .

[0169] exist Figure 3 In this paper, we compare the NMSE performance and SNR of various estimation algorithms under different RIS configuration state L values. According to the results, the proposed method significantly outperforms the MCB method, especially when L is relatively small. In this case, the system aims to use fewer L values ​​(the number of RIS phase configurations required for channel estimation) to reduce training overhead and latency. Simulation results also show that for different L values, even small L values, the proposed method can achieve performance close to that of the OracleLS estimation method.

[0170] exist Figure 4 In the middle, change the value of L and check again. Figure 3 The performance of each estimation method is compared, with SNR set to 20 dB. Simulation results show that, as L increases, the performance of all estimation methods improves as expected. Specifically, for Specifically, when NMSE = -45dB, the method proposed in this paper can save approximately 42.2% of system overhead. In this regard, when NMSE=-35dB, the proposed method can save approximately 43.7% of system overhead, which also demonstrates the performance lower limit of the Oracle LS estimation method.

[0171] Figure 5 The system architecture diagram of this invention is a system architecture diagram of a channel estimation method based on sparse Bayesian learning, including: an initialization module 1, a sparse channel Ω estimation module 2, and a sparse channel Σ estimation module 3. Specifically:

[0172] Initialize module 1 by setting appropriate initial parameters to activate the algorithm's iterative mechanism;

[0173] Channel estimation module 2 uses a sparse Bayesian learning algorithm to derive the corresponding message passing process, calculate the marginal posterior probability distribution of the sparse channel Ω, and obtain the estimated value.

[0174] Noise accuracy module 3 uses a sparse Bayesian learning algorithm to derive the corresponding message passing process, calculate the marginal posterior probability distribution of the sparse channel Σ, and obtain the estimated value.

[0175] For the specific channel estimation calculation process based on sparse Bayesian learning in the RIS-assisted MIMO communication system, please refer to the above embodiments. The embodiments of the present invention will not be repeated here.

[0176] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A channel estimation method based on sparse Bayesian learning, characterized in that, Includes the following steps: Step A: Utilize the sparsity characteristics of millimeter-wave channels to perform channel modeling and construct the corresponding reconfigurable smart metasurface-assisted multi-input multi-output communication system model. Step B: First, construct two layers of sparse prior information for the channel, then factorize the joint posterior probability density function of the parameters, and finally draw the corresponding factor graph model based on the factorization. Step C: For the factor graph model in Step B, channel estimation is performed using the sparse Bayesian algorithm framework, combined with the unitary transform approximate message passing. Step C specifically includes the following steps: Step C1: In part I of the factor graph model, an approximate message-passing algorithm framework based on unitary transformation is used to process the input message. and output messages Update; Step C2: In Part II of the factor graph model, based on the relationships between variables and the various rules of message passing, first update the reverse message. and Update positive messages again , and Then, based on the symmetry of the variables in the factor graph model, the corresponding backpropagation message is calculated. , and positive message dissemination , and ; Step C3: In Part III of the factor graph model, the sparse Bayesian learning algorithm framework is used to estimate the sparse variables, first updating the reverse message. , and Then update the positive message. and Next, based on the symmetry of the variables in the factor graph model, the backpropagation messages are updated. , and Then update the positive message. and Finally, the approximate marginal posterior of the sparse variable to be estimated is calculated from the obtained information, and the estimated value is obtained. Step D, repeat step C, until the algorithm converges.

2. The channel estimation method based on sparse Bayesian learning according to claim 1, characterized in that: In step A, consider a RIS-assisted uplink millimeter-wave communication system, in which a RIS plane equipped with N reflector elements is arranged between a base station with M antennas and K users; the channel between the base station and the RIS is... The channel between RIS and the user is Assuming the base station antenna uses a uniform linear array, and the RIS uses... A uniform planar antenna array, in which ,but Specifically, it is expressed as follows: ， in, Indicates average path loss. For the number of paths, This represents the gain on the p-th path. For the angle of arrival, and To leave the angle, and These represent the response vectors of the base station and the RIS, respectively. ， and , and Let wavelength and antenna spacing represent the wavelength and antenna spacing, respectively. Then, the channel can be represented in the angular domain as follows: ， in, , , , Represents the discrete Fourier transform matrix. Let represent a sparse matrix containing P non-zero elements. Similarly, the channel between the k-th user and the RIS can be represented as: ， And it can be represented in the angle domain as: ， This will be expanded to matrix form, i.e.: ， in, Considering that RIS has L phase configuration states, the received signal at the base station during the coherence time is represented as: ， in, Represents the phase shift matrix The OK, This indicates a mean of 0 and a noise precision of [value missing]. Additive white Gaussian noise, after removing the pilot signal and quantizing, yields: ， in, , ,Will Denoted in matrix form, Transpose it to get: ， in .

3. The channel estimation method based on sparse Bayesian learning according to claim 1, characterized in that: In step B, for the sparse channel parameters in the angle domain and Assume that both follow a Gaussian distribution, i.e.: ， ， And variance and All follow a Gamma distribution: , in, It corresponds to the hyperparameter in the probability density function, and is related to the phase shift matrix. Perform SVD decomposition, i.e. Therefore, we can obtain After sorting, we get , in, In the receiving matrix Given the channel and Angular domain sparse matrix and variance matrix and intermediate variables , and and noise accuracy The joint posterior probability density function is factored as follows: , Then, based on the results of factorization, the corresponding factor graph model can be drawn.

4. The channel estimation method based on sparse Bayesian learning according to claim 1, characterized in that: Step C1 specifically includes: In Part I of the factor graph model, the UAMP algorithm framework is used to process the input message. and output messages Update: , in, This represents the mean and variance of the variables in the above message.

5. The channel estimation method based on sparse Bayesian learning according to claim 1, characterized in that: Step C2 specifically includes: In Part II of the factor graph model, based on the relationships between variables and the various rules of message passing, the reverse message is updated first. : , in, This indicates the mean and variance of the variables in the above message; then update the positive message. : , , in, This represents the mean and variance of the variables in the above message; then, based on the symmetry of the variables in the factor graph model, the corresponding backpropagation message is calculated. , : , in, This represents the mean and variance of the variables in the above message; forward propagation message. : , in, This represents the mean and variance of the variables in the above message.

6. The channel estimation method based on sparse Bayesian learning according to claim 1, characterized in that: Step C3 specifically includes: In Part III of the factor graph model, a sparse Bayesian learning algorithm framework is used to estimate sparse variables, first by updating the reverse message. : , in, express The estimated value, This indicates the mean and variance of the variables in the above message; then the positive message is updated. : , in, This represents the mean and variance of the variables in the above message; next, based on the symmetry of the variables in the factor graph model, the backpropagation message is updated. , : , in, This indicates the mean and variance of the variables in the above message; then the positive message is updated. : , in, This represents the mean and variance of the variables in the above message; finally, the approximate marginal posterior of the sparse variable to be estimated is calculated from the obtained message, and the estimated value is obtained: , in, This represents the mean and variance of the variables in the above message.

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