Upa near field channel estimation method based on two-dimensional block sparsity

Abstract

This invention provides a UPA near-field channel estimation method based on two-dimensional block sparsity, comprising: representing the UPA near-field channel matrix as the sum of the outer products of the horizontal and vertical ULA near-field steering vectors; constructing improved DFT dictionaries in the horizontal and vertical directions respectively; representing the channel matrix as a total coefficient matrix under these dictionaries, which presents a two-dimensional block sparse structure determined by the outer product of the horizontal and vertical block sparse representation vectors, thereby transforming channel estimation into a two-dimensional block sparse signal recovery problem; and solving the problem using the 2D-PCSBL algorithm, in which the accuracy parameter of each sparse coefficient in the prior distribution is determined by the weighted sum of its own hyperparameter and the hyperparameters of its two-dimensional neighbors, to capture the sparse coupling characteristics of the UPA near-field channel in the horizontal and vertical dimensions. This invention achieves high-precision channel estimation with fewer pilots and a lower signal-to-noise ratio, and its computational complexity is comparable to that of the one-dimensional block sparse method.

Description

Technical Field

[0001] This invention relates to communication technology, and more specifically to a near-field channel estimation technique for ultra-large-scale uniform planar arrays (UPA) used in millimeter-wave / terahertz communication. Background Technology

[0002] Very large-scale antenna arrays (ELAAs) have become a key enabling technology for next-generation communications, achieving ultra-high array gain and providing an effective solution to the severe path loss in millimeter-wave / terahertz (mmWave / THz) communications. Unfortunately, accurate channel state information (CSI) is crucial to fully realizing the potential of ELAAs, but obtaining such CSI faces significant practical challenges. As their Rayleigh distance extends to tens or even hundreds of meters, the spherical wavefront assumption must be employed to accurately capture propagation characteristics, resulting in a near-field channel determined by both distance and angle parameters. In this context, traditional far-field channel estimation methods, such as orthogonal matched pursuit (OMP), sparse Bayesian learning (SBL), and atomic norm minimization (ANM), become inapplicable. Therefore, a novel channel estimation method is needed for efficient estimation of near-field ELAA channels.

[0003] 1) The idea behind the polar-domain method is to construct a dictionary by jointly sampling the two-dimensional angle domain and distance domain, which can effectively alleviate the energy diffusion problem caused by traditional angle domain transformation.

[0004] 2) The idea behind the improved Discrete Fourier Transform (DFT) matrix approach is to introduce an improved DFT matrix as a dictionary and represent the near-field channel as a block-sparse mode. Based on this, methods such as Block Orthogonal Matching Pursuit (BOMP) and Mode Coupled Sparse Bayesian Learning (PCSBL) can be used to estimate the near-field channel with lower pilot overhead.

[0005] The number of atoms in polar-domain-based methods far exceeds the channel dimension, significantly increasing computational complexity. Furthermore, the non-unitary nature of the dictionary used, often exhibiting high coherence, leads to poor Restricte Disometry Property (RIP), thus degrading channel estimation performance. Additionally, existing methods were initially designed for uniform linear array ULAs (Uniform Linear Assemblies). While polar-domain-based methods can be extended to ULA scenarios, their channel estimation accuracy remains unsatisfactory. In contrast, while block-sparse methods offer good estimation performance and low pilot overhead in ULA systems, they cannot be directly extended to ULA scenarios. Summary of the Invention

[0006] The technical problem to be solved by this invention is to address the shortcomings of existing near-field channel estimation methods when applied to ultra-large-scale uniform planar arrays, which fail to consider the coupling characteristics of the sparse structure of the channel in the horizontal and vertical dimensions, resulting in redundancy in dictionary representation and poor condition number of compressed sensing measurement matrix. This invention provides a UPA near-field channel estimation method that can utilize a two-dimensional sparsely coupled structure.

[0007] The technical solution adopted by this invention to solve the above-mentioned technical problems is a near-field channel estimation method based on two-dimensional block sparsity UPA, comprising the following steps:

[0008] Step 1: Represent the near-field channel matrix of the uniform planar array UPA as the sum of the outer products of the near-field steering vectors of the horizontal dimension uniform linear array ULA and the near-field steering vectors of the vertical dimension ULA;

[0009] Step 2: Construct improved Discrete Fourier Transform (DFT) dictionaries for the horizontal direction. And vertically improved DFT dictionary The near-field channel matrix of the UPA is represented as follows: ;

[0010] in, , ;diag indicates converting a vector into a diagonal matrix; The standard DFT matrix in the horizontal direction. The standard DFT matrix in the vertical direction; Indicates definition, For including near-field range parameters The nonlinear correction vector, Here are the direction cosine parameters. Direction cosine parameter for reference antenna-to-user distance Including horizontal cosine parameters and vertical sine parameters ;

[0011] Total coefficient matrix , For the first The dictionary of paths in the horizontal direction The block sparse representation vector below, For the first The path in the vertical dictionary The block sparse representation vector, the total coefficient matrix Presented by and The two-dimensional block sparse structure is determined by the outer product; Indicates the first The equivalent complex channel gain of each propagation path, It is the number of transmission paths. This is the propagation path index; l=0 represents the line-of-sight path. This is a non-line-of-sight path; Indicates transpose;

[0012] Step 3: The vectorized received signal is represented as a linear model of the sensing matrix and the two-dimensional block sparse vector. The two-dimensional pattern coupled sparse Bayesian learning (2D-PCSBL) algorithm is used to recover the two-dimensional block sparse vector. In the prior distribution of the 2D-PCSBL algorithm, the accuracy parameter of each sparse coefficient is determined by the weighted sum of its own hyperparameter and the hyperparameters of its neighbors in the two-dimensional neighborhood, so as to capture the sparse coupling characteristics of the UPA near-field channel in the horizontal and vertical dimensions, and finally obtain the channel estimation result.

[0013] This invention utilizes the sparse coupling characteristics of the UPA near-field channel in the horizontal and vertical dimensions to improve channel estimation performance and reduce the required pilot overhead.

[0014] The beneficial effects of this invention are that by decomposing the UPA near-field channel into the outer product of two ULA near-field channels and constructing a two-dimensional improved DFT dictionary, the channel exhibits a two-dimensional block sparse structure under this dictionary, thereby reducing the inter-atomic coherence of the compressed sensing measurement matrix. The 2D-PCSBL algorithm is then used to recover this two-dimensional block sparse signal, utilizing the coupling characteristics of the sparse structure of the UPA channel in both the horizontal and vertical dimensions. This allows channel estimation to be completed with fewer pilot symbols and a lower signal-to-noise ratio, while maintaining the same order of magnitude of computational complexity as the one-dimensional block sparse method. Attached Figure Description

[0015] Figure 1 It is a two-dimensional sparse structure of Σ;

[0016] Figure 2 For a two-dimensional mode coupling structure of β;

[0017] Figure 3 Comparison of NMSE and SNR for each scheme;

[0018] Figure 4 Comparison of the number of sampling points and SNR for each scheme. Detailed Implementation

[0019] The near-field channel estimation of the uniform planar array (UPA) of this invention includes three steps:

[0020] 1) The UPA near-field channel is represented as the outer product of the column vectors of two ULA near-field channels.

[0021] 2) Design an improved 2D-DFT matrix as a near-field channel dictionary to transform the UPA channel estimation task into a 2D block sparse signal recovery problem.

[0022] 3) Calculate the sparse signal recovery problem using the 2D-PCSBL algorithm.

[0023] Specifically as follows:

[0024] Step 1: Represent the UPA near-field channel as the outer product of the column vectors of two ULA near-field channels.

[0025] Consider a downlink transmission scenario where the operating carrier frequency is... The wireless communication system serves multiple single-antenna users. The transmitter is equipped with an ELAA configured as UPA, which contains... One antenna, of which and These represent the number of antennas along the horizontal and vertical axes, respectively. This represents the total number of array antennas. To reduce hardware complexity, the transmitter uses... Hybrid beamforming architecture for a single radio frequency (RF) chain. Indicates the number of radio frequency links. The carrier wavelength is... ,in It is the speed of light. The antenna elements are equidistant along both the horizontal and vertical axes. Each user estimates its channel by using pilot signals broadcast by the transmitter during downlink transmission.

[0026] This invention makes the following three assumptions. First, the user is located in the near-field region of the transmitter, and a spherical wavefront assumption is adopted. Second, the sparse scattering characteristics of millimeter-wave / terahertz signals mean that only a few dominant paths exist between the transmitter and the user. Third, only the narrowband case is considered.

[0027] Under the above assumptions, the channel between the transmitter and the user is denoted as... The model is as follows:

[0028] ;

[0029] in, For complex fields, It is the number of transmission paths. This is the propagation path index; l=0 represents the line-of-sight path. This is a non-line-of-sight path; ,in and These represent the distance from the transmitting reference antenna to the [missing information]. The complex channel gain and propagation delay of the target along the propagation path. Indicates definition, Indicates the first The propagation path combines the path gain and the carrier phase shift into an equivalent complex channel gain; They represent the first The distance from the transmitting reference antenna to the target in each propagation path. and with the Pitch angle related to propagation path and azimuth ; This is the near-field steering matrix for UPA, i.e., at a specific angle and distance. Phase response of the spherical wavefront on each antenna; Indicates the location UPA near-field steering matrix:

[0030] ;

[0031] in, and . Indicates that in UPA, it is located The distance from the antenna at the location to the target user. For horizontal axis antenna index, For vertical axis antenna index, reference distance Indicates reference antenna The distance to the user.

[0032] In the The transmitted signal matrix of the UPA array at each sampling time. It can be represented as:

[0033] ;

[0034] in, Represents the Hadamaji. Here, This indicates that the equal modulus constraint is satisfied. Hybrid beamforming matrix, Indicates modulo, For UPA located in The signal amplitude weighting coefficient on the antenna. This represents the pilot signal matrix. Definition Let be the number of samples (pilot number, assuming one sample per pilot). Without loss of generality, we assume that for... The pilot symbols are set to a constant unit amplitude. Thus, we can conclude So, in the first... The signal received at each sampling time Written as:

[0035] ;

[0036] Among them, it means The first in the matrix One element, Indicates the first The sampling time, the first Transmitted signals on each antenna, vectorized channel And the vectorized beamforming vector vec(.) represents the matrix vectorization operation. This indicates transposition. By... Sub-pilot sampling Stacking to obtain the received signal vector for:

[0037] ;

[0038] in, Beamforming matrix ,and This represents additive white Gaussian noise (AWGN). This represents the variance of Gaussian white noise.

[0039] UPA steering matrix is ​​primarily based on the distance from the antenna to the target user. Therefore, we first explore The precise expression is as follows:

[0040] ;

[0041] in, For the first The precise physical distance from the antenna to the user The horizontal cosine parameter is used as a reference for the distance from the antenna to the user. And the vertical sinusoidal parameter In step (a) of the above equation, we used an approximate relation. In step (b), we neglect the bilinear quadratic term. The near-field steering matrix of UPA... Decomposed into:

[0042] ;

[0043] Here, The direction cosine parameter represents the angular part of the far-field steering vector. And its first element , For the antenna index of a uniform linear array ULA. Similarly, the range part of the near-field correction vector. The entries are by Provided. That is, including near-field distance parameters The nonlinear correction vector. Furthermore, Let be the near-field guidance vector of ULA, and its first... The elements are:

[0044] ;

[0045] Channel matrix It can be rewritten as:

[0046] ;

[0047] in, For the first The horizontal cosine parameter of the path, For the first The vertical sinusoidal parameter of the path, For the first The path references the distance from the antenna to the target. The horizontal dimension of the ULA near-field steering vector. This is the ULA near-field steering vector in the vertical dimension. From here, we will define the channel matrix. It was rewritten as the outer product of two ULA near-field guidance vectors.

[0048] Step 2: Design an improved 2D-DFT matrix as the near-field channel dictionary, and prove that under the proposed 2D-DFT dictionary, the UPA near-field channel exhibits a 2D block sparse structure, thus transforming the UPA channel estimation task into a 2D block sparse signal recovery problem.

[0049] This step is based on the following premise: For a ULA near-field channel, if a unitary matrix obtained by multiplying a standard DFT matrix by a phase diagonal matrix determined by the effective range parameter is constructed as a dictionary, then the representation vector of the near-field steering vector under this dictionary is... and It will naturally exhibit a block sparse structure. Its physical essence is that the nonlinear quadratic phase of the spherical wave causes the energy of the channel path to be continuously concentrated in a few adjacent grid points that match the actual distance and angle in the dictionary (for detailed theoretical proof, see H. Wang et al., IEEE Trans. Commun., vol. 74, pp. 2683-2698, 2026).

[0050] This invention extends this discovery to UPA. Based on the breakdown of step one... Construct improved DFT dictionaries in two dimensions respectively. and :

[0051] Based on the aforementioned block-sparse method using the improved DFT matrix, the ULA near-field guidance vector can be represented in block-sparse form on a specified improved DFT basis. Therefore, we obtain:

[0052] ;

[0053] ;

[0054] in, It is a block sparse vector in the horizontal direction. For vertically sparse vectors; for horizontally near-field steering vectors. Improved DFT dictionary by horizontal direction Sparse vectors This indicates the near-field steering vector in the vertical direction. Improved DFT dictionary by vertical direction Sparse vectors express.

[0055] Specifically, and These are the improved DFT matrices, denoted as:

[0056] ;

[0057] ;

[0058] Where diag represents the transformation of a vector into a diagonal matrix; The standard DFT matrix in the horizontal direction. The standard DFT matrix in the vertical direction;

[0059] Substituting the block sparse form into the channel matrix, the channel matrix... Rewritten as:

[0060] Among them, the total coefficient matrix And the system matrix corresponding to each path .

[0061] It can be proven that, due to the first The dictionary of paths in the horizontal direction The block sparse representation vector and due to the The path in the vertical dictionary The block sparse representation vector They all exhibit sparse characteristics, and their outer product matrix... It has a two-dimensional block sparse structure.

[0062] The coefficient matrix for each path Presented by each path and The two-dimensional block sparse structure determined by the outer product. Specifically, let... and The block partitions are respectively the block partition sets. and , that is, horizontal direction dimensional vector partitioning A series of consecutive blocks, in the vertical direction dimensional vector partitioning A series of consecutive blocks. and The non-zero block index sets are respectively and ,get:

[0063] ;

[0064] in, It is a matrix No. Line 1 Column elements, Block sparse representation vector The i-th element, Block sparse representation vector The j-th element;

[0065] because It is non-zero if and only if and hour, Only then is it a non-zero value. This indicates that... support set for:

[0066] ;

[0067] in, Denotes the Cartesian product of sets, For the union operation, p is the index of the non-zero block in the horizontal direction, and q is the index of the non-zero block in the vertical direction. Let p be the set of indices contained in the p-th block in the horizontal direction. Let be the set of indices contained in the q-th block in the vertical direction. Since... and The support set itself has block clustering properties (each consisting of a non-zero block index set). and (Description), their Cartesian product naturally forms the union of multiple two-dimensional rectangular blocks. That is, Non-zero support set is composed of Decision, therefore It can be viewed as a matrix composed of multiple two-dimensional rectangular non-zero blocks. It should be noted that due to the sparse scattering characteristics of millimeter-wave / terahertz channels (L is typically very small) and the dominance of line-of-sight path energy, the total coefficient matrix after superposition is... It still retains the sparse properties of the two-dimensional block.

[0068] In order to explain The sparse structure described, we have a sparse structure containing A path (consisting of one line-of-sight (LoS) path and two non-line-of-sight (NLoS) paths) The UPA was simulated. sparsity such as Figure 1 As shown, in the derived dictionary and Down, The coefficient matrix mainly consists of the line-of-sight (LOS) path coefficients for l=0. Decision. Therefore. It also exhibits a similar two-dimensional block sparse structure.

[0069] Step 3: Use the 2D-PCSBL algorithm to solve the above sparse signal recovery problem.

[0070] Vectorized channel vectors for:

[0071] ;

[0072] in And the total dictionary matrix ;

[0073] in This represents the Kronecker product. The received signal is rewritten as:

[0074] ;

[0075] Among them, the perception matrix ;

[0076] Obviously, It is by The derived two-dimensional (2D) block sparse vectors. Thus, the uniform array UPA channel estimation problem has been transformed into a two-dimensional block sparse compressed sensing problem.

[0077] Based on the proposed dictionary Given the corresponding measurement matrix, the compressed sensing problem in the received signal can be solved using Block Orthogonal Matching Pursuit (BOMP) or Pattern Coupled Sparse Bayesian Learning (PCSBL) algorithms. However, existing block sparse methods based on improved DFT matrices, such as BOMP and PCSBL, cannot utilize these algorithms. Two-dimensional block sparse structure in.

[0078] In this invention, we propose a two-dimensional block sparse sensing channel estimation algorithm by applying the 2D-PCSBL method. Specifically, our goal is to estimate the posterior distribution. And targeting Maximize it. Represents given observation data and hyperparameters Under the condition of 2D block sparse vector The posterior distribution. Let be a hyperparameter vector, and each element of it... Controlling the corresponding sparsity coefficient ,Right now The sparsity of a function is determined by its hyperparameters. The hyperparameters of the model and its neighbors determine the model's performance. The details of the 2D-PCSBL algorithm are as follows:

[0079] Because in a given Under these conditions, the observed values and Conditional independence, posterior distribution It is given by the following formula:

[0080] ;

[0081] in, Let be the likelihood function, given At that time, it was observed The probability of; Given a prior distribution and known hyperparameters... At that time, The prior assumptions. It means proportional to.

[0082] because From The prior distribution of the two-dimensional block sparse vectors obtained by vectorization Modeled as a complex Gaussian distribution with a mean of zero, its variance is related to the hyperparameter in two dimensions. Coupling, as shown in the following equation:

[0083] ;

[0084] in, Represents a cyclically symmetric complex Gaussian distribution, with the nth precision parameter. ;parameter express and The correlation coefficient between them. Index of neighbor hyperparameters. , express The neighbor hyperparameter index set, that is, in Figure 2 In the two-dimensional grid shown Adjacent hyperparameter indices. Hyperparameters prior distribution Gamma represents the gamma distribution. Let Gamma be the shape parameter of the distribution. The rate parameters of the Gamma distribution are all prior parameters and , .

[0085] Posterior distribution It can be easily verified that it follows a complex Gaussian distribution with a mean of Covariance :

[0086] ;

[0087] ;

[0088] Among them, the diagonal matrix , diag denotes vector diagonalization. For the perception matrix, This is the conjugate transpose. This is the index of the outer iteration round of the EM algorithm. This represents the current value of the nth precision parameter in the t-th iteration, where n ranges from 1 to N. It is the reciprocal of the noise variance in the rewritten received signal expression, assuming it is a known prior.

[0089] covariance The expression gives the estimated hyperparameters , The maximum a posteriori (MAP) estimate is the mean. It is given by the following formula:

[0090] ;

[0091] Here, in order to obtain the final channel estimate... We only need to estimate the hyperparameters. ^ represents the final estimate. ~ represents the estimated value. Therefore, the Expectation-Maximization (EM) algorithm is used to estimate the hyperparameters by iterating alternately between the E-step and M-step. .

[0092] 1) E-Step: Posterior Distribution We need to calculate the approximate posterior mean. and approximate posterior covariance , This represents the index of the inner iteration rounds of GAMP. To avoid costly matrix inversion operations, a generalized approximate message-passing GAMP algorithm is used to obtain the given... Approximate mean of time and approximate covariance ,in , This represents the total number of iterations within the GAMP inner layer.

[0093] 2) M-Step: Maximizing the posterior probability The lower bound (also known as the Q function) is calculated based on the previously calculated lower bound. Because it only affects ,in Therefore, maximizing the Q function can be expressed as:

[0094] ;

[0095] in, Let Q be the Q-function, i.e., the expected log-likelihood, with the th... Parameters of round estimation Given the condition, construct a parameter to be optimized. Auxiliary functions; operators Indicates the posterior distribution Find the expected value, where c represents an arbitrary constant. The maximization process in the above equation can be further rewritten as:

[0096] ;

[0097] in, Intermediate calculation variables during update , For the first Approximate posterior mean of round estimation n elements in For the first Approximate posterior variance of round estimation The element in the nth row and nth column.

[0098] Finally, when the EM algorithm converges, we obtain... .

[0099] Simulation experiment:

[0100] The performance of the proposed method is evaluated through numerical simulations using the Monte Carlo method. We compare the proposed invention with several state-of-the-art methods, including the near-field OMP (polar-OMP) algorithm based on polar-domain dictionaries, the BOMP algorithm based on improved DFT matrices, and the PCSBL algorithm. The Polar-OMP algorithm is based on the application of polar-domain dictionaries. The dictionaries derived by the BOMP and PCSBL algorithms are also shown. Furthermore, the proposed invention, based on a 2D-PCSBL algorithm, aims to fully utilize the two-dimensional block sparse structure of the UPA near-field channel in both the horizontal and vertical dimensions.

[0101] The simulation parameters are shown in Table 1, where and These represent Fresnel distance and Rayleigh distance, respectively. This represents the antenna aperture.

[0102] Table 1 Simulation Parameters

[0103]

[0104] Therefore, in the simulation settings, path distance It lies within the entire near-field region. The signal-to-noise ratio (SNR) is:

[0105] ;

[0106] The performance evaluation uses the normalized mean square error (NMSE) as follows:

[0107]

[0108] in, yes The estimated value.

[0109] Figure 3 The performance of the normalized mean square error (MSE) is depicted as a function of the signal-to-noise ratio (SNR). It can be seen that as the SNR increases, all functions based on the proposed reconstruction dictionary... The NMSE performance of all algorithms has been improved. The NMSE performance of the Polar-OMP algorithm initially decreases and then stabilizes because it relies on the polar domain dictionary, which ignores the proposed dictionary. Utilized The block sparsity is achieved. Furthermore, the 2D-PCSBL algorithm used in this invention achieves a SNR of 5dB. The NMSE is dB, while the BOMP algorithm in the block sparse method based on the improved DFT matrix requires at least 10 dB to achieve the same NMSE performance. Furthermore, compared to the PCSBL algorithm in the block sparse method based on the improved DFT matrix, this invention exhibits superior robustness in low SNR scenarios. These improvements stem from the utilization of a two-dimensional 2D block sparse structure in the UPA near-field channel.

[0110] Figure 4 This demonstrates the NMSE performance as a function of the number of sampling points at an SNR of 5dB. The changes in NMSE are shown in the figure. The NMSE of all algorithms changes with... The value decreases as the quantity increases. It is worth noting that the algorithm of this invention only... It was reached in time The dB NMSE significantly outperforms the Polar-OMP algorithm and surpasses BOMP and PCSBL. This demonstrates that utilizing the sparsity of two-dimensional blocks is key to reducing the pilots required for channel estimation.

[0111] The computational complexity analysis covers theoretical evaluations and simulation results, summarized in Table 2. and represent the number of iterations for the existing PCSBL and BOMP algorithms based on improved DFT matrix methods, respectively. This represents the number of atoms in existing polar-domain dictionary-based representations. By utilizing the GAMP framework, the proposed 2D-PCSBL algorithm circumvents... The costly matrix inversion operation in the maximum a posteriori (MAP) estimate expression is eliminated, thus significantly reducing the overall complexity. It can be seen that the proposed 2D-PCSBL-based algorithm exhibits almost the same computational complexity as the PCSBL algorithm. The main difference lies in that the PCSBL algorithm only utilizes the block sparse structure, while the 2D-PCSBL algorithm fully captures the coupling characteristics of the sparse structure of the UPA near-field channel in both the horizontal and vertical dimensions. Since the overall algorithm framework remains unchanged, the two-dimensional block sparse hyperparameters are updated iteratively. The additional computational overhead is negligible.

[0112] Table 2 Comparison of theoretical complexity and relative running time (RT) for channel estimation of ultra-large area array (UPA-ELAA)

[0113]

[0114] Table 2 shows the results for different numbers of sampling points when the SNR is 5dB. The computational complexity is compared below. Complexity is evaluated using relative runtime (RT), which is defined as the actual execution time compared to the reference implementation (specifically...). The ratio of the running time of the Polar-OMP algorithm to the running time of the time.

Claims

1. A near-field channel estimation method for UPA based on two-dimensional block sparsity, characterized in that, Includes the following steps: Step 1: Represent the near-field channel matrix of the uniform planar array UPA as the sum of the outer products of the near-field steering vectors of the horizontal dimension uniform linear array ULA and the near-field steering vectors of the vertical dimension ULA; Step 2: Construct improved Discrete Fourier Transform (DFT) dictionaries for the horizontal direction. And vertically improved DFT dictionary The near-field channel matrix of the UPA is represented as follows: ; in, , ;diag indicates converting a vector into a diagonal matrix; The standard DFT matrix in the horizontal direction. The standard DFT matrix in the vertical direction; Indicates definition, For including near-field range parameters The nonlinear correction vector, Here are the direction cosine parameters. Direction cosine parameter for reference antenna-to-user distance Including horizontal cosine parameters and vertical sine parameters ; Total coefficient matrix , For the first The dictionary of paths in the horizontal direction The block sparse representation vector below, For the first The path in the vertical dictionary The block sparse representation vector, the total coefficient matrix Presented by and The two-dimensional block sparse structure is determined by the outer product; Indicates the first The equivalent complex channel gain of each propagation path, It is the number of transmission paths. This is the propagation path index; l=0 represents the line-of-sight path. This is a non-line-of-sight path; Indicates transpose; Step 3: The vectorized received signal is represented as a linear model of the sensing matrix and the two-dimensional block sparse vector. The two-dimensional pattern coupled sparse Bayesian learning (2D-PCSBL) algorithm is used to recover the two-dimensional block sparse vector. In the prior distribution of the 2D-PCSBL algorithm, the accuracy parameter of each sparse coefficient is determined by the weighted sum of its own hyperparameter and the hyperparameters of its neighbors in the two-dimensional neighborhood, so as to capture the sparse coupling characteristics of the UPA near-field channel in the horizontal and vertical dimensions, and finally obtain the channel estimation result.

2. The method as described in claim 1, characterized in that, UPA near-field channel matrix The model is as follows: ； in, For the first The horizontal cosine parameter of the path, For the first The vertical sinusoidal parameter of the path, For the first The path references the distance from the antenna to the target. and These represent the number of antennas along the horizontal and vertical axes, respectively. The horizontal dimension of the ULA near-field steering vector. is the ULA near-field steering vector in the vertical dimension.

3. The method as described in claim 1, characterized in that, Total coefficient matrix It presents a two-dimensional block sparse structure, specifically: the coefficient matrix of each path. Non-zero elements are clustered within two-dimensional rectangular blocks determined by the horizontal and vertical sets of non-zero block indices. The resulting total coefficient matrix is... Preserve the sparsity properties of this two-dimensional block.

4. The method as described in claim 1, characterized in that, Step three specifically includes: Vectorized channel vectors Represented as Among them, the total dictionary matrix , For Kronecker product, It is a two-dimensional block sparse vector; Constructing a received signal model Among them, the perception matrix , Beamforming matrix, It is additive white Gaussian noise; Posterior scores are estimated using the 2D-PCSBL algorithm. To obtain The maximum a posteriori estimate is used as the final channel estimate. ,in This is a hyperparameter vector.

5. The method as described in claim 1, characterized in that, The 2D-PCSBL algorithm includes the following steps: Define prior distribution ,in, Represents a cyclically symmetric complex Gaussian distribution, with the nth precision parameter. ; For correlation coefficient, index of neighbor hyperparameters , express The neighbor hyperparameter index set; Define hyperparameters prior distribution Wherein, Gamma represents the gamma distribution. Let Gamma be the shape parameter of the distribution. For the rate parameter of the Gamma distribution; The hyperparameters are estimated iteratively using the Expectation-Maximization (EM) algorithm. In the E-step, the approximate posterior mean is calculated using the generalized approximate message-passing GAMP algorithm. and approximate posterior covariance In the M-step process, the hyperparameters are updated until convergence, yielding the final channel estimate. ,in, This is the index for the inner iteration rounds of GAMP.

6. The method as described in claim 5, characterized in that, The accuracy parameters Neighbor index set introduced in It is a set of indices adjacent to the current hyperparameter in a two-dimensional grid, so that mode coupling is formed between adjacent sparse coefficients to capture the sparse coupling characteristics of the UPA near-field channel in the horizontal and vertical dimensions.

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