XL-MIMO far-field channel estimation method based on two-stage sparse optimization

Abstract

The present invention relates to the field of wireless communication technologies, and in particular, provides an XL-MIMO far-field channel estimation method based on two-stage sparse optimization. The method comprises constructing an XL-MIMO multi-user broadband spatial channel model based on hybrid precoding; converting the channel recovery problem into a sparse matrix recovery problem based on the constructed model and solving the problem; employing an improved CoSaMP algorithm for initial sparse channel estimation; and applying a synchronous iterative gridless weighted optimization algorithm, SIGW-LBFG, in combination with L-BFGS direction search, line search step size adjustment, and pruning strategies to perform synchronous iterative gridless weighted optimization on the initial estimate, and performing simulation verification. The method achieves high-precision, low-overhead channel estimation, improving its applicability and engineering practice value.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to an XL-MIMO far-field channel estimation method based on dual-stage sparse optimization. Background Art

[0002] With the rapid development of ultra-large-scale multiple-input, multiple-output (XL-MIMO) technology, the demand for channel state information (CSI) estimation in 6G communication systems has become increasingly significant. XL-MIMO systems offer significant spatial diversity gains through massive antenna arrays, but this also presents challenges in channel estimation accuracy and computational complexity. In particular, traditional channel estimation methods struggle to meet the high accuracy and efficiency requirements for far-field signal estimation due to signal sparsity and multipath effects.

[0003] In the existing technology, the traditional orthogonal matching pursuit (OMP) algorithm has low accuracy in recovering high-dimensional sparse signals and poor noise robustness due to fixed grid division; while the traditional compressed sampling matching pursuit (CoSaMP) algorithm has difficulty capturing the common sparse structure of multi-antenna systems and suffers from grid mismatch problems. Summary of the Invention

[0004] In view of this, the present invention provides an XL-MIMO far-field channel estimation method based on two-stage sparse optimization to achieve high-precision, low-overhead channel estimation and improve applicability and engineering practice value.

[0005] In a first aspect, the present invention provides an XL-MIMO far-field channel estimation method based on two-stage sparse optimization, the method comprising:

[0006] Step 1: Construct an XL-MIMO multi-user broadband spatial channel model based on hybrid precoding;

[0007] Step 2: According to the hybrid precoding-based XL-MIMO multi-user broadband spatial channel model, the channel recovery problem is converted into a sparse matrix recovery problem and solved;

[0008] Step 3: Use the improved CoSaMP algorithm to perform initial sparse channel estimation;

[0009] Step 4: Apply the synchronous iterative gridless weighted optimization algorithm SIGW-LBFG, combined with L-BFGS direction search, line search step size adjustment and pruning strategy, to perform synchronous iterative gridless weighted optimization on the initial sparse channel estimate to improve the initial sparse channel estimation accuracy of the CoSaMP algorithm;

[0010] Step 5: Simulate and verify the algorithm performance by evaluating the normalized mean square error (NMSE). Set multiple sets of transmission distance, pilot length, and signal-to-noise ratio (SNR) parameters to verify the robustness in far-field, low SNR, and pilot resource-limited scenarios.

[0011] Optionally, step 1 includes adopting an XL-MIMO orthogonal frequency division multiplexing (OFDM) communication system based on a time division duplex (TDD) mode, configuring a base station with a hybrid precoding architecture, and performing multi-user uplink channel estimation and beamforming optimization through orthogonal pilot sequences, wherein the communication system includes multiple subcarriers, multiple RF chains, and multiple paths;

[0012] At the user end, K single-antenna users generate pilot signals through orthogonal pilot sequences. , data is distributed to M subcarriers through orthogonal frequency division multiplexing OFDM, and then the time domain signal is generated through inverse fast Fourier transform IFFT and transmitted to the base station through the wireless channel, where After the base station receives the time domain signal from the user end, the signal passes through the analog synthesis matrix Precoding, matrix The size is , and satisfy the norm constraint , propagates through the channel, and for the mth subcarrier, the received signal Expressed as:

[0013] (1)

[0014] in, is the spatial domain channel matrix, is Gaussian noise, is the transmitted pilot signal; after the received signal is processed by the synthesis matrix, the overall observation matrix A is formed, and combined with the signal transmission conditions of P time slots, the final received signal is obtained:

[0015] (2)

[0016] in, , the elements in A are independent and come from the set Randomly generated in For noise;

[0017] Base station equipped with N RF RF chains and N antennas, with a spacing of ,in The base station performs channel estimation on the received signal, recovers the user data symbols through inverse calculation, and completes symbol demodulation using baseband processing. After OFDM demodulation, the signal is restored to the frequency domain, and is equalized and de-precoded in combination with the channel matrix H to restore the original data. The base station adjusts the phase of different antennas through the phase shifter array and antenna array. Generate directional beams directed to target users to improve spatial gain and optimize signal transmission efficiency; the phase parameters of the phase shifter array is generated by an angle optimization algorithm and based on , , adjust the phase, and focus the signal in the direction of the target user; finally, the base station outputs the channel state information (CSI) of K users and uses the channel state information (CSI) for optimized scheduling and beamforming to improve the system capacity and energy efficiency.

[0018] Optionally, step 2 includes decomposing the user channel into a superposition of finite paths based on a plane wave assumption, constructing a discrete Fourier transform (DFT) dictionary matrix for sparse representation, converting the channel estimation into a sparse matrix recovery problem, and solving the problem;

[0019] The complex gain of each path is related to the distance between the user and the base station and the angle of arrival;

[0020] The channel is represented as:

[0021] (3)

[0022] in, , is the complex gain of the lth path; is the path distance; is the normalized angle of arrival; is the array response vector, and its expression is:

[0023] (4)

[0024] By adjusting the phase of each antenna, directional reception of the signal is achieved; the phase shift value of the nth antenna With angle parameters Directly related, the formula is: ; ; Represents the row index of the nth antenna; in order to capture the sparsity of the channel in the angular domain, a discrete Fourier transform DFT dictionary matrix is constructed; the column vector of the DFT dictionary matrix covers the entire angular space, and the oversampling factor s is used to improve the angular resolution. The sparse representation of the channel is:

[0025] (5)

[0026] in, is the Fourier transform matrix, is a sparse gain matrix with only L non-zero elements in each column, corresponding to the angular position of the effective path;

[0027] Substituting the sparse representation into the received signal model, we get:

[0028] (6)

[0029] The channel estimation problem is transformed into recovering a high-dimensional sparse matrix from low-dimensional observations, which is expressed as:

[0030] (7)

[0031] in, represents the number of non-zero elements, and L is the sparsity of the channel.

[0032] Optionally, step 3 includes recovering the channel sparse structure from low-dimensional observation data based on a dynamic support set expansion and smoothing weight mechanism; generating an initial sparse channel estimate through proxy calculation, support set expansion, sub-dictionary pseudo-inverse solution and iterative optimization of the smoothing mechanism.

[0033] Optionally, the synchronous iterative gridless weighted optimization algorithm SIGW-LBFG in step 4 includes:

[0034] Input: Observation data matrix , perception matrix , initial angle matrix , gain matrix , angle parameters , minimum number of paths , pruning threshold , maximum number of iterations , learning rate , convergence threshold , L-BFGS memory size ;

[0035] Initialization: Residual Matrix , set the initial parameters A=A0, G=G0, , and initialize the L-BFGS memory to an empty set;

[0036] Iterate the following steps until convergence conditions are met:

[0037] (o) Calculate the loss function for the angle parameter through Cholesky decomposition Gradient ;

[0038] (p) Based on the historical parameter changes s and gradient changes stored in the L-BFGS memory , recursively generate search directions ,in is a finite memory approximation of the inverse Hessian matrix;

[0039] (q) Determine the step size by line search Update parameters , reconstruct the angle matrix ;

[0040] (w) Update the gain matrix G through Cholesky decomposition and back substitution;

[0041] (u) If the number of paths And the number of iterations is greater than the threshold, and the gain energy is less than the reduction Path;

[0042] Apply weighted smoothing mechanism to suppress gain matrix jitter;

[0043] Output optimized angle matrix A, gain matrix G and angle parameters .

[0044] Optionally, the Cholesky decomposition and back-substitution method includes:

[0045] Constructing a Matrix and ,right Perform Cholesky decomposition to obtain the lower triangular matrix ;

[0046] By forward substitution With backward substitution Solve for the gain matrix G.

[0047] Optionally, the L-BFGS memory mechanism includes:

[0048] Store the most recent m groups of parameter changes s and gradient changes ;

[0049] The search direction p is generated by recursive calculation from reverse order to forward order to avoid explicit storage of high-dimensional Hessian matrix.

[0050] In a second aspect, an embodiment of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium includes a stored program, wherein when the program is running, the device where the computer-readable storage medium is located is controlled to execute the XL-MIMO far-field channel estimation method based on two-stage sparse optimization in the first aspect or any possible implementation of the first aspect.

[0051] In a third aspect, an embodiment of the present invention provides an electronic device, comprising: one or more processors; a memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, and the one or more computer programs include instructions that, when executed by the device, enable the device to perform the XL-MIMO far-field channel estimation method based on two-stage sparse optimization in the first aspect or any possible implementation of the first aspect.

[0052] In the technical solution provided by the present invention, the method includes constructing an XL-MIMO multi-user broadband spatial channel model based on hybrid precoding; according to the XL-MIMO multi-user broadband spatial channel model based on hybrid precoding, converting the channel recovery problem into a sparse matrix recovery problem and solving it; using an improved CoSaMP algorithm to perform initial sparse channel estimation; applying the synchronous iterative gridless weighted optimization algorithm SIGW-LBFG, combined with L-BFGS direction search, line search step size adjustment and pruning strategy, to perform synchronous iterative gridless weighted optimization on the initial estimation to improve the initial sparse channel estimation accuracy of the CoSaMP algorithm; simulation verification, evaluating the algorithm performance through normalized mean square error (NMSE), setting multiple groups of transmission distance, pilot length and signal-to-noise ratio (SNR) parameters, and verifying the robustness in far-field, low signal-to-noise ratio and pilot resource-limited scenarios. This method achieves high-precision, low-overhead channel estimation, and improves applicability and engineering practice value. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0054] Figure 1 A flowchart of an XL-MIMO far-field channel estimation method based on two-stage sparse optimization provided in an embodiment of the present invention;

[0055] Figure 2 A schematic diagram of an XL-MIMO multi-user broadband spatial channel model based on hybrid precoding provided in an embodiment of the present invention;

[0056] Figure 3 A performance curve diagram of distance and normalized mean square error provided by an embodiment of the present invention;

[0057] Figure 4 A performance curve diagram showing the relationship between pilot length and normalized mean square error provided by an embodiment of the present invention;

[0058] Figure 5A performance curve diagram of the signal-to-noise ratio and normalized mean square error provided by an embodiment of the present invention;

[0059] Figure 6 A schematic diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0060] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0061] It should be understood that the embodiments described are only a portion of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative work are within the scope of protection of the present invention.

[0062] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The singular forms "a", "the" and "the" used in the embodiments of the present invention are also intended to include plural forms, unless the context clearly indicates other meanings.

[0063] It should be understood that the term "and / or" as used herein simply describes a relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A alone, A and B together, or B alone. Furthermore, the character " / " in this document generally indicates an "or" relationship between the associated objects.

[0064] The word "if," as used herein, may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0065] Figure 1 A flowchart of the XL-MIMO far-field channel estimation method based on two-stage sparse optimization provided in an embodiment of the present invention is shown in FIG. Figure 1 As shown, the method includes:

[0066] Step 1: Construct an XL-MIMO multi-user broadband spatial channel model based on hybrid precoding.

[0067] In the embodiment of the present invention, Figure 2 As shown, step 1 involves adopting an XL-MIMO orthogonal frequency division multiplexing (OFDM) communication system based on time division duplex (TDD) mode. Specifically, this system implements efficient multi-user uplink channel estimation and beamforming optimization. The system architecture and workflow are as follows:

[0068] At the user end, K single-antenna users generate pilot signals through orthogonal pilot sequences. , data is distributed to M subcarriers through orthogonal frequency division multiplexing (OFDM), and then a time domain signal is generated through inverse fast Fourier transform (IFFT) and transmitted to the base station through a wireless channel. . User signals meet strict orthogonality constraints , to avoid multi-user interference.

[0069] After the base station receives the signal from the user end, the signal passes through the analog synthesis matrix For precoding, the size of the matrix is , and satisfy the norm constraint , propagates through the channel, and for the mth subcarrier, the received signal Expressed as:

[0070] (1)

[0071] in, is the spatial domain channel matrix, is Gaussian noise, is the transmitted pilot signal; after the received signal is processed by the synthesis matrix, the overall observation matrix A is formed, and combined with the signal transmission conditions of P time slots, the final received signal is obtained:

[0072] (2)

[0073] in, , the elements in A are independent and come from the set Randomly generated in For noise.

[0074] Base station equipped with N RF RF chains and N antennas, with a spacing of ,in The base station performs channel estimation on the received signal and recovers the user data symbols through inverse operations, completing symbol demodulation using baseband processing. After OFDM demodulation, the signal is restored to the frequency domain and equalized and de-precoded in combination with the channel matrix H to restore the original data. The base station adjusts the phase of different antennas through the phase shifter array and antenna array. Generate directional beams that point to target users, increase spatial gain, and optimize signal transmission efficiency. Phase parameters of the phase shifter array is generated by an angle optimization algorithm and based on , , adjusting the phase to focus the signal in the direction of the target user. Ultimately, the base station outputs the channel state information (CSI) of K users and uses this CSI to optimize scheduling and beamforming to improve system capacity and energy efficiency.

[0075] Step 2: According to the XL-MIMO multi-user broadband spatial channel model based on hybrid precoding, the channel recovery problem is transformed into a sparse matrix recovery problem and solved.

[0076] In the embodiment of the present invention, step 2 includes decomposing the user channel into a superposition of finite paths based on the plane wave assumption, constructing a discrete Fourier transform (DFT) dictionary matrix for sparse representation, converting the channel estimation into a sparse matrix recovery problem, and solving the problem.

[0077] The complex gain of each path is related to the distance between the user and the base station and the angle of arrival;

[0078] The channel is represented as:

[0079] (3)

[0080] in, , is the complex gain of the lth path; is the path distance; is the normalized angle of arrival; is the array response vector, and its expression is:

[0081] (4)

[0082] By adjusting the phase of each antenna, directional reception of the signal is achieved; the phase shift value of the nth antenna With angle parameters Directly related, the formula is: ; ; Represents the row index of the nth antenna; in order to capture the sparsity of the channel in the angular domain, a discrete Fourier transform DFT dictionary matrix is constructed; the column vector of the DFT dictionary matrix covers the entire angular space, and the oversampling factor s is used to improve the angular resolution. The sparse representation of the channel is:

[0083] (5)

[0084] in, is the Fourier transform matrix, is a sparse gain matrix with only L non-zero elements in each column, corresponding to the angular position of the effective path;

[0085] Substituting the sparse representation into the received signal model, we get:

[0086] (6)

[0087] The channel estimation problem is transformed into recovering a high-dimensional sparse matrix from low-dimensional observations, which is expressed as:

[0088] (7)

[0089] in, represents the number of non-zero elements, and L is the sparsity of the channel.

[0090] Step 3: Use the improved CoSaMP algorithm to perform initial sparse channel estimation.

[0091] In an embodiment of the present invention, step 3 includes recovering the channel sparse structure from low-dimensional observation data based on a dynamic support set expansion and smoothing weight mechanism; generating an initial sparse channel estimate through proxy calculation, support set expansion, sub-dictionary pseudo-inverse solution and smoothing mechanism iterative optimization.

[0092] In the embodiment of the present invention, the improved CoSaMP algorithm is specifically implemented as follows:

[0093] a. Input: Observation Matrix , perception matrix Phi, sparsity K, convergence tolerance tol, maximum number of iterations maxiterations, smoothing weight ;

[0094] b. Output: estimated sparse signal , the final support set T;

[0095] c. Initialization: ;

[0096] d. ;

[0097] e. Calculate the proxy matrix ;

[0098] f. Select the top K maximum energy indexes ;

[0099] g. Update support set ;

[0100] h. Construct sub-dictionary , orthogonal projection solves the coefficient matrix ;

[0101] i. Prune the support set T and retain the K rows with the largest energy in B;

[0102] j. Update sparse signal estimates , and apply a smoothing mechanism ;

[0103] k. Update the residual matrix ;

[0104] 1. , break;

[0105] m, End for;

[0106] n. Return: , T;

[0107] In the initialization phase of the algorithm, first let the residual matrix R = Y and set the sparse support set T to an empty set, then in step e, Calculate the similarity matrix and select the top K column indices with the largest contribution in step f and incorporate them into the public support set; then step h constructs a sub-dictionary based on the preliminary support set The coefficient matrix B is obtained by pseudo-inverse operation, and then B is pruned according to the energy of each row coefficient to retain the K rows with the largest contribution, and B is updated again using the least squares method; in step j, the signal is estimated After the assignment, a smoothing mechanism is introduced to weightedly fuse the current estimate with the result of the previous iteration to suppress jitter. Step k updates the residual matrix R. Finally, in step l, it is checked whether the ratio of the residual to the observation is less than the threshold. If so, the iteration is stopped and the final sparse signal and support set are output.

[0108] Step 4: Apply the synchronous iterative gridless weighted optimization algorithm SIGW-LBFG, combined with L-BFGS direction search, line search step size adjustment and pruning strategy, to perform synchronous iterative gridless weighted optimization on the initial sparse channel estimation to improve the initial sparse channel estimation accuracy of the CoSaMP algorithm.

[0109] In the embodiment of the present invention, the synchronous iterative gridless weighted optimization algorithm SIGW-LBFG in step 4 includes:

[0110] Input: Observation data matrix , perception matrix , initial angle matrix , gain matrix , angle parameters , minimum number of paths , pruning threshold , maximum number of iterations , learning rate , convergence threshold , L-BFGS memory size ;

[0111] Initialization: Residual Matrix , set the initial parameters , and initialize the L-BFGS memory to an empty set, that is, ;

[0112] Iterate the following steps until convergence conditions are met:

[0113] (o) Calculate the loss function for the angle parameter through Cholesky decomposition Gradient ;

[0114] (p) Based on the historical parameter changes s and gradient changes stored in the L-BFGS memory , recursively generate search directions ,in is a finite memory approximation of the inverse Hessian matrix;

[0115] (q) Determine the step size by line search Update parameters , reconstruct the angle matrix ;

[0116] (w) Update the gain matrix G through Cholesky decomposition and back substitution;

[0117] (u) If the number of paths And the number of iterations is greater than the threshold, and the gain energy is less than the reduction Path;

[0118] Apply weighted smoothing mechanism to suppress gain matrix jitter;

[0119] Output optimized angle matrix A, gain matrix G and angle parameters .

[0120] In an embodiment of the present invention, the Cholesky decomposition and back substitution method includes:

[0121] Constructing a Matrix and ,right Perform Cholesky decomposition to obtain the lower triangular matrix ;

[0122] By forward substitution With backward substitution Solve for the gain matrix G.

[0123] In an embodiment of the present invention, the L-BFGS memory mechanism includes:

[0124] Store the most recent m groups of parameter changes s and gradient changes ;

[0125] The search direction p is generated by recursive calculation from reverse order to forward order to avoid explicit storage of high-dimensional Hessian matrix.

[0126] In the embodiment of the present invention, the specific process of step 4 includes:

[0127] S4-1、For ;

[0128] S4-2. Calculate the gradient by Cholesky decomposition: ;

[0129] S4-3. Search direction based on L-BFGS memory calculation ;

[0130] S4-4, Line search adjustment step Update parameters ;

[0131] S4-5. Reconstructing the angle matrix ;

[0132] S4-6, update the gain matrix ;

[0133] S4-7, update L-BFGS memory and record the difference ;

[0134] S4-8, , break;

[0135] S4-9, path pruning (when the number of paths and ): The screening gain energy is greater than the reduction Path;

[0136] S4-10, Application Smoothing Mechanism ;

[0137] S4-11, End for;

[0138] S4-12, return A, G, ;

[0139] In the initialization phase of the algorithm, the initial parameters are set and the initial residual matrix is calculated. ;in and are the initial estimates of the angle matrix and gain matrix respectively, and the square Frobenius norm of the residual is: ;

[0140] The angle offset vector row is:

[0141] (8)

[0142] Using the angle parameter Generate the antenna array response matrix:

[0143] (9)

[0144] This formula realizes the physical mapping of phase parameters.

[0145] During the iteration, (S4-2) first uses the current matrix A to calculate the residual matrix R: , and construct the matrix in the normal equation: : Then, perform Cholesky decomposition on E to obtain the lower triangular factor L, that is, ; Then use forward and backward substitution to calculate (Recorded as ) and then combine the chain rule and A's The derivative of , calculate the objective function with respect to Gradient ;

[0146] In order to avoid explicitly storing the high-dimensional Hessian matrix (S4-3), the algorithm uses the L-BFGS method to generate the search direction. Specifically, it uses the historical parameter changes , and the corresponding gradient change , by forward computing the coefficients , adjust the current gradient q, and then calculate the scale factor , and use the reverse loop to correct, and finally get the search direction ;

[0147] In the online search phase (S4-4 to S4-5), the algorithm gradually reduces the step size (If the condition is not met, multiply by 0.5) to ensure that the updated residual meets the Armijo condition: , when the conditions are met, update the angle parameter along the search direction , and reconstruct the antenna array response matrix A;

[0148] After fixing A (S4-6 to S4-9), by constructing And the normal equation matrix , and then use Cholesky decomposition to get ; Finally, solve the least squares problem by forward and backward substitution and obtain the closed-form solution Thus the gain matrix is updated;

[0149] In terms of sparsity maintenance, the algorithm dynamically prunes redundant paths whose energy is less than the threshold pruning, and limits the number of paths to be greater than or equal to , thereby enforcing the sparsity constraint; (S4-10 to S4-12) The later iterations are smoothed by a weighted ; Suppress gain jitter and monitor parameter update amount at the same time (in ), if it is less than the convergence threshold Or when the maximum number of iterations is reached, the iteration is terminated and the optimized A, G, .

[0150] L-BFGS direction search and line search step size are dynamically adjusted, and the angle parameter Efficient iteration is performed in the continuous domain of , thus avoiding the limitations and high computational overhead brought by discrete grid division. At the same time, in the process of solving the gain matrix G, Cholesky decomposition is used to replace the traditional pseudo-inverse operation, which greatly improves the efficiency of numerical calculations and reduces the overall complexity. Finally, by introducing a smoothing mechanism in the late iteration (proportionally fusing the current gain with the result of the previous iteration), it can effectively suppress the estimation jitter in low signal-to-noise ratio environments and improve the robustness and stability of the algorithm.

[0151] Step 5: Simulate and verify the algorithm performance by evaluating the normalized mean square error (NMSE). Set multiple sets of transmission distance, pilot length, and signal-to-noise ratio (SNR) parameters to verify the robustness in far-field, low SNR, and pilot resource-limited scenarios.

[0152] In the embodiment of the present invention, the simulation results verify the effectiveness and advantages of the solution;

[0153] To verify the effectiveness and advantages of the proposed channel estimation scheme, we compared the performance of different channel estimation algorithms through simulation results. Specifically, five channel estimation algorithms were selected for the simulation: least squares (LS), ideal least squares (Oracle LS), simultaneous orthogonal matching pursuit (SOMP), improved CoSaMP (CoSaMP+), and the optimized CoSaMP combined with SIGW-LBFG (Co-SIGW-LBFG). Performance was evaluated using the normalized mean square error (NMSE), and the simulation configurations are shown in Table 1.

[0154] Table 1 Simulation configuration

[0155] ;

[0156] In the embodiment of the present invention, the following performance comparison is carried out from different dimensions:

[0157] NMSE performance under different transmission distances, such as Figure 3 As shown, Figure 3 The paper presents a performance comparison of different algorithms in terms of normalized mean square error (NMSE) as transmission distance varies. The SNR is fixed at 10dB, the pilot length P = 32, and the distance between the user and the base station is extended from 100 meters to 230 meters, corresponding to a Rayleigh distance of approximately 100 meters. The proposed method achieves significant NMSE improvements compared to traditional algorithms (LS / SOMP / improved CoSaMP) in far-field scenarios with long distances, low SNR, and limited pilot resources. The NMSE approaches the theoretical limit under high pilot conditions, validating the technical advantages of dynamic support set expansion, continuous domain optimization, and a two-stage collaborative architecture.

[0158] In the embodiment of the present invention, the NMSE performance under different signal-to-noise ratios (SNRs) is shown, where the pilot length is P = 32. Figure 4 As shown in the figure, in low SNR scenarios (SNR<5 dB): the traditional LS algorithm ignores sparsity, and the NMSE deteriorates sharply; the proposed Co-SIGW-LBFG algorithm significantly suppresses noise interference through the anti-noise weight mechanism and path pruning strategy, and the NMSE is significantly optimized compared with LS / SOMP; in high SNR scenarios (SNR>5 dB): the performance of the improved CoSaMP algorithm tends to saturation, while the proposed method further approaches the theoretical limit (Oracle LS) through the refined parameter optimization of SIGW-LBFG, showing higher estimation accuracy.

[0159] In the embodiment of the present invention, the NMSE performance under different pilot lengths (P) is as follows: Figure 5 As shown, Figure 5The NMSE performance for pilot length P is given, with an SNR of 10 dB. The distances are randomly sampled from U (200 m, 220 m). The length of the test sequence P increases from 8 to 64. Simulations show that: for low pilot overhead (P < 30), the traditional OMP algorithm suffers from high NMSE due to insufficient sparsity estimation. The improved CoSaMP algorithm, through dynamic support set optimization, significantly improves performance over LS / OMP / SOMP when P ≥ 30. For high pilot resources (P > 40), the proposed Co-SIGW-LBFG algorithm, through joint parameter refinement, further optimizes performance compared to the improved CoSaMP and gradually approaches the theoretical limit (Oracle LS), while significantly improving pilot utilization.

[0160] Therefore, through this simulation result, it can be concluded that the optimization scheme proposed in the present invention is significantly superior to traditional channel estimation algorithms in terms of accuracy, robustness, computational efficiency and resource utilization, and has the advantage of being widely used in large-scale MIMO systems.

[0161] The proposed method addresses the problem of high-precision channel estimation in very large-scale multiple-input, multiple-output (XL-MIMO) systems in far-field multi-user scenarios. This method is implemented through a two-stage collaborative optimization. In the first stage, an improved CoSaMP algorithm is used to rapidly recover the channel sparse structure from low-dimensional observation data using proxy computing, dynamic support set expansion, and a smoothing weight mechanism, generating a highly robust initial estimate. In the second stage, a high-resolution angle-gain joint optimization is performed on the initial estimate using a synchronous iterative gridless weighted optimization (SIGW-LBFG) approach based on L-BFGS direction search, dynamic line search step size adjustment, and path energy pruning. This eliminates mismatch errors caused by traditional gridding, further suppresses noise interference, and improves the accuracy of sparse representation. This two-stage sparse optimization architecture significantly improves the efficiency and noise immunity of channel state information (CSI) recovery. Simulation results show that the proposed algorithm outperforms traditional algorithms (SOMP / OMP) under low signal-to-noise ratio (SNR<5 dB), suppresses grid mismatch and energy leakage in far-field and long-distance scenarios, has higher resource utilization in scenarios with limited pilot resources, significantly improves far-field channel estimation accuracy and pilot efficiency, and exhibits strong robustness in high-noise environments. It provides a high-precision, low-overhead channel estimation solution for large-scale data transmission in 6G communication systems, and has wide applicability and engineering practice value.

[0162] The technical effects of the present invention are as follows:

[0163] 1. Dynamic support set expansion and grid mismatch suppression;

[0164] Traditional CoSaMP algorithms rely on fixed grid divisions, which are prone to grid mismatch in far-field multipath scenarios due to discrete angle-range sampling, leading to energy leakage and estimation bias. This paper uses a dynamic support set expansion strategy, combined with proxy calculation and a smoothing weight mechanism, to adaptively capture channel sparsity, significantly reducing grid mismatch errors and improving sparse representation accuracy.

[0165] 2. Joint optimization of continuous domains and improvement of computational efficiency;

[0166] Traditional SIGW algorithms require a joint angle-gain search in a high-dimensional parameter space, resulting in high computational complexity and insufficient robustness under low signal-to-noise ratio (SNR) conditions. This paper proposes a synchronous iterative gridless weighted optimization (SIGW-LBFG) algorithm. Based on L-BFGS directional search and dynamic adjustment of the line search step, this algorithm extends the parameter optimization range to the continuous domain, eliminating the limitations of discrete meshing. It also employs a path energy pruning strategy and smoothing mechanism to avoid redundant computations, significantly improving algorithm efficiency and convergence stability. Furthermore, Cholesky decomposition replaces the traditional pseudo-inverse operation in the gain matrix solution, significantly reducing computational complexity and improving numerical efficiency, thereby maintaining high accuracy and robustness even under low SNR conditions.

[0167] 3. Optimize pilot resource utilization;

[0168] Traditional algorithms rely on high pilot overhead to compensate for grid mismatch, resulting in reduced spectral efficiency. This invention significantly reduces pilot resource requirements through a two-stage collaborative optimization (CoSaMP fast sparse acquisition and SIGW-LBFG refined iteration), providing a high-precision, low-overhead channel estimation solution for XL-MIMO systems.

[0169] In the technical solution provided by the present invention, the method includes constructing an XL-MIMO multi-user broadband spatial channel model based on hybrid precoding; according to the XL-MIMO multi-user broadband spatial channel model based on hybrid precoding, converting the channel recovery problem into a sparse matrix recovery problem and solving it; using an improved CoSaMP algorithm to perform initial sparse channel estimation; applying a synchronous iterative gridless weighted optimization algorithm SIGW-LBFG, combined with L-BFGS direction search, line search step size adjustment and pruning strategy, to perform synchronous iterative gridless weighted optimization on the initial sparse channel estimation to improve the initial sparse channel estimation accuracy of the CoSaMP algorithm; simulation verification, evaluating the algorithm performance through normalized mean square error (NMSE), setting multiple groups of transmission distances, pilot lengths and signal-to-noise ratio (SNR) parameters, and verifying the robustness in far-field, low signal-to-noise ratio and pilot resource-limited scenarios. This method achieves high-precision, low-overhead channel estimation, and improves applicability and engineering practice value.

[0170] Each step of the embodiment of the present invention may be performed by an electronic device, including but not limited to a mobile phone, a tablet computer, a portable PC, a desktop computer, etc.

[0171] An embodiment of the present invention provides a computer-readable storage medium, which includes a stored program. When the program is executed, the computer-readable storage medium is controlled to execute an embodiment of the above-mentioned XL-MIMO far-field channel estimation method based on two-stage sparse optimization.

[0172] Figure 6 A schematic diagram of an electronic device provided by an embodiment of the present invention is shown in FIG. Figure 6 As shown, the electronic device 21 includes: a processor 211, a memory 212, and a computer program 213 stored in the memory 212 and executable on the processor 211. When the computer program 213 is executed by the processor 211, the XL-MIMO far-field channel estimation method based on two-stage sparse optimization in the embodiment is implemented. To avoid repetition, they are not described here one by one.

[0173] The electronic device 21 includes, but is not limited to, a processor 211 and a memory 212. Those skilled in the art will understand that Figure 6 It is only an example of the electronic device 21 and does not constitute a limitation of the electronic device 21. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the electronic device may also include input and output devices, network access devices, buses, etc.

[0174] The processor 211 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0175] The memory 212 can be an internal storage unit of the electronic device 21, such as the hard drive or memory of the electronic device 21. The memory 212 can also be an external storage device of the electronic device 21, such as a plug-in hard drive, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc. equipped on the electronic device 21. Furthermore, the memory 212 can include both the internal storage unit of the electronic device 21 and an external storage device. The memory 212 is used to store computer programs and other programs and data required by the network device. The memory 212 can also be used to temporarily store data that has been output or is about to be output.

[0176] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0177] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A XL-MIMO far-field channel estimation method based on two-stage sparse optimization, characterized in that: The method comprises: Step 1: Construct an XL-MIMO multi-user broadband spatial channel model based on hybrid precoding; Step 2: According to the hybrid precoding-based XL-MIMO multi-user broadband spatial channel model, the channel recovery problem is converted into a sparse matrix recovery problem and solved; Step 3: Use the improved CoSaMP algorithm to perform initial sparse channel estimation; Step 4: Apply the synchronous iterative gridless weighted optimization algorithm SIGW-LBFG, combined with L-BFGS direction search, line search step size adjustment and pruning strategy, to perform synchronous iterative gridless weighted optimization on the initial sparse channel estimate to improve the initial sparse channel estimation accuracy of the CoSaMP algorithm; Step 5: Simulation verification: evaluate the algorithm performance through normalized mean square error (NMSE). Set multiple sets of transmission distance, pilot length, and signal-to-noise ratio (SNR) parameters to verify the robustness in far-field, low SNR, and pilot resource-limited scenarios. The synchronous iterative gridless weighted optimization algorithm SIGW-LBFG in step 4 includes: Input: Observation data matrix , perception matrix , initial angle matrix , gain matrix , angle parameters , minimum number of paths , pruning threshold , maximum number of iterations , learning rate , convergence threshold , L-BFGS memory size ; Initialization: Residual Matrix , set the initial parameters A=A0, G=G0, , and initialize the L-BFGS memory to an empty set; Iterate the following steps until convergence conditions are met: (o) Calculate the loss function for the angle parameter through Cholesky decomposition Gradient ; (p) Based on the historical parameter changes s and gradient changes stored in the L-BFGS memory , recursively generate search directions ,in is a finite memory approximation of the inverse Hessian matrix; (q) Determine the step size by line search Update parameters , reconstruct the angle matrix ; (w) Update the gain matrix G through Cholesky decomposition and back substitution; (u) If the number of paths And the number of iterations is greater than the threshold, and the gain energy is less than the reduction Path; Apply weighted smoothing mechanism to suppress gain matrix jitter; Output optimized angle matrix A, gain matrix G and angle parameters ; The Cholesky decomposition and back-substitution method includes: Constructing a Matrix and ,right Perform Cholesky decomposition to obtain the lower triangular matrix ; By forward substitution With backward substitution Solve the gain matrix G; The L-BFGS memory mechanism includes: Store the most recent m groups of parameter changes s and gradient changes ; The search direction p is generated by recursive calculation from reverse order to forward order to avoid explicit storage of high-dimensional Hessian matrix.

2. The method according to claim 1, characterized in that Step 1 includes adopting an XL-MIMO orthogonal frequency division multiplexing (OFDM) communication system based on a time division duplex (TDD) mode, configuring a base station with a hybrid precoding architecture, and performing multi-user uplink channel estimation and beamforming optimization using orthogonal pilot sequences. The communication system includes multiple subcarriers, multiple RF chains, and multiple paths. At the user end, K single-antenna users generate pilot signals through orthogonal pilot sequences. , data is distributed to M subcarriers through orthogonal frequency division multiplexing (OFDM), and then the time domain signal is generated through inverse fast Fourier transform (IFFT) and transmitted to the base station through the wireless channel. After the base station receives the time domain signal from the user end, the signal passes through the analog synthesis matrix Precoding, matrix The size is , and satisfy the norm constraint , propagates through the channel, and for the mth subcarrier, the received signal Expressed as: (1) in, is the spatial domain channel matrix, is Gaussian noise, is the transmitted pilot signal; after the received signal is processed by the synthesis matrix, the overall observation matrix A is formed, and combined with the signal transmission conditions of P time slots, the final received signal is obtained: (2) in, , the elements in A are independent and come from the set Randomly generated in For noise; Base station equipped with N RF RF chains and N antennas, with a spacing of ,in The base station performs channel estimation on the received signal, recovers the user data symbols through inverse calculation, and completes symbol demodulation using baseband processing. After OFDM demodulation, the signal is restored to the frequency domain, and is equalized and de-precoded in combination with the channel matrix H to restore the original data. The base station adjusts the phase of different antennas through the phase shifter array and antenna array. Generate directional beams directed to target users to improve spatial gain and optimize signal transmission efficiency; the phase parameters of the phase shifter array is generated by an angle optimization algorithm and based on , adjust the phase and focus the signal in the direction of the target user; finally, the base station outputs the channel state information CSI of K users and uses the channel state information CSI for optimized scheduling and beamforming to improve the system capacity and energy efficiency; among them, Indicates the phase shift value of the nth antenna; represents the row index of the nth antenna; θ represents the angle parameter.

3. The method according to claim 1, characterized in that Step 2 includes decomposing the user channel into a superposition of finite paths based on a plane wave assumption, constructing a discrete Fourier transform (DFT) dictionary matrix for sparse representation, converting the channel estimation into a sparse matrix recovery problem, and solving the problem. The complex gain of each path is related to the distance between the user and the base station and the arrival angle. The channel is expressed as: (3) in, , is the complex gain of the lth path; is the path distance; is the normalized angle of arrival; is the array response vector, and its expression is: (4) By adjusting the phase of each antenna, directional reception of the signal is achieved; the phase shift value of the nth antenna With angle parameters Directly related, the formula is: ; ; Represents the row index of the nth antenna; in order to capture the sparsity of the channel in the angular domain, a discrete Fourier transform DFT dictionary matrix is constructed; the column vector of the DFT dictionary matrix covers the entire angular space, and the oversampling factor s is used to improve the angular resolution. The sparse representation of the channel is: (5) in, is the Fourier transform matrix, is a sparse gain matrix with only L non-zero elements in each column, corresponding to the angular position of the effective path; Substituting the sparse representation into the received signal model, we get: (6) Where A represents the angle matrix; The channel estimation problem is transformed into recovering a high-dimensional sparse matrix from low-dimensional observations, which is expressed as: (7) in, represents the number of non-zero elements, and L is the sparsity of the channel.

4. The method according to claim 1, wherein The step 3 includes recovering the channel sparse structure from low-dimensional observation data based on a dynamic support set expansion and smoothing weight mechanism; generating an initial sparse channel estimate through proxy calculation, support set expansion, sub-dictionary pseudo-inverse solution and smoothing mechanism iterative optimization.

5. A computer-readable storage medium, characterized in that The computer-readable storage medium includes a stored program, wherein when the program is executed, the device where the computer-readable storage medium is located is controlled to execute the XL-MIMO far-field channel estimation method based on two-stage sparse optimization according to any one of claims 1 to 4.

6. An electronic device, characterized in that: include: one or more processors; Memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, and the one or more computer programs include instructions, which, when executed by the device, enable the device to perform the XL-MIMO far-field channel estimation method based on two-stage sparse optimization according to any one of claims 1 to 4.

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