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

Abstract

The invention relates to the technical field of wireless communication, and particularly provides an XL-MIMO far-field channel estimation method based on dual-stage sparse optimization. The method comprises the following steps: constructing an XL-MIMO multi-user broadband space channel model based on hybrid precoding; converting a channel recovery problem into a sparse matrix recovery problem according to the constructed model, and solving the problem; carrying out initial sparse channel estimation by adopting an improved CoSaMP algorithm; according to the method, the SIGW-LBFG algorithm is applied, L-BFGS direction search, line search step size adjustment and pruning strategies are combined, synchronous iteration meshless weighted optimization is carried out on initial estimation, simulation verification is carried out, high-precision and low-overhead channel estimation is achieved, and applicability and engineering practice value are improved.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly to a method for far-field channel estimation of XL-MIMO based on two-stage sparse optimization. Background Art

[0002] With the rapid development of the extremely 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. The XL-MIMO system provides a great spatial diversity gain through a large-scale antenna array, but it also brings challenges in terms of channel estimation accuracy and computational complexity. Especially in far-field signal estimation, due to the sparsity of signals and multipath effects, traditional channel estimation methods are difficult to meet the requirements of high accuracy and high efficiency.

[0003] In the prior art, the traditional orthogonal matching pursuit (OMP) algorithm has low accuracy in recovering high-dimensional sparse signals due to fixed grid partitioning and poor noise robustness; while the traditional compressive sampling matching pursuit (CoSaMP) algorithm is difficult to capture the common sparse structure of multi-antenna systems and has a problem of grid mismatch. Summary of the Invention

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

[0005] In a first aspect, the present invention provides a method for far-field channel estimation of XL-MIMO based on two-stage sparse optimization, and the method includes: Step 1, construct an XL-MIMO multi-user broadband spatial channel model based on hybrid precoding; Step 2, according to the XL-MIMO multi-user broadband spatial channel model based on hybrid precoding, transform the channel recovery problem into a sparse matrix recovery problem and solve it; Step 3, use an improved CoSaMP algorithm for initial sparse channel estimation; Step 4, apply the synchronous iterative meshless weighted optimization algorithm SIGW-LBFG, combine L-BFGS direction search, line search step size adjustment and pruning strategy, and perform synchronous iterative meshless weighted optimization on the initial sparse channel estimation to improve the initial sparse channel estimation accuracy of the CoSaMP algorithm; Step 5, simulation verification, evaluate the algorithm performance through the normalized mean square error NMSE, set multiple groups of transmission distance, pilot length and signal-to-noise ratio SNR parameters, and verify the robustness in far-field, low signal-to-noise ratio and pilot resource-constrained scenarios.

[0006] Optionally, step 1 includes using an XL-MIMO orthogonal frequency division multiplexing (OFDM) communication system based on the time division duplex (TDD) mode. The base station is configured with a hybrid precoding architecture, and multi-user uplink channel estimation and beamforming optimization are performed through orthogonal pilot sequences. The communication system includes multiple subcarriers, multiple RF chains, and multiple paths; At the user side, K single-antenna users generate pilot signals through orthogonal pilot sequences , allocate data to M subcarriers through orthogonal frequency division multiplexing (OFDM), generate a time-domain signal through inverse fast Fourier transform (IFFT), and transmit it to the base station through a wireless channel, where ; after the base station receives the time-domain signal from the user side, the signal is precoded through an analog synthesis matrix , and the size of matrix is , and it satisfies the constant modulus constraint . Through channel propagation, for the m-th subcarrier, the received signal is expressed as: (1) where, is the spatial domain channel matrix, is Gaussian noise, is the transmitted pilot signal; after the received signal is processed by the synthesis matrix, an overall observation matrix A is formed, and combined with the signal transmission situation of P time slots, the final received signal is obtained: (2) where, , the elements in A are independent and randomly generated from the set ; is noise; The base station is equipped with N RF RF chains and N antennas, and the spacing between the antennas is , where is the carrier wavelength; the base station performs channel estimation on the received signal, recovers the user data symbols through inverse operations, and completes symbol demodulation using baseband processing; after the signal is demodulated by OFDM, it is restored to the frequency domain, and combined with the channel matrix H for equalization and de-precoding to restore the original data; the base station adjusts the phases of different antennas through a phase shifter array and an antenna array to generate a directional beam pointing to the target user, which is used to improve the spatial gain and optimize the signal transmission efficiency; the phase parameters of the phase shifter array are generated through an angle optimization algorithm, and according to , , adjust the phase to concentrate 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 capacity and energy efficiency of the system.

[0007] Optionally, 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, transforming the channel estimation into a sparse matrix recovery problem, and solving it; The complex gain of each path is related to factors such as the distance between the user and the base station and the angle of arrival; The representation of the channel is: (3) where , is the complex gain of the l-th 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 n-th antenna is directly related to the angle parameter by the formula: ; represents the row index of the n-th antenna; to capture the sparsity of the channel in the angle domain, a discrete Fourier transform DFT dictionary matrix is constructed; the column vectors of the DFT dictionary matrix cover the entire angle space, and the oversampling factor s is used to improve the angle resolution. The sparse representation of the channel is: (5) where is the Fourier transform matrix, is the sparse gain matrix, and each column has only L non-zero elements corresponding to the angle positions of the effective paths; Substituting the sparse representation into the received signal model, we get: (6) The channel estimation problem is transformed into recovering a high-dimensional sparse matrix from low-dimensional observations, and its expression is: (7) where represents the number of non-zero elements, and L is the sparsity of the channel.

[0008] 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; and generating an initial sparse channel estimate through iterative optimization of proxy calculation, support set expansion, sub-dictionary pseudo-inverse solution, and smoothing mechanism.

[0009] Optionally, the synchronous iterative gridless weighted optimization algorithm SIGW-LBFG in step 4 includes: Input: Observation data matrix , sensing matrix , initial angle matrix , gain matrix , angle parameter , minimum number of paths , pruning threshold , maximum number of iterations , learning rate , convergence threshold , L-BFGS memory size ; Initialization: Residual matrix , set initial parameters A = A 0 , G = G 0 , , and initialize the L-BFGS memory as an empty set; Iteratively execute the following steps until the convergence condition is met: (o) Calculate the gradient of the loss function with respect to the angle parameter through Cholesky decomposition; (p) Recursively generate the search direction based on the historical parameter change amount s and gradient change amount stored in the L-BFGS memory, where is the finite memory approximation of the Hessian inverse matrix; (q) Determine the step size through line search, update the parameter , and reconstruct the angle matrix ;

[0010] (w) Update the gain matrix G through Cholesky decomposition and back substitution; (u) If the number of paths and the number of iterations are greater than the threshold, remove the paths with gain energy less than the cut-off ; Apply a weighted smoothing mechanism to suppress the jitter of the gain matrix; Output the optimized angle matrix A, gain matrix G, and angle parameter .

[0011] Optionally, the Cholesky decomposition and back substitution method include: Construct matrix and , and perform Cholesky decomposition on to obtain a lower triangular matrix ; Solve for the gain matrix G through forward substitution and back substitution .

[0012] Optionally, the L-BFGS memory mechanism includes: Store the most recent m sets of parameter change amounts s and gradient change amounts ; Generate a search direction p through reverse-order and forward-order recursion calculations to avoid explicitly storing a high-dimensional Hessian matrix.

[0013] In a second aspect, an embodiment of the present invention provides a computer-readable storage medium, where the computer-readable storage medium includes a stored program, and when the program runs, it controls the device where the computer-readable storage medium is located to execute the XL-MIMO far-field channel estimation method based on two-stage sparse optimization in the first aspect or any possible implementation manner of the first aspect.

[0014] In a third aspect, an embodiment of the present invention provides an electronic device, including: one or more processors; a memory; and one or more computer programs, where 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, cause the device to execute the XL-MIMO far-field channel estimation method based on two-stage sparse optimization in the first aspect or any possible implementation manner of the first aspect.

[0015] 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, transforming the channel recovery problem into a sparse matrix recovery problem and solving it; using an improved CoSaMP algorithm for initial sparse channel estimation; applying the synchronous iterative meshless weighted optimization algorithm SIGW-LBFG, combining L-BFGS direction search, line search step size adjustment, and pruning strategies, to perform synchronous iterative meshless weighted optimization on the initial estimation to improve the initial sparse channel estimation accuracy of the CoSaMP algorithm; through simulation verification, evaluating the algorithm performance through the 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 scenarios of far field, low signal-to-noise ratio, and limited pilot resources. This method achieves high-precision and low-overhead channel estimation, improving applicability and engineering practice value. Brief Description of the Drawings

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0017] Figure 1 It is a flowchart of the XL-MIMO far-field channel estimation method based on two-stage sparse optimization provided by an embodiment of the present invention; Figure 2 It is a schematic diagram of the XL-MIMO multi-user broadband spatial channel model based on hybrid precoding provided by an embodiment of the present invention; Figure 3 It is a performance curve diagram between distance and normalized mean square error provided by an embodiment of the present invention; Figure 4 It is a performance curve diagram between pilot length and normalized mean square error provided by an embodiment of the present invention; Figure 5 It is a performance curve diagram between signal-to-noise ratio and normalized mean square error provided by an embodiment of the present invention; Figure 6 It is a schematic diagram of an electronic device provided by an embodiment of the present invention. Detailed Embodiments

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0019] It should be clear that the described embodiments are only some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0020] 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 "said" used in the embodiments of the present invention are also intended to include the plural forms unless the context clearly indicates otherwise.

[0021] It should be understood that the term "and / or" used herein is merely a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone. Additionally, the character " / " in this text generally indicates that the associated objects before and after are in an "or" relationship.

[0022] Depending on the context, the word "if" as used herein can be interpreted as "when" or "while" or "in response to determining" or "in response to detecting". Similarly, depending on the context, the phrase "if it is determined" or "if it is detected (the stated condition or event)" can be interpreted as "when it is determined" or "in response to determining" or "when (the stated condition or event) is detected" or "in response to detecting (the stated condition or event)".

[0023] Figure 1 It is a flowchart of the XL-MIMO far-field channel estimation method based on two-stage sparse optimization provided by an embodiment of the present invention. As Figure 1 shown, the method includes: Step 1: Construct an XL-MIMO multi-user broadband spatial channel model based on hybrid precoding.

[0024] In an embodiment of the present invention, as Figure 2 shown, Step 1 includes adopting an XL-MIMO orthogonal frequency division multiplexing (OFDM) communication system based on the time division duplex (TDD) mode. Specifically, it realizes efficient estimation of the multi-user uplink channel and beamforming optimization. The system architecture and working process are as follows: At the user side, K single-antenna users generate pilot signals through orthogonal pilot sequences , allocate data to M subcarriers through orthogonal frequency division multiplexing (OFDM), then generate a time-domain signal through inverse fast Fourier transform (IFFT), and transmit it to the base station through a wireless channel, where . The user signals satisfy strict orthogonality constraints , avoiding multi-user interference.

[0025] After the base station receives the signals from the user side, the signals are precoded through an analog synthesis matrix , the size of this matrix is , and it satisfies the constant modulus constraint . Through channel propagation, for the m-th subcarrier, the received signal is expressed as: (1) Wherein, 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 situation of P time slots, the final received signal is obtained: (2) Among them, the elements in A are independent and randomly generated from the set ; is noise.

[0026] The base station is equipped with N RF radio frequency links and N antennas, and the spacing between the antennas is where is the carrier wavelength. The base station performs channel estimation on the received signal, restores the user data symbols through inverse operations, and completes symbol demodulation using baseband processing. The signal is restored to the frequency domain after OFDM demodulation, and equalization and de-precoding are performed in combination with the channel matrix H to restore the original data. The base station adjusts the phases of different antennas through the phase shifter array and the antenna array to generate a directional beam, which points to the target user, improves the spatial gain, and optimizes the signal transmission efficiency. The phase parameters of the phase shifter array are generated by an angle optimization algorithm, and according to , , the phases are adjusted to concentrate 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 capacity and energy efficiency of the system.

[0027] Step 2: According to the XL-MIMO multi-user broadband spatial channel model based on hybrid precoding, transform the channel restoration problem into a sparse matrix restoration problem and solve it.

[0028] In the embodiment of the present invention, Step 2 includes decomposing the user channel into the superposition of finite paths based on the plane wave assumption, constructing a discrete Fourier transform DFT dictionary matrix for sparse representation, transforming the channel estimation into a sparse matrix restoration problem, and solving it; The complex gain of each path is related to factors such as the distance between the user and the base station and the arrival angle; The representation of the channel is: (3) Among them, , is the complex gain of the l-th path; is the path distance; is the normalized arrival angle; is the array response vector, and its expression is: (4) By adjusting the phase of each antenna, the directional reception of the signal is achieved; the phase shift value of the nth antenna is directly related to the angle parameter by the formula: ; ; represents the row index of the nth antenna; to capture the sparsity of the channel in the angular domain, a discrete Fourier transform (DFT) dictionary matrix is constructed; the column vectors of the DFT dictionary matrix cover the entire angular space, and the oversampling factor s is used to improve the angular resolution. The sparse representation of the channel is: (5) where is the Fourier transform matrix, is the sparse gain matrix, and each column has only L non-zero elements corresponding to the angular positions of the effective paths; Substituting the sparse representation into the received signal model, we get: (6) The channel estimation problem is transformed into recovering a high-dimensional sparse matrix from low-dimensional observations, and its expression is: (7) where represents the number of non-zero elements, and L is the sparsity of the channel.

[0029] Step 3: Use an improved CoSaMP algorithm for initial sparse channel estimation.

[0030] In the 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; through proxy calculation, support set expansion, sub-dictionary pseudo-inverse solution, and smoothing mechanism iterative optimization, an initial sparse channel estimation is generated.

[0031] In the embodiment of the present invention, the improved CoSaMP algorithm is specifically implemented as follows: a. Input: Observation matrix , sensing matrix Phi, sparsity K, convergence tolerance tol, maximum number of iterations maxiterations, smoothing weight ; b. Output: Estimated sparse signal , final support set T; c. Initialization: ; d. ; e. Calculate the proxy matrix ; f. Select the first K maximum energy indices ; g. Update the support set ; h. Construct a sub-dictionary , and solve the coefficient matrix by orthogonal projection ; i. Prune the support set T, and retain the K rows with the largest energy in B; j. Update the sparse signal estimation , and apply a smoothing mechanism ; k. Update the residual matrix ; l. , break; m. End for; n. Return: , T; In the initialization stage of the algorithm, first set the residual matrix R = Y and set the sparse support set T as an empty set. Subsequently, 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 common support set; then in step h, construct a sub-dictionary based on the preliminary support set and obtain the coefficient matrix B by using the pseudo-inverse operation. Then, in step i, prune B according to the energy of each row coefficient to retain the K rows with the largest contribution, and update B again using the least squares method; in step j, after assigning a value to the signal estimation , introduce a smoothing mechanism to weight and fuse the current estimation with the result of the previous iteration to suppress jitter, and step k updates the residual matrix R; finally, in step l, check whether the ratio of the residual to the observed quantity is less than the threshold. If it is less than the threshold, stop the iteration and output the final sparse signal and support set.

[0032] Step 4. Apply the synchronous iterative meshless weighted optimization algorithm SIGW-LBFG, combine the L-BFGS direction search, line search step size adjustment and pruning strategy, and perform synchronous iterative meshless weighted optimization on the initial sparse channel estimation to improve the accuracy of the initial sparse channel estimation of the CoSaMP algorithm.

[0033] In the embodiment of the present invention, the synchronous iterative meshless weighted optimization algorithm SIGW-LBFG in step 4 includes: Input: Observation data matrix , sensing matrix , initial angle matrix , gain matrix , angle parameter , minimum number of paths , pruning threshold , maximum number of iterations , learning rate , Convergence threshold , L-BFGS memory size ; Initialization: Residual matrix , Set initial parameters , and initialize the L-BFGS memory as an empty set, i.e., ; Iteratively execute the following steps until the convergence condition is met: (o) Calculate the gradient of the loss function with respect to the angular parameter through Cholesky decomposition ; (p) Based on the historical parameter change amounts s and gradient change amounts stored in the L-BFGS memory, recursively generate the search direction , where is the limited-memory approximation of the inverse Hessian matrix; (q) Determine the step size through line search, update the parameter , and reconstruct the angular matrix ;

[0034] (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, remove the paths with gain energy less than the reduction ; Apply a weighted smoothing mechanism to suppress the jitter of the gain matrix; Output the optimized angular matrix A, gain matrix G, and angular parameter .

[0035] In the embodiment of the present invention, the Cholesky decomposition and back substitution method includes: Construct matrices and , perform Cholesky decomposition on to obtain the lower triangular matrix ; Solve the gain matrix G through forward substitution and back substitution .

[0036] In the embodiment of the present invention, the L-BFGS memory mechanism includes: Store the most recent m sets of parameter change amounts s and gradient change amounts ; Generate the search direction p through reverse-order - forward-order recursion to avoid explicitly storing the high-dimensional Hessian matrix.

[0037] In the embodiment of the present invention, the specific process of step 4 includes: S4-1. For ; S4-2. Calculate the gradient through Cholesky decomposition: ; S4-3. Calculate the search direction based on L-BFGS memory ; S4-4. Line search to adjust the step size Update the parameters ; S4-5. Reconstruct the angle matrix ; S4-6. Update the gain matrix ; S4-7. Update the L-BFGS memory and record the difference ; S4-8. , break; S4-9. Path pruning (when the number of paths and ): Screen the paths with gain energy greater than the cut ; S4-10. Apply the smoothing mechanism ; S4-11. End for; S4-12. Return return A, G, ; In the initialization stage of the algorithm, set the initial parameters and calculate the initial residual matrix ; where and are the initial estimates of the angle matrix and the gain matrix respectively, and the square Frobenius norm of the residual is: ; The angle offset vector row is: (8) Generate the antenna array response matrix using the angle parameter : (9) This formula realizes the physical mapping of the phase parameter.

[0038] During the iteration process, in (S4-2), first calculate the residual matrix R using the current matrix A: , and construct the matrix in the normal equation: : Subsequently, perform Cholesky decomposition on E to obtain the lower triangular factor L, that is ; Then calculate using forward and backward substitution (denoted as ), and then, combined with the chain rule and the derivative of A with respect to , the gradient of the objective function with respect to is calculated ; 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 change , and the corresponding gradient change . By calculating the coefficients forward, the current gradient q is adjusted, and then the scale factor is calculated, and finally the search direction is obtained through reverse cycle correction; In the online search stage (S4-4 to S4-5), the algorithm ensures that the updated residual satisfies the Armijo condition by gradually reducing the step size (multiplying by 0.5 if the condition is not met): . When the condition is satisfied, the angular parameter is updated along the search direction, and the antenna array response matrix A is reconstructed; After fixing A (S4-6 to S4-9), by constructing and the normal equation matrix , and then using Cholesky decomposition to obtain ; finally, the least squares problem is solved by forward and backward substitution to obtain the closed-form solution to update the gain matrix; In terms of sparsity maintenance, the algorithm dynamically prunes redundant paths with energy less than the threshold pruning, restricting the number of paths to be greater than or equal to , thereby enforcing the sparsity constraint; (S4-10 to S4-12) In the later stage of iteration, through the weighted smoothing mechanism ; suppressing gain jitter, and at the same time monitoring the parameter update amount (where ), if it is less than the convergence threshold or reaches the maximum number of iterations, terminate the iteration and output the optimized A, G, .

[0039] Using the L-BFGS direction search and dynamic adjustment of the line search step size, for the angular parameter Perform efficient iteration in the continuous domain, 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 adopted to replace the traditional pseudo-inverse operation, greatly improving the numerical operation efficiency and reducing the overall complexity; finally, by introducing a smoothing mechanism in the later stage of iteration (fusing the current gain with the previous iteration result in proportion), the estimation jitter in the low signal-to-noise ratio environment can be effectively suppressed, and the robustness and stability of the algorithm can be improved.

[0040] Step 5, Simulation verification, evaluate the performance of the algorithm through the Normalized Mean Square Error (NMSE), set multiple groups of parameters such as transmission distance, pilot length, and Signal-to-Noise Ratio (SNR), and verify the robustness in scenarios of far field, low signal-to-noise ratio, and limited pilot resources.

[0041] In the embodiments of the present invention, the effectiveness and advantages of the simulation result verification scheme are verified; To verify the effectiveness and advantages of the channel estimation scheme proposed in the present invention, the present invention compares and analyzes the performance of different channel estimation algorithms through simulation results. Specifically, five channel estimation algorithms are selected in the simulation: Least Squares (LS), Ideal Least Squares (Oracle LS), Simultaneous Orthogonal Matching Pursuit (SOMP), Improved CoSaMP Algorithm (CoSaMP+), and Optimized CoSaMP Combined with SIGW-LBFG Algorithm (Co-SIGW-LBFG). The performance is evaluated by the Normalized Mean Square Error (NMSE), and the simulation configuration is shown in Table 1.

[0042] Table 1 Simulation Configuration ; In the embodiments of the present invention, the performance comparison is carried out from different dimensions as follows: The NMSE performance under different transmission distances, as Figure 3 shown, Figure 3 shows the performance comparison of different algorithms in the change of Normalized Mean Square Error (NMSE) with the transmission distance, where the SNR is fixed at 10 dB, the pilot length P = 32, and the distance between the user and the base station extends from 100 meters to 230 meters, corresponding to the Rayleigh distance of about 100 meters. The proposed method has a significant optimization in NMSE compared with the traditional algorithms (LS / SOMP / Improved CoSaMP) in the scenarios of far field, large distance, low SNR, and limited pilot resources, and approaches the theoretical limit under high pilot conditions, verifying the technical advantages of dynamic support set expansion, continuous domain optimization, and two-stage collaborative architecture.

[0043] In the embodiments of the present invention, the NMSE performance under different Signal-to-Noise Ratios (SNR), where the pilot length is P = 32, as Figure 4As shown, for the low SNR scenario (SNR < 5 dB): due to ignoring sparsity, the NMSE of the traditional LS algorithm deteriorates sharply; the proposed Co-SIGW-LBFG algorithm significantly suppresses noise interference through the anti-noise weight mechanism and the path pruning strategy, and the NMSE is significantly optimized compared with LS / SOMP; for the high SNR scenario (SNR > 5 dB): the performance of the improved CoSaMP algorithm tends to saturate, while the proposed method further approaches the theoretical limit (Oracle LS) through the refined parameter optimization of SIGW-LBFG, showing higher estimation accuracy.

[0044] In the embodiments of the present invention, the NMSE performance under different pilot lengths (P) is as Figure 5 shown Figure 5 shown in [Figure], which gives the NMSE performance under the pilot length P, where the SNR is 10 dB. The distance is randomly sampled from U(200m, 220 m). The length of the test sequence P increases from 8 to 64. The simulation shows that: for low pilot overhead (P < 30): due to insufficient sparsity estimation, the NMSE of the traditional OMP algorithm remains high; the improved CoSaMP algorithm significantly improves the performance compared with LS / OMP / SOMP when P ≥ 30 through dynamic support set optimization; for high pilot resources (P > 40): the proposed Co-SIGW-LBFG algorithm is further optimized compared with the improved CoSaMP through joint parameter refinement, and gradually approaches the theoretical limit (Oracle LS), while the pilot utilization rate is significantly improved.

[0045] Therefore, based on this simulation result, it can be concluded that the optimization scheme proposed by the present invention is significantly superior to the traditional channel estimation algorithms in terms of accuracy, robustness, computational efficiency, and resource utilization rate, and has the advantage of being widely applied in large-scale MIMO systems.

[0046] The method proposed in the present invention is used to solve the problem of high-precision channel estimation in a far-field multi-user scenario of a very large-scale multiple-input multiple-output (XL-MIMO) system. This method is achieved through the collaborative optimization of the following two stages: In the first stage, an improved CoSaMP algorithm is adopted. Based on surrogate calculation, dynamic support set expansion, and smooth weight mechanism, it quickly recovers the channel sparse structure from low-dimensional observation data and generates an initial estimate with high robustness. In the second stage, combined with synchronous iterative gridless weighted optimization (SIGW-LBFG), based on L-BFGS direction search, dynamic adjustment of the line search step size, and path energy pruning strategy, it performs high-resolution angle-gain joint optimization on the initial estimation result, eliminates the mismatch error caused by traditional grid division, further suppresses noise interference, and improves the sparse representation accuracy. Through the two-stage sparse optimization architecture, the present invention significantly improves the recovery efficiency and anti-noise ability of channel state information (CSI). Simulation results show that the algorithm proposed in the present invention outperforms traditional algorithms (SOMP / OMP) at low signal-to-noise ratios (SNR < 5 dB), suppresses grid mismatch and energy leakage in far-field large-distance scenarios, has higher resource utilization in scenarios with limited pilot resources, significantly improves far-field channel estimation accuracy and pilot efficiency, and demonstrates strong robustness in high-noise environments, providing a high-precision and low-overhead channel estimation solution for large-scale data transmission in 6G communication systems, with wide applicability and engineering practice value.

[0047] The technical effects of the present invention are as follows: 1. Dynamic support set expansion and grid mismatch suppression; The traditional CoSaMP algorithm relies on fixed grid division. In a far-field multipath scenario, it is prone to grid mismatch due to angular-distance discrete sampling, resulting in energy leakage and estimation bias. Through the dynamic support set expansion strategy, combined with surrogate calculation and smooth weight mechanism, the present invention adaptively captures the channel sparse structure, significantly reduces the grid mismatch error, and improves the sparse representation accuracy.

[0048] 2. Continuous domain joint optimization and computational efficiency improvement; The traditional SIGW algorithm needs to perform angular-gain joint search in a high-dimensional parameter space, with high computational complexity and insufficient robustness at low signal-to-noise ratios. The present invention proposes a synchronous iterative gridless weighted optimization (SIGW-LBFG) algorithm: Based on L-BFGS direction search and dynamic adjustment of the line search step size, it expands the parameter optimization range to the continuous domain, eliminating the limitation of discrete grid division; at the same time, it adopts a path energy pruning strategy and a smooth mechanism to avoid redundant calculations, significantly improving the algorithm efficiency and convergence stability; and in the gain matrix solution process, it uses Cholesky decomposition to replace the traditional pseudo-inverse operation, greatly reducing the computational complexity and improving the numerical calculation efficiency, so as to maintain high accuracy and robustness even under low signal-to-noise ratio conditions.

[0049] 3. Pilot resource utilization optimization; Traditional algorithms rely on high pilot overhead to compensate for grid mismatch, resulting in a decrease in spectral efficiency. The present invention significantly reduces the pilot resource requirements through two-stage collaborative optimization (CoSaMP fast sparse capture, SIGW-LBFG refined iteration), providing a high-precision and low-overhead channel estimation scheme for XL-MIMO systems.

[0050] 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; converting the channel recovery problem into a sparse matrix recovery problem according to the XL-MIMO multi-user broadband spatial channel model based on hybrid precoding and solving it; using an improved CoSaMP algorithm for initial sparse channel estimation; applying the synchronous iterative meshless weighted optimization algorithm SIGW-LBFG, combining L-BFGS direction search, line search step size adjustment and pruning strategy, to perform synchronous iterative meshless weighted optimization on the initial sparse channel estimation to improve the initial sparse channel estimation accuracy of the CoSaMP algorithm; through simulation verification, evaluating the algorithm performance by the 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 scenarios of far field, low signal-to-noise ratio and limited pilot resources. This method realizes high-precision and low-overhead channel estimation, improving applicability and engineering practice value.

[0051] Each step of the embodiments of the present invention can be executed by an electronic device. Among them, the electronic device includes but is not limited to mobile phones, tablet computers, portable PCs, desktop computers, etc.

[0052] The embodiments of the present invention provide a computer-readable storage medium. The computer-readable storage medium includes a stored program. When the program runs, it controls the execution of the embodiments of the above-mentioned XL-MIMO far-field channel estimation method based on two-stage sparse optimization on the computer-readable storage medium where it is located.

[0053] Figure 6 Schematic diagram of an electronic device provided by an embodiment of the present invention, as Figure 6 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, it implements the XL-MIMO far-field channel estimation method based on two-stage sparse optimization in the embodiments. To avoid repetition, it will not be elaborated here one by one.

[0054] The electronic device 21 includes, but is not limited to, a processor 211 and a memory 212. Those skilled in the art can understand, Figure 6This is only an example of the electronic device 21, which does not constitute a limitation on the electronic device 21. It may include more or fewer components than those shown in the figure, or combine certain components, or different components. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0055] The so-called processor 211 may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0056] The memory 212 may be an internal storage unit of the electronic device 21, such as the hard disk or memory of the electronic device 21. The memory 212 may also be an external storage device of the electronic device 21, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the electronic device 21. Further, the memory 212 may also include both the internal storage unit and the external storage device of the electronic device 21. The memory 212 is used to store computer programs and other programs and data required by the network device. The memory 212 may also be used to temporarily store data that has been output or will be output.

[0057] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the above-described systems, devices, and units can refer to the corresponding processes in the foregoing method embodiments, and will not be described herein again.

[0058] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within 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 XL-MIMO multi-user broadband spatial channel model based on hybrid precoding, 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 estimation 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 groups of transmission distance, pilot length and signal-to-noise ratio (SNR) parameters, and verify the robustness in far-field, low signal-to-noise ratio and pilot resource-limited scenarios.

2. The method according to claim 1, characterized in that The 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 an orthogonal pilot sequence, wherein 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 Pre-coding, matrix The size is , and satisfy the norm constraint , propagates through the channel, and for the mth subcarrier, the received signal It is expressed as: (1) in, is the spatial domain channel matrix, is Gaussian noise, is the pilot signal for transmission; the received signal is processed by the synthesis matrix to form the overall observation matrix A, 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 are from the set Randomly generated in; for noise; Base station equipped with N RF RF chains and N antennas, with a spacing of ,in is the carrier wavelength; the base station estimates the channel of the received signal, recovers the user data symbol through inverse operation, and completes the symbol demodulation through baseband processing; the signal is restored to the frequency domain after OFDM demodulation, 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 pointing to the target user to improve spatial gain and optimize signal transmission efficiency; 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.

3. The method according to claim 1, characterized in that: The 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 it; 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 angle domain, a discrete Fourier transform DFT dictionary matrix is ​​constructed; the column vector of the DFT dictionary matrix covers the entire angle space, and the oversampling factor s is used to improve the angle 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) 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, characterized in that: The step 3 includes recovering the channel sparse structure from low-dimensional observation data based on 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. The method according to claim 1, characterized in that 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; The following steps are iterated 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 It is a finite memory approximation for 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 .

6. The method according to claim 5, characterized in that The Cholesky decomposition and back-substitution method includes: Constructing the Matrix and ,right Perform Cholesky decomposition to obtain the lower triangular matrix ; By forward substitution With backward substitution Solve for the gain matrix G.

7. The method according to claim 5, characterized in that 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 reverse-forward recursive calculation to avoid explicit storage of high-dimensional Hessian matrices.

8. 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 dual-stage sparse optimization according to any one of claims 1 to 7.

9. 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 dual-stage sparse optimization as described in any one of claims 1 to 7.

Images