Reconfigurable intelligent surface blind beamforming method based on decomposition spectral gradient descent

Abstract

The application discloses a reconfigurable intelligent metasurface blind beamforming method based on decomposition spectral gradient descent, and belongs to the technical field of wireless communication signal processing. In view of the problems of high calculation complexity and poor performance stability of the existing blind beamforming technology, the coefficient matrix in a received signal strength model is decomposed into a low-rank factor form, the parameter space is reduced from O(N square) to O(rN), and the positive semi-definite and low-rank constraints are automatically satisfied. The method comprises the following steps: a spectral initialization and a decomposition gradient descent are used to fit a quadratic model parameter; and then, an optimal binary phase configuration is solved through a continuous relaxation and a sign rounding strategy. Experiments show that the application can realize more than 99% of the perfect channel state information performance under the condition of unknown channel state information, and the standard deviation is reduced from 3.60 dB of the existing method to 0.61 dB, so that the calculation efficiency and the performance stability are significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication signal processing technology, and particularly relates to a reconfigurable intelligent metasurface blind beamforming method based on decomposed spectral gradient descent. Background Technology

[0002] Reconfigurable smart metasurfaces (RIS) are a key enabling technology for sixth-generation (6G) wireless communication. By deploying numerous low-cost passive reflective elements, RIS can precisely manipulate the propagation direction of electromagnetic waves, thereby enhancing coverage, suppressing interference, and improving energy efficiency. Optimization of RIS phase configuration is crucial for achieving optimal signal propagation.

[0003] Most current research relies on channel estimation to obtain perfect channel state information (CSI) for configuring the RIS phase. However, obtaining perfect CSI in real-world scenarios faces multiple challenges: the RIS reflection channel is highly susceptible to interference from other signals and background noise; existing network protocols are often incompatible with RIS channel estimation, requiring significant protocol modifications; and many commercial systems can only measure received signal strength due to cost constraints.

[0004] To address the overhead associated with channel estimation, researchers have proposed a blind beamforming method. Currently, the closest existing implementations to this invention include:

[0005] (1) RFocus method: The optimal configuration is determined by adjusting the switching state of each reflective element one by one and using a voting mechanism. After a large number of samples, about half of the theoretical maximum performance gain can be achieved.

[0006] (2) CSM (Conditional Sample Mean) method: This method uses the idea of ​​conditional expectation to calculate the sample mean under a given phase configuration as an optimization guide. For a RIS system with K discrete phase shifts, CSM can theoretically achieve a quadratic signal-to-noise ratio improvement.

[0007] (3) GCSM (Grouped Conditional Sample Mean) method: A grouping optimization strategy is proposed, dividing RIS components into several subsets and constructing effective virtual direct paths by randomly configuring the phase of each subset. In the worst case, GCSM guarantees that the performance is not lower than the optimal cosine value. 2 (π / K) times.

[0008] (4) BORN method: The relationship between signal-to-noise ratio and RIS phase configuration is modeled as a quadratic model, and the blind beamforming problem is divided into two stages: sensing and optimization. The sensing stage estimates the quadratic model parameters, and the optimization stage calculates the optimal configuration based on the estimated model. Proven near-optimal performance can be achieved with only O(N log2(N / ε)) RSS measurements. This method is the closest existing technical solution to the present invention.

[0009] The aforementioned existing technologies still have the following drawbacks: Methods based on voting mechanisms, such as RFocus, CSM, and GCSM, essentially employ a coordinate descent strategy, optimizing the phase of N RIS elements one by one or group by group. This ignores the coupling structure between elements, resulting in low sample efficiency, slow convergence speed, and difficulty in providing stable performance gains. This deficiency is even more pronounced in large-scale RIS deployments.

[0010] While the BORN method utilizes a quadratic model structure and provides a provable near-optimal performance guarantee, its perception phase involves direct operations on an N×N matrix, resulting in a computational complexity of O(N×N). 2 This becomes a practical bottleneck in large-scale RIS deployments. Furthermore, BORN has a standard deviation of 3.60 dB, indicating poor performance stability.

[0011] Data-driven methods based on deep reinforcement learning often face problems such as slow training convergence, limited generalization ability to environmental changes, and the need for retraining or fine-tuning. More importantly, they cannot provide strict theoretical performance guarantees.

[0012] The root cause of the aforementioned shortcomings lies in the fact that existing methods fail to incorporate the inherent low-rank structure of the channel matrix into the decomposition and optimization framework to reduce computational dimensionality. In the RIS system, the coefficient matrix M = (P / σ) of the quadratic model. 2 V V is a positive semidefinite matrix with a rank not exceeding 2, a structure that has been well-proven a priori by matrix recovery theory. However, existing methods either completely ignore this structure (voting methods) or, while utilizing the quadratic model structure, fail to perform low-rank decomposition (BORN methods), resulting in redundant parameter space and low computational efficiency.

[0013] Therefore, how to utilize the low-rank characteristics of the RIS channel to design a low-complexity, high-stability, and provably near-optimal blind beamforming method is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0014] The purpose of this invention is to provide a reconfigurable intelligent metasurface blind beamforming method based on decomposed spectral gradient descent (FSGD) to solve the problem of how to efficiently and stably configure the phase of each reflective element of the RIS (Reflection Array of Reflectors) to maximize the signal-to-noise ratio at the receiver using only Received Signal Strength (RSS) measurements under conditions of unknown Channel State Information (CSI). Specifically, this invention aims to achieve the following objectives: (1) Achieve over 99% of perfect CSI performance; (2) Reduce the standard deviation to a level comparable to the perfect CSI.

[0015] To achieve the above objectives, the present invention adopts the following technical solution: The reconfigurable smart metasurface blind beamforming method based on decomposed spectral gradient descent includes the following steps: S1. Decompose gradient descent for model fitting: S1.1 Obtain the S received signal intensity measurements of N reflective elements in the reconfigurable smart metasurface; S1.2 Construct a quadratic model of the receiver's signal-to-noise ratio with respect to the phase vector x of the reflecting element: SNR(x) = x T Mx+w T x+c Where M is an N×N positive semidefinite coefficient matrix with a rank not exceeding 2, w is an N-dimensional linear coefficient vector, and c is a constant term; the superscript T indicates the transpose operation; S1.3 Decompose the coefficient matrix M into: M=UU T Where U is an N×r factor matrix, and r is the target rank with a value of 2; S1.4 Constructing the initial factor matrix U0 using the spectral initialization method: Construct a weighted sample matrix using all S measurement data, perform eigenvalue decomposition on the weighted sample matrix, extract the first r largest eigenvalues ​​and corresponding eigenvectors to construct U0; initialize the linear coefficient vector w to a zero vector, and initialize the constant term c to the arithmetic mean of all received signal strength measurements. S1.5 Define the loss function as the mean square error between the predicted received signal strength value and the measured received signal strength value on all samples. Calculate the gradient of the loss function with respect to the factor matrix U, the linear coefficient vector w, and the constant term c. Perform gradient descent updates with a fixed learning rate. After T1 iterations, output the estimated matrix and the estimated linear coefficient vector. S2. Phase optimization is performed using spectral relaxation and rounding: S2.1 Relax the discrete constraint of the phase vector x of the reflecting element into a continuous box constraint, that is, each component takes a value in the interval [-1,1]. S2.2. Use the largest eigenvector of the estimated matrix output in S1 to initialize the spectrum and construct an initial continuous solution x0; wherein the largest eigenvector is calculated by the power iteration method, and the complexity of each matrix-vector multiplication is O(rN); S2.3 Perform projection gradient ascent iteration on the continuous box constraint domain: Each iteration ascends along the gradient direction of the objective function, and then the iteration point is projected back to the interval [-1,1] through element-wise clipping operation; S2.4 When the number of iterations reaches the preset value T2 or the change between two adjacent iterations is less than the convergence threshold, stop the iteration. Take the sign function of each component of the final continuous solution to get +1 or -1, which is used as the binary phase configuration vector output of the reconfigurable smart metasurface.

[0016] Preferably, the gradient calculation of the factor matrix U in S1 is implemented using vectorization, and matrix multiplication is performed sequentially from right to left. The computational complexity of each iteration is O(SrN), where S is the number of measurements, r is the target rank, and N is the number of reflective elements.

[0017] Preferably, the weighted sample matrix is ​​constructed by appropriately weighting the phase configuration vectors of each measurement, calculating the outer product, and summing them, so that the principal feature direction of the matrix approximates the principal feature direction of the true coefficient matrix M.

[0018] Preferably, in the projection gradient ascent iteration of S2, the gradient of the objective function is calculated based on the estimated matrix and estimated linear coefficient vector output by S1.

[0019] Preferably, the reconfigurable smart metasurface-assisted wireless communication system consists of a single-antenna transmitter, an N-ary reconfigurable smart metasurface, and a single-antenna receiver. The transmitted signal reaches the receiver via a direct channel and a reconfigurable smart metasurface reflection channel. The receiver measures the received signal strength and feeds it back to the controller for phase optimization.

[0020] Preferably, the phase of the reflective element is configured as binary, corresponding to phase 0 or π, and each component of the phase vector x is +1 or -1.

[0021] Preferably, the target rank r is determined to be 2 based on the physical characteristics of the channel structure, in order to match the inherent rank of the coefficient matrix M.

[0022] Preferably, the number of gradient descent iterations T1 for S1 and the number of projection gradient ascent iterations T2 for S2 are preset according to the computational resources and convergence accuracy requirements.

[0023] The present invention further protects a computer device, the computer device including a processor and a memory, the memory storing at least one instruction, at least one program, code set or instruction set, the instruction, program, code set or instruction set being loaded and executed by the processor to implement the above-mentioned reconfigurable intelligent metasurface blind beamforming method based on decomposed spectral gradient descent.

[0024] The present invention further provides a computer-readable storage medium storing at least one instruction, at least one program, code set, or instruction set, wherein the instruction, program, code set, or instruction set is loaded and executed by a processor to implement the above-described reconfigurable intelligent metasurface blind beamforming method based on decomposed spectral gradient descent.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) Superior performance: FSGD achieves an SNR of 21.48 dB, the highest among all blind beamforming methods, reaching 99.3% of the perfect CSI performance (21.63 dB). It is 0.51 dB higher than BORN, 0.92 dB higher than GCSM, and 5.73 dB higher than RMS. This is due to the fact that this invention fully exploits the intrinsic structure of the channel matrix by utilizing low-rank matrix decomposition.

[0026] (2) Higher stability: The standard deviation of FSGD is only 0.61 dB, which is comparable to 0.64 dB of perfect CSI and 83.1% lower than BORN's 3.60 dB. This is due to the deterministic spectral initialization strategy and the implicit regularization effect of the decomposition framework, which eliminates the variance caused by random initialization and constraint processing.

[0027] (3) Better scalability: As N increases from 64 to 200, FSGD consistently maintains a difference of no more than 0.3 dB from the perfect CSI, while BORN and GCSM show differences of 1.06 dB and 1.37 dB, respectively, when N=200. This is due to the fact that the sample complexity of O(rNlogN) only grows nearly linearly with N when r is fixed.

[0028] (4) Complete theoretical guarantee: This invention establishes a strict sample complexity of O(rNlogN), linear convergence rate, and approximation guarantee for FSGD, providing reliable theoretical support for the algorithm's performance. Existing voting-based methods and data-driven methods cannot provide such a complete theoretical analysis.

[0029] In summary, this invention combines spectral initialization and continuous relaxation rounding strategies to significantly improve computational efficiency and performance stability while ensuring near-optimal performance. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings involved in the embodiments are now briefly described. Obviously, the drawings in the following description are merely illustrative of some embodiments of the present invention. For those skilled in the art, other forms of drawings can be constructed based on these drawings without creative effort.

[0031] Figure 1This is an overall flowchart of the reconfigurable intelligent metasurface blind beamforming method based on decomposed spectral gradient descent proposed in this invention. Figure 2 This is a flowchart of the decomposition gradient descent stage proposed in Embodiment 1 of the present invention; Figure 3 This is a flowchart of the spectral relaxation and rounding stage proposed in Embodiment 1 of the present invention; Figure 4 This is a diagram showing the singular value distribution of matrix M proposed in Embodiment 2 of the present invention; Figure 5 This is a comparison chart of SNR and standard deviation for different configurations in the ablation experiment proposed in Example 2 of the present invention; Figure 6 This is a comparison chart of SNR and standard deviation for different blind beamforming methods in Embodiment 2 of the present invention; Figure 7 The above are Pareto front plots of SNR versus running time for each method proposed in Embodiment 2 of this invention. Figure 8 The above are the SNR performance graphs of the methods at different RIS scales proposed in Embodiment 2 of the present invention. Figure 9 This is the two-stage convergence behavior curve of FSGD proposed in Embodiment 2 of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] This invention proposes a reconfigurable smart metasurface blind beamforming method based on decomposed spectral gradient descent, which decomposes the coefficient matrix M into M=UU T (in (where r is the target rank), transforming the parameter space from O(N) 2 The computational complexity is reduced to O(rN), automatically satisfying positive semidefinite constraints and low-rank constraints. By combining spectral initialization and continuous relaxation rounding strategies, computational efficiency and performance stability are significantly improved while maintaining near-optimal performance.

[0034] The key point protected by this invention is: Key Point 1: Matrix Decomposition Strategy. Decompose the N×N coefficient matrix M into U0... Form, in which This decomposition expands the parameter space from O(N) to O(N). 2The computational complexity is reduced to O(rN), while automatically applying positive semidefinite and low-rank constraints, eliminating the need for additional constraint processing. Existing techniques (such as BORN) directly operate on N×N matrices, resulting in a parameter space of O(N). 2 This invention reduces the number of parameters by about 50 times (when N=100, r=2) through decomposition.

[0035] Key Point Two: Two-Stage Spectral Initialization. Stage One uses the principal eigenvectors of the weighted sample matrix to construct the initialization factor matrix U0; Stage Two uses the largest eigenvector of the estimated matrix to construct continuous initialization points. Both stages utilize spectral information to provide deterministic, informative starting points, rather than random initialization. Existing voting methods lack the concept of initialization; BORN does not employ a spectral initialization strategy.

[0036] Key Point 3: Phase Optimization Combining Continuous Relaxation and Sign Rounding. The NP-hard discrete optimization problem is relaxed into an optimization over a continuous domain. This is achieved through progressive optimization via projected gradient ascent, culminating in a discrete solution obtained by sign function rounding. Existing methods (such as BORN) use geometric optimization for phase recovery, introducing additional variance; the rounding strategy of this invention reduces the standard deviation from 3.60 dB to 0.61 dB.

[0037] The following description, in conjunction with the accompanying drawings and specific examples, illustrates a reconfigurable intelligent metasurface blind beamforming method based on decomposed spectral gradient descent proposed in this invention.

[0038] Example 1: This example proposes a blind beamforming method for reconfigurable intelligent surface (RIS) based on factorized spectral gradient descent (FSGD). This method optimizes the phase configuration of each reflective element of the RIS using only the received signal strength (RSS) measurement under unknown channel state information (CSI) conditions, thereby maximizing the signal-to-noise ratio (SNR) at the receiver.

[0039] The RIS-assisted wireless communication system described in this example consists of three parts: a single-antenna transmitter (TX), an N-ary reconfigurable smart metasurface (RIS), and a single-antenna receiver (RX). The transmitter transmits a signal at power P, which reaches the receiver via a direct channel and a RIS reflection channel. The RIS is composed of N passive reflective elements, each with a phase that can be configured to 0 or pi, corresponding to +1 or -1 in the binary phase vector x. The receiver measures the RSS and feeds it back to the controller for phase optimization. The receiver's SNR can be represented as a quadratic model of the RIS phase vector x: SNR(x) = x T Mx+w T x+c Where M is an N-by-N quadratic coefficient matrix, w is an N-dimensional linear coefficient vector, and c is a constant term.

[0040] Due to the physical characteristics of the channel structure, matrix M naturally possesses positive semi-definiteness and its rank does not exceed 2. This low-rank structure is the theoretical basis for the decomposition method of this invention.

[0041] Based on the aforementioned quadratic model, this invention decomposes the blind beamforming problem into two stages: model fitting and phase optimization. The overall process of the FSGD algorithm is as follows: Figure 1 As shown.

[0042] Phase 1: Decompose gradient descent for model fitting The goal of Phase 1 is to recover the parameters M, w, and c of the quadratic model from S RSS measurement data. The core innovation of this invention lies in not directly optimizing the N x N matrix M, but rather decomposing it into M = UU T Where U is an N-times-r factor matrix, and r is the target rank, which is set to r=2 in the RIS system. This decomposition reduces the number of parameters to be optimized from N squared to rN, and the number of parameters is reduced by about 50 times when N=100 and r=2. More importantly, this decomposition automatically satisfies positive semidefinite constraints and low-rank constraints without the need to introduce additional constraint processing mechanisms, which is the key difference between this invention and existing technologies.

[0043] The factor matrix U is initialized using a spectral initialization method. First, a weighted sample matrix is ​​constructed using all S measurements. Then, eigenvalue decomposition is performed on this matrix to extract the top r largest eigenvalues ​​and their corresponding eigenvectors, which are used to construct the initial factor matrix U0. The linear coefficient vector is initialized to zero, and the constant term is initialized to the arithmetic mean of all RSS measurements. Spectral initialization utilizes the second-order statistical information of the measurement data, providing a starting point close to the true solution for subsequent non-convex optimization, significantly accelerating the convergence process and avoiding getting trapped in undesirable local minima.

[0044] In the iterative optimization process, the loss function is defined as the mean squared error between the predicted RSS values ​​and the measured RSS values ​​for all samples. The gradients of the loss function are calculated for the factor matrix U, the linear coefficient vector w, and the constant term c, respectively, and then gradient descent updates are performed with a fixed learning rate. The gradient calculation for U is vectorized, performing matrix multiplication sequentially from right to left. The computational complexity of each iteration is O(SrN), which is significantly lower than the O(Sn) complexity required for directly multiplying an N matrix. 2 After T1 iterations, the estimated matrix and the estimated linear coefficient vector are output. The detailed process of Stage 1 is as follows: Figure 2 As shown.

[0045] Phase 2: Spectral relaxation and rounding for phase optimization The goal of Phase Two is to find the optimal binary phase configuration that maximizes the objective function, based on the model parameters estimated in Phase One. This problem is essentially an NP-hard quadratic integer programming problem, and this invention employs a strategy of continuous relaxation combined with sign rounding to solve it efficiently.

[0046] First, the discrete constraints are relaxed to continuous box constraints, allowing each component of the phase configuration vector to take any real value within the interval [-1, 1]. In the relaxation region, the spectrum is initialized using the largest eigenvector of the stage-one estimation matrix, constructing an initial point x0. Since the estimation matrix has a low-rank decomposition form, the largest eigenvector can be efficiently calculated using a power iteration method, with the complexity of each matrix-vector multiplication being only O(rN). This initialization preserves information about the principal eigendirections of the estimation matrix, providing a physically meaningful deterministic starting point for subsequent optimization.

[0047] Subsequently, a projection gradient ascent iteration is performed on the relaxation region. Each iteration first ascends along the gradient direction of the objective function, then projects the iteration points back into the feasible region through an element-wise pruning operation, ensuring that each component remains within the range [-1, 1]. Iteration stops when the number of iterations reaches a preset value T2 or the change between two adjacent iterations is less than the convergence threshold. Finally, the continuous solution is mapped to a discrete solution using a sign function; that is, each component of the continuous solution is signed to obtain +1 or -1, which is then output as the final RIS phase configuration vector. The detailed process of Phase Two is as follows... Figure 3 As shown.

[0048] Example 2: Based on Embodiment 1, but with a difference, in order to verify the good effect of the FSGD method proposed in this invention, this embodiment designed four sets of comparative experiments. The specific experimental data are used to demonstrate the performance, stability and scalability of this invention and the improvement and advantages of the prior art. The specific content is as follows.

[0049] I. Low-rank hypothesis verification experiment This experiment verifies the low-rank structure of matrix M. For example... Figure 4 As shown, singular values ​​are taken from matrix M. The first two singular values ​​dominate 100% of the total energy, and the ratio of the first to the third singular value exceeds 10 to the power of 12, indicating that M is numerically a rank-2 matrix. This result verifies the rationality of the low-rank assumption of this invention: since M = (P / σ) 2 V T V, where VR is a 2xN dimensional space, and the rank of matrix M does not exceed 2. This low-rank structure allows the present invention to reduce the parameter space from O(N) through hierarchical layering of M = UU^T. 2 It becomes possible to reduce it to O(rN).

[0050] II. Ablation Experiment To evaluate the contributions of each component of the FSGD algorithm, this experiment designed four configurations for comparison. The baseline method uses traditional matrix acquisition and geometric optimization, employing the existing BORN method, with an SNR of 20.97 dB and a standard deviation of 3.60 dB. Replacing only Stage 1 with the gradient descent method of this invention significantly improved the SNR to 21.52 dB, and the standard deviation decreased dramatically from 3.60 dB to a maximum of 0.84 dB, a reduction of 76.7%, indicating that gradient descent is the main contributor to the performance improvement. Replacing only Stage 2 with the spectral shrinkage rounding method of the relevant invention resulted in an SNR of 20.53 dB, lower than the baseline, with a standard deviation of 3.53 dB, comparable to the baseline, indicating that the effectiveness of Stage 2 depends on the high-quality model estimation provided by Stage 1. The complete FSGD algorithm, employing both stages simultaneously, achieved an SNR of 21.48 dB and a standard deviation of 0.61 dB, representing 99.3% of the perfect CSI performance of 21.63 dB, with a standard deviation comparable to the perfect CSI of 0.64 dB. Compared to baseline, FSGD improved SNR by 0.51 dB and reduced the standard deviation by 83.1%. Ablation experimental results are as follows... Figure 5 As shown above, the data demonstrates that both stages of the present invention have good effects and are indispensable.

[0051] III. Method Comparison Experiment This experiment comprehensively compares FSGD with five existing blind beamforming methods. The experimental results are as follows: Figure 6 and Figure 7As shown. Regarding SNR, the proposed FSGD achieves 21.48 dB, the highest among all blind beamforming methods, surpassing perfect CSI by 0.15 dB. Specifically, FSGD improves upon BORN's 20.97 dB by 0.51 dB, GCSM's 20.56 dB by 0.92 dB, and RMS's 15.75 dB by 5.73 dB. The conventional methods RFocus and CSM have SNRs of 4.59 dB and 7.33 dB respectively, confirming their inability to utilize the second structure of received SNR. In terms of stability, FSGD has a standard deviation of 0.61 dB, comparable to perfect CSI's 0.64 dB, representing an 83.1% reduction compared to BORN's 3.60 dB and an 89.2% reduction compared to RFocus's 5.65 dB. In terms of computational efficiency, FSGD runs in 795.3 milliseconds, which is 1.89 times faster than BORN's 1500.8 milliseconds. This is thanks to the reduction in per-iteration complexity from O(SN) after this reorganization. 2 The efficiency of SNR is reduced to O(SrN). As shown in Figure 7, in the trade-off between SNR and operation, FSGD is positioned at the Pato front, achieving both high performance and high efficiency.

[0052] IV. Scalability Experiment This experiment evaluates the performance of each method on different RIS scales under a fixed measurement budget. The experimental results are as follows: Figure 8 As shown, when N=64, FSGD reaches 17.96 dB, almost indistinguishable from the perfect CSI of 17.97 dB. When N=100, FSGD reaches 21.48 dB, while the perfect CSI is 21.63 dB, a difference of 0.15 dB. When N=150, FSGD reaches 24.87 dB, while the perfect CSI is 25.10 dB, a gap of 0.23 dB. When N=200, FSGD reaches 27.20 dB, only 0.29 dB below the upper limit of the perfect CSI of 27.49 dB, while BORN only reaches 26.43 dB at N=200, widening the gap with the perfect CSI to 1.06 dB, and GCSM reaches 26.12 dB, widening the gap to 1.37 dB. These results demonstrate that as the scale of RIS increases as described above, the advantage of FSGD over existing methods becomes increasingly apparent, exhibiting strong scalability in large-scale RIS deployments.

[0053] V. Convergence Rate Verification Experiment The convergence behavior of the two-phase FSGD in this experiment is shown in the following results. Figure 9 As shown. Figure 9(a) shows the change of the Stage 1 loss function with the number of iterations, exhibiting a linear decreasing trend on a semi-logarithmic scale. It recovers more than an order of magnitude within the first 50 iterations, and then undergoes gradual refinement, consistent with the linear relationship established in this invention. Figure 9 (b) shows the change of the objective function value in stage two with the number of iterations. Starting from the initial point of the spectrum, the objective function rises rapidly within about 14 iterations until it approaches the peak and tends to stabilize, indicating that the initial spectrum provides a high-quality initial point and verifies the approximation guarantee established by the present invention.

[0054] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A reconfigurable intelligent metasurface blind beamforming method based on decomposed spectral gradient descent, characterized in that, Includes the following steps: S1. Decompose gradient descent for model fitting: S1.1 Obtain the S received signal intensity measurements of N reflective elements in the reconfigurable smart metasurface; S1.2 Construct a quadratic model of the receiver's signal-to-noise ratio with respect to the phase vector x of the reflecting element: SNR(x)=x T Mx+w T x+c Where M is an N×N positive semidefinite coefficient matrix with a rank not exceeding 2, w is an N-dimensional linear coefficient vector, and c is a constant term; the superscript T indicates the transpose operation; S1.3 Decompose the coefficient matrix M into: M=UU T Where U is an N×r factor matrix, and r is the target rank with a value of 2; S1.4 Constructing the initial factor matrix U0 using the spectral initialization method: Construct a weighted sample matrix using all S measurement data, perform eigenvalue decomposition on the weighted sample matrix, extract the first r largest eigenvalues ​​and corresponding eigenvectors to construct U0; initialize the linear coefficient vector w to a zero vector, and initialize the constant term c to the arithmetic mean of all received signal strength measurements. S1.5 Define the loss function as the mean square error between the predicted received signal strength value and the measured received signal strength value on all samples. Calculate the gradient of the loss function with respect to the factor matrix U, the linear coefficient vector w, and the constant term c. Perform gradient descent updates with a fixed learning rate. After T1 iterations, output the estimated matrix and the estimated linear coefficient vector. S2. Phase optimization is performed using spectral relaxation and rounding: S2.1 Relax the discrete constraint of the phase vector x of the reflecting element into a continuous box constraint, that is, each component takes a value in the interval [-1,1]. S2.

2. Use the largest eigenvector of the estimated matrix output in S1 to initialize the spectrum and construct an initial continuous solution x0; wherein the largest eigenvector is calculated by the power iteration method, and the complexity of each matrix-vector multiplication is O(rN); S2.3 Perform projection gradient ascent iteration on the continuous box constraint domain: Each iteration ascends along the gradient direction of the objective function, and then the iteration point is projected back to the interval [-1,1] through element-wise clipping operation; S2.4 When the number of iterations reaches the preset value T2 or the change between two adjacent iterations is less than the convergence threshold, stop the iteration. Take the sign function of each component of the final continuous solution to get +1 or -1, which is used as the binary phase configuration vector output of the reconfigurable smart metasurface.

2. The method according to claim 1, characterized in that, The gradient calculation of the factor matrix U in S1 is implemented using vectorization. Matrix multiplication is performed sequentially from right to left, and the computational complexity of each iteration is O(SrN), where S is the number of measurements, r is the target rank, and N is the number of reflective elements.

3. The method according to claim 1, characterized in that, The weighted sample matrix is ​​constructed by appropriately weighting the phase configuration vectors of each measurement, calculating the outer product, and summing them, so that the principal feature direction of the matrix approximates the principal feature direction of the true coefficient matrix M.

4. The method according to claim 1, characterized in that, In the projection gradient ascent iteration of S2, the gradient of the objective function is calculated based on the estimated matrix and estimated linear coefficient vector output by S1.

5. The method according to claim 1, characterized in that, The reconfigurable smart metasurface-assisted wireless communication system consists of a single-antenna transmitter, an N-ary reconfigurable smart metasurface, and a single-antenna receiver. The transmitted signal reaches the receiver via a direct channel and a reconfigurable smart metasurface reflection channel. The receiver measures the received signal strength and feeds it back to the controller for phase optimization.

6. The method according to claim 1, characterized in that, The phase configuration of the reflective element is binary, corresponding to phase 0 or π, and each component of the phase vector x is +1 or -1.

7. The method according to claim 1, characterized in that, The target rank r is determined to be 2 based on the physical characteristics of the channel structure, and is matched with the inherent rank of the coefficient matrix M.

8. The method according to claim 1, characterized in that, The number of gradient descent iterations T1 for S1 and the number of projection gradient ascent iterations T2 for S2 are preset according to the computational resources and convergence accuracy requirements.

9. A computer device, characterized in that, The computer device includes a processor and a memory, wherein the memory stores at least one instruction, at least one program, code set, or instruction set, and the instruction, program, code set, or instruction set is loaded and executed by the processor to implement the reconfigurable intelligent metasurface blind beamforming method based on decomposed spectral gradient descent as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one instruction, at least one program, code set, or instruction set, which is loaded and executed by a processor to implement the reconfigurable smart metasurface blind beamforming method based on decomposed spectral gradient descent as described in any one of claims 1-8.

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