Metasurface DOA estimation method based on denoising CNN and MUSIC

Abstract

The invention provides a metasurface DOA estimation method based on a denoising CNN and MUSIC, and the method comprises the following steps: calculating a covariance matrix of a noisy incident signal as training data through simulation according to an established programmable metasurface receiving signal model, calculating a covariance matrix of a non-noisy incident signal as label data, and constructing a data set; constructing a denoising CNN network for a covariance matrix denoising task, and training the network by using the data set; calculating a covariance matrix estimated value of the noisy incident signal; inputting a noisy covariance matrix estimation value into the trained denoising CNN network, and outputting to obtain a denoised covariance matrix estimation value; and calculating a MUSIC spatial spectrum based on the denoised covariance matrix estimation value, and obtaining a direction-of-arrival estimation result through spectrum peak search. The technical problem that the expected estimation effect cannot be achieved under the conditions of low signal-to-noise ratio and small snapshot number in the prior art is solved.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a metasurface DOA estimation method based on denoising CNN and MUSIC. Background Technology

[0002] Direction of arrival (DOA) estimation is a key technology in array signal processing, with wide applications in numerous scenarios such as wireless communication, radar detection, sonar systems, and astronomical observation. Traditional DOA estimation algorithms, such as Capon, Multiple Signal Classification (MUSIC), and Rotation Invariant Subspace (ESPRIT), mainly rely on the statistical characteristics of the received signals from the antenna array or the principle of subspace decomposition to achieve angle estimation. These methods perform well under ideal or high signal-to-noise ratio conditions, forming the theoretical foundation for the long-term development of this field.

[0003] In existing technologies, algorithms based on compressed sensing theory have been developed to address DOA estimation under conditions of limited snapshot numbers and low signal-to-noise ratio (SNR). These methods leverage the sparsity of signals in the spatial domain to achieve a certain level of DOA estimation with fewer snapshots and lower SNR. Typical representative algorithms include Orthogonal Matching Pursuit (OMP), Singular Value Decomposition based on the L1 norm (L1-SVD), Alternating Direction Multiplier Method (ADMM), and Sparse Bayesian Learning (SBL).

[0004] However, due to external noise, these algorithms face challenges in obtaining accurate DOA estimation results when the SNR decreases further. To address this issue, a novel approach combining data-driven and model-driven strategies is proposed to improve the accuracy of DOA estimation and exhibit stronger robustness in complex electromagnetic environments. Summary of the Invention

[0005] The purpose of this invention is to provide a metasurface DOA estimation method based on denoised CNN and MUSIC, which solves the technical problem that existing methods often fail to achieve the expected estimation results under conditions of low signal-to-noise ratio (SNR) and small snapshot number.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: This invention provides a metasurface DOA estimation method based on denoised CNN and MUSIC, comprising the following steps: Dataset Construction: Based on the established programmable metasurface signal receiving model, the covariance matrix of the noisy incident signal is calculated by simulation as training data, and the covariance matrix of the noisy incident signal is calculated as label data, and the dataset is constructed accordingly. Network Construction and Training: Construct a denoising CNN network for the covariance matrix denoising task, and train the network using the dataset. Covariance matrix estimation: Calculate the estimated value of the covariance matrix of the noisy incident signal; Covariance matrix denoising: The noisy covariance matrix estimate is input into the trained denoising CNN network, and the denoised covariance matrix estimate is output. DOA estimation: Based on the estimated value of the denoised covariance matrix, a MUSIC spatial spectrum is constructed, and the direction of arrival estimation result is obtained by searching the spectral peaks.

[0007] Furthermore, the programmable metasurface signal receiving model is: having M Each unit, after N Secondary encoding, received from K A narrowband far-field source L The received signal matrix for each snapshot signal is represented as follows:

[0008] in, Represents the encoding matrix, Represents the guidance matrix. Represents the input signal amplitude matrix. This represents the noise matrix.

[0009] Furthermore, the method for constructing the dataset includes the following sub-steps: For the single-target case, the range of the sine value of the incident angle is uniformly divided into... P For each grid, multiple noisy covariance matrix samples and their corresponding noiseless covariance matrix labels are generated under different signal-to-noise ratio conditions. For multi-objective scenarios, the aforementioned P The grids are combined to obtain multiple angle combinations. For each angle combination, multiple noisy covariance matrix samples and their corresponding noiseless covariance matrix labels are generated under different signal-to-noise ratio conditions. Data samples and labels from single-objective and multi-objective datasets are integrated to form a hybrid dataset, and all samples and labels are normalized.

[0010] Furthermore, the noisy covariance matrix estimate is calculated according to the following formula:

[0011] in, This represents the received signal matrix under noise-free conditions. These represent the estimation of the ideal signal covariance matrix and the estimation of the noise covariance matrix, respectively. This indicates the conjugate transpose.

[0012] Furthermore, the denoising CNN network learns through residual learning. Mapping relationship between f .

[0013] Furthermore, the denoising CNN network includes: Input layer: The real and imaginary parts of the noisy covariance matrix estimate are used as dual-channel inputs; Feature extraction layer: includes multiple concatenated modules containing convolutional layers, batch normalization layers, and activation functions; Output layer: A convolutional layer with 2 output channels, corresponding to the real and imaginary parts of the output matrix; Residual connection: The network output is used as an estimate of the noise covariance matrix, and the preliminary denoising result is obtained by subtracting this estimate from the input; Hermitian layer: Receives the preliminary denoising result and, through calculation, outputs the final denoised covariance matrix estimate that satisfies the Hermitian property.

[0014] Furthermore, the DOA estimation specifically includes: The range of the sine value of the incident angle is evenly divided into... P One search grid; The denoised covariance matrix estimate is subjected to eigenvalue decomposition, and based on the final... N K Each feature vector forms a noise subspace; The spatial spectrum value corresponding to each search grid is calculated based on the MUSIC algorithm; DOA estimation results were obtained through spectral peak search.

[0015] Compared with the prior art, the present invention has at least the following beneficial effects: This invention proposes a DnCNN-MUSIC method that combines a denoising convolutional neural network (DnCNN) with a multiple signal classification (MUSIC) algorithm. By combining data-driven deep learning with model-driven signal processing, it effectively improves DOA estimation performance. Specifically, this method uses a denoising DnCNN to denoise the covariance matrix and then employs the MUSIC algorithm for direction of arrival estimation. Simulation results show that under conditions of low SNR and small snapshot number, this method outperforms existing techniques in terms of DOA estimation accuracy. Furthermore, this method is applicable to both single-target and dual-target scenarios, exhibits advantages in resolving targets with small angular intervals, and maintains low computational complexity, achieving an effective balance between estimation accuracy and computational efficiency. Attached Figure Description

[0016] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 This is a flowchart of the metasurface DOA estimation method provided in this embodiment; Figure 2 This is a schematic diagram of the programmable metasurface signal receiving model provided in this embodiment; Figure 3 The improved DnCNN-MUSIC workflow diagram provided in this embodiment; Figure 4 This is a schematic diagram of the improved DnCNN network structure provided in this embodiment; Figure 5 This embodiment presents a comparison chart of the RMSE of DOA estimation for a single target using different algorithms on different grids. Figure 6 A comparison chart of the RMSE of DOA estimation for a single target under different SNR conditions provided in this embodiment; Figure 7 This is a comparison chart of the RMSE of DOA estimation for a single target by different algorithms provided in this embodiment under different snapshot numbers; Figure 8 shows the spatial spectra of the dual-target MUSIC obtained with and without the DnCNN method in this embodiment ((a) SNR=-15 dB; (b) SNR=-5 dB). Figure 9 shows a comparison of the covariance matrices provided in this embodiment (SNR=-15 dB): (a) Input covariance matrix; (b) Noise covariance matrix; (c) Denoising covariance matrix; Figure 10 shows a comparison of the DOA estimation results of different algorithms provided in this embodiment for bitargets with 8 grid intervals ((a) ADMM algorithm; (b) MUSIC algorithm; (c) DnCNN-MUSIC algorithm). Figure 11 shows a comparison of the DOA estimation errors of different algorithms provided in this embodiment for two targets with 8 grid intervals ((a) ADMM algorithm; (b) MUSIC algorithm; (c) DnCNN-MUSIC algorithm). Figure 12 Comparison of RMSE of DOA estimation for bitargets with different grid spacing using different algorithms provided in this embodiment; Figure 13This is a comparison chart of the RMSE of DOA estimation for two targets under different SNR conditions provided in this embodiment using different algorithms. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0019] This embodiment provides a metasurface DOA estimation method based on denoised CNN and MUSIC. Please refer to... Figure 1 As shown, the method includes the following steps: First, a dataset is constructed. A noisy covariance matrix is ​​generated by simulation using a programmable metasurface signal receiving model as training data, and a noiseless covariance matrix is ​​used as label data. Next, we construct and train a CNN network specifically for covariance matrix denoising; Next, calculate the estimate of the noisy covariance matrix (this step can also be a second step). Then, the estimated value is input into the trained CNN network for noise reduction. Finally, the spatial spectrum is constructed based on the MUSIC algorithm using the denoised covariance matrix estimation, and DOA estimation is achieved through spectral peak search.

[0020] This method introduces a denoising CNN to preprocess the covariance matrix, effectively suppressing the impact of noise on the performance of the MUSIC algorithm. In particular, it significantly improves the DOA estimation accuracy under conditions of low signal-to-noise ratio and limited snapshot number. By combining the adaptive denoising capability of deep learning with the MUSIC algorithm, it realizes a hybrid-driven DOA estimation system that can maintain high estimation performance in complex noise environments.

[0021] This invention is specifically implemented through the following methods: I. Signal Model Establishment like Figure 2 As shown, this embodiment performs DOA estimation based on a programmable metasurface received signal model, wherein the programmable metasurface has M One unit, the horn antenna is located at [ r x , r z [Location]. K A narrowband far-field source radiates a signal into the metasurface from an unknown direction. The metasurface phase-modulates the signal and reflects it to a horn antenna for reception. For the first...n In the second modulation (i.e., coding) stage, time... t The received signal can be represented as:

[0022] In the formula, n = 1,2,…, N , N Indicates the number of encodings. Indicates in t Time of the first k The complex amplitude of the received signal Denotes the encoding matrix, where Indicates the ( m,n ) elements. The wavelength of the incident signal. j Represents the imaginary unit. Indicates the first m A metasurface element in x Position on the axis d Indicates the spacing between array elements. Indicates the first k An incident signal The sine value, This represents additive white Gaussian noise.

[0023] After N Encode and receive L After capturing a snapshot, the received signal matrix can be represented as: (2) In the formula Represents the encoding matrix, its ( ) m,n ) elements are , Represents the guidance matrix. Indicates the guide vector. , The input signal amplitude matrix. , , Represents the noise matrix. Represents the received signal matrix. and These are the transpose and the conjugate transpose, respectively.

[0024] II. Improved workflow of the DnCNN-MUSIC algorithm like Figure 3As shown, the workflow of the improved DnCNN-MUSIC algorithm in this embodiment includes: First, estimating the covariance matrix using the signal received by the horn antenna. Then, denoising the covariance matrix using the improved DnCNN. Finally, processing the denoised covariance matrix using the MUSIC algorithm to obtain the spatial spectrum, thereby obtaining the DOA estimation result through spectral peak search.

[0025] 2.1 Covariance Matrix Estimation The covariance matrix estimate derived from the received signal can be expressed as: (3) In the formula,

[0026] in, This represents the received signal matrix under noise-free conditions. These represent the estimation of the ideal signal covariance matrix and the estimation of the noise covariance matrix, respectively. This indicates the conjugate transpose.

[0027] When the number of quick photos L As the value approaches infinity, the covariance matrix of the received signal can be expressed as: (4) In the formula, and These represent the signal covariance matrix and the noise covariance matrix, respectively. In fact, the number of snapshots... L It is usually finite. Therefore, the coupling term of signal and noise ( and It cannot be ignored.

[0028] 2.2 Covariance Matrix Denoising When the number of quick shots L When the number of snapshots is large, traditional algorithms (such as MUSIC) can achieve reliable DOA estimation performance even under low SNR conditions. However, in practical applications, the performance of traditional algorithms degrades significantly due to the limited number of snapshots. To address this issue, deep learning methods can be employed to... Remove from To obtain .

[0029] The deep learning network used in this invention is an improved version of DnCNN, specifically designed for covariance matrix denoising. The processing flow for covariance matrix denoising is as follows: Figure 4As shown, firstly, the covariance matrix is ​​divided into real and imaginary parts, and these are used as dual-channel inputs to Conv + ReLU, where Conv represents a convolutional layer and ReLU is the activation function. After processing the input data through convolution, the number of channels increases from 2 to 64. Then, the output of Conv + ReLU is fed into 18 Conv + BN + ReLU layers to extract deep features, where BN represents a batch normalization layer. The input and output channels of these convolutions are both 64. Finally, the output of the last Conv + BN + ReLU layer is fed into a single convolutional layer, reducing the number of channels to 2. Then, the real and imaginary parts of the output of the last convolutional layer are summed to obtain an approximate value. Finally, and The difference between them is input into the Hermitian layer to obtain... Hermitian layers force their inputs to satisfy the Hermitian property through specific computational methods. Let the input of a Hermitian layer be... X The output is H The calculation for this layer can be represented as: (5) In this network, all convolutional layers have a kernel size of 3×3, a stride of 1, and zero-padding after each convolution operation. The network learns through residual learning. Mapping relationship between f .here, f It can be represented as: (6) In the formula, Represents network parameters, W Conv and b Conv These represent the weights and biases of the convolutional layer, respectively. and These represent the scaling and offset parameters of the BN layer, respectively.

[0030] 2.3 Spatial Spectrum Estimation After denoising the covariance matrix using a network, the resulting matrix is ​​denoted as... Based on this, the DOA estimate can be obtained using the MUSIC algorithm. First, the range of sine values ​​is defined as follows: 1,1] (corresponding to the spatial angle range [ 90 ° 90 ° ]) evenly divided into P One grid. Then, for Perform eigenvalue decomposition, based on the final N K The eigenvectors form the noise subspace. Then, spatial spectrum estimation is performed, expressed as: (7) III. Simulation Experiment 3.1 Simulation conditions, parameter settings, and network training The simulation platform in this embodiment is a 64-bit Windows 11 system, equipped with a 3.7GHz 12th generation Intel i5-12600KF processor and an NVIDIA GeForce RTX 4060 Ti graphics card. The simulation software is MATLAB 2024a and Python 3.9 + PyTorch 2.6.0. The simulation conditions are set as follows: a system containing... M = 21-element metasurface, element spacing d = 0.01 meters, number of encodings N = 16, number of snapshots L = 5, the receiving horn antenna position is [0, 0.148]. The following method is used to construct the dataset for training the DnCNN network: 1) Define the range of sine values ​​[ [1,1] are evenly divided into P = 121 grids.

[0031] 2) For the single-target case, for each grid cell, 12 signal covariance matrices are generated (10 for training and 2 for validation), with SNR values ​​of [missing information]. 15 dB 10 dB 5 dB and 0 dB. This creates a training dataset with 4840 samples and a validation dataset with 968 samples.

[0032] 3) For the dual-objective case, 7260 angle distributions are obtained by combining the 121 grids in pairs. For each angle combination and each SNR set in 2), 12 data samples are generated, thus forming a training dataset containing 290,400 samples and a validation dataset containing 58,080 samples.

[0033] 4) The single-objective and dual-objective datasets are integrated to generate a mixed training dataset containing a total of 295,240 samples and a mixed validation dataset containing 59,048 samples. For each sample, a corresponding ideal signal covariance matrix is ​​generated as a label. Subsequently, each sample and label are normalized using the Frobenius norm of the label. The normalized training dataset and labels are then input into the network for training.

[0034] For each sample, a corresponding ideal signal covariance matrix will be generated. R 0 is used as the label. Subsequently, each sample and label will be processed according to the label... R The Frobenius norm of 0 is used for normalization. The normalized training dataset and labels are then input into the network for training.

[0035] Using NMSE as the loss function, its expression is: (8) in This represents the total number of samples in the training dataset. This represents the Frobenius norm of the matrix.

[0036] In network training, Adam was chosen as the optimizer. The number of training epochs was set to 300, the batch size to 121, the initial learning rate to 0.002, and a learning rate scheduler was used (the learning rate was reduced to 0.9 times its previous value every 10 epochs).

[0037] A series of simulation experiments were conducted to verify the performance of the proposed DnCNN-MUSIC algorithm and compare it with the MUSIC and ADMM algorithms. The root mean square error (RMSE) was used to evaluate the performance of different algorithms, and its expression is: (9) In the formula, and They represent the first k The estimated angle of arrival and the actual angle of arrival for each signal.

[0038] 3.2 Single-objective simulation Figure 5 This demonstrates the RMSE of DOA estimation for a single target across different grids. The SNR is set to... At 10 dB, 1000 samples were generated per grid, and the average RMSE of different algorithms was calculated. It is evident that the proposed algorithm achieves an RMSE close to zero across all grids. In contrast, the MUSIC and ADMM algorithms exhibit relatively large RMSEs across multiple grids, indicating that their DOA estimation accuracy is lower than that of the proposed algorithm.

[0039] Figure 6 Three algorithms are demonstrated for DOA estimation RMSE under different SNR values. First, the SNR range is set from... 15 dB change to The step size was 1 dB. Then, 100 Monte Carlo simulations were performed for each SNR and each grid, and the RMSE of the DOA estimate for different algorithms was calculated. As shown in the figure, in the low SNR region, the RMSE of the proposed algorithm is significantly lower than that of the ADMM and MUSIC algorithms, indicating that it has better estimation accuracy. This shows that the DnCNN network can effectively suppress noise interference under low SNR conditions, thereby improving the estimation performance of the MUSIC algorithm. When the SNR exceeds... At 7 dB, the estimation accuracy of the MUSIC algorithm improves significantly, at which point the proposed denoising network's effect becomes less noticeable. It is worth noting that the proposed DnCNN effectively denoises the covariance matrix within the tested SNR range, demonstrating its good generalization ability and capacity to handle continuous variations in SNR conditions not covered during training.

[0040] Figure 7 The algorithm demonstrates the root mean square error (RMSE) of DOA estimation under different snapshot numbers. First, the number of snapshots is set to vary between 3 and 10, with a step size of 1, and the SNR is set to... The algorithm was set to 10 dB, and 100 Monte Carlo simulations were performed at each grid point for each number of snapshots. It can be observed that the ADMM algorithm has the worst estimation accuracy, while the proposed algorithm outperforms the MUSIC algorithm with a smaller number of snapshots. When the number of snapshots exceeds 6, the denoising effect of DnCNN becomes less significant. In this case, the MUSIC algorithm already achieves relatively high estimation accuracy.

[0041] 3.3 Dual-objective simulation exist 15 dB and Figure 8 shows the MUSIC spatial spectra of the two targets obtained with and without DnCNN under two SNR conditions of 5 dB. The target positions are set to the 35th and 80th grids. It can be clearly seen that after the DnCNN denoising of the covariance matrix, the spatial spectrum obtained using the MUSIC algorithm has good DOA estimation accuracy under low SNR conditions. Compared with directly using the MUSIC algorithm, the sidelobes of the spatial spectrum are significantly suppressed. The above results can be interpreted by Figure 9, where SNR = Figures 9 (a-c) show the magnitudes of the input signal covariance matrix, the output covariance matrix after denoising by DNCNN, and the noise-free covariance matrix. It can be seen that the denoised covariance matrix is ​​highly similar to the noise-free covariance matrix, but significantly different from the input covariance matrix.

[0042] Figures 10 and 11 show the results when the SNR is... The DOA estimation results and estimation errors of different algorithms for two targets at 10 dB are presented. The grid variation range for the first target location was set from 1 to 113, and the grid variation range for the second target location was set from 9 to 121. Both varied in step size of 1, maintaining an interval of 8 grids. A total of 113 targets were represented. Simulation results were obtained by performing 1000 Monte Carlo simulations for each target group and averaging the results. By comparing Figures 10 (a-c), the proposed algorithm has higher DOA estimation accuracy in all grids, while the MUSIC and ADMM algorithms are inaccurate in some grids. Observations in Figures 11 (a-c) also show that the proposed algorithm's DOA estimation error in each grid is closer to 0. The MUSIC algorithm has a relatively large estimation error in some grids, while the ADMM algorithm cannot accurately estimate both targets simultaneously.

[0043] Figure 12 The root mean square error (RMSE) of bi-objective DOA estimation using different algorithms under varying grid differences is shown, with SNR being [value missing]. 10dB. First, position the first target at the 61st grid, with the sine of its incident angle being... u 1. The sine of the incident angle of the second target is... Specifically, The values ​​are 1, 2, 3, 4, 5, 7, 10, 15, and 20 grids. Then for each... Perform 2000 Monte Carlo simulations and calculate the RMSE. It can be observed that when... When the number of grid cells is increased from 1 to 5, the RMSE of ADMM and DnCNN-MUSIC decreases significantly, while the MUSIC algorithm... The trend decreases when the number of grids increases from 3 to 7. When the number of grid cells exceeds seven, the RMSE obtained by these three algorithms tends to stabilize. It can also be observed that regardless of the variation in grid differences, the proposed algorithm consistently outperforms the other two.

[0044] Figure 13 The root mean square error of bi-objective DOA estimation using different algorithms under varying SNRs is demonstrated. First, the range of SNR variation is set to... The step size was 1 dB, ranging from 15 dB to 0 dB. Then, 2000 Monte Carlo simulations were performed under each SNR condition, with two grid cells randomly selected as target locations in each simulation. It can be observed that the RMSE of the three algorithms gradually decreases with increasing SNR, while the RMSE of the proposed algorithm is consistently lower than the other two.

[0045] 3.4 Comparison of computational complexity Table 1 compares the computational complexity of different algorithms. 10,000 Monte Carlo simulations were performed on a single target, and the running time of each algorithm was calculated, with the average value obtained. The running time of the proposed algorithm is obtained by adding the time used for denoising with DnCNN to the time of the MUSIC algorithm. It can be seen that the proposed algorithm has lower computational complexity compared to the ADMM algorithm.

[0046] Table 1. Computation time of the three algorithms

[0047] 3.5 Simulation Results This invention proposes a method combining data-driven and model-driven approaches for DOA estimation of programmable metasurfaces. The core of this method lies in utilizing an improved DnCNN to denoise the signal covariance matrix, thereby enhancing the estimation accuracy of the subsequent MUSIC algorithm.

[0048] Simulation results show that the proposed method is applicable to both single-target and dual-target scenarios, and can effectively handle situations with low SNR and a small number of snapshots. Compared with the MUSIC and ADMM algorithms, the proposed algorithm significantly improves the DOA estimation accuracy.

[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for super surface DOA estimation based on denoising CNN and MUSIC, characterized in that, The method comprises the following steps: Dataset construction: according to the established programmable metasurface received signal model, the covariance matrix of the noisy incident signal is calculated by simulation as training data, the covariance matrix of the incident signal without noise is calculated as label data, and a dataset is constructed; Network construction and training: a denoising CNN network for covariance matrix denoising task is constructed, and the network is trained using the dataset; Covariance matrix estimation: calculate the covariance matrix estimate of the noisy incident signal; Covariance matrix denoising: input the noisy covariance matrix estimate into the trained denoising CNN network, and output the denoised covariance matrix estimate; DOA estimation: calculate the MUSIC spatial spectrum based on the denoised covariance matrix estimate, and obtain the DOA estimation result by spectral peak search.

2. The denoising CNN and MUSIC based metasurface DOA estimation method according to claim 1, characterized in that, The programmable metasurface receives a signal model having M units, after N encodings, receives K snapshots of signals from L narrowband far-field sources, a received signal matrix is represented as: wherein denotes the encoding matrix, denotes the steering matrix, denotes the input signal amplitude matrix, denotes the noise matrix.

3. The denoising CNN and MUSIC based metasurface DOA estimation method according to claim 1, characterized in that, The method for constructing the dataset comprises the following sub-steps: For the single-target case, the range of the sine value of the incident angle is evenly divided into P grid, and a plurality of noisy covariance matrix samples and corresponding noise-free covariance matrix labels are generated for each grid under different signal-to-noise ratio conditions. For multi-target case, the grids are combined to obtain multiple angle combinations, and multiple noisy covariance matrix samples and their corresponding noise-free covariance matrix labels are generated for each angle combination under different signal-to-noise ratio conditions. P For multi-target case, the grids are combined to obtain multiple angle combinations, and multiple noisy covariance matrix samples and their corresponding noise-free covariance matrix labels are generated for each angle combination under different signal-to-noise ratio conditions. Integrate single-target and multi-target data samples and labels to form a mixed dataset, and normalize all samples and labels.

4. The denoising CNN and MUSIC based metasurface DOA estimation method according to claim 2, characterized in that, The noisy covariance matrix estimate is calculated according to the following formula: wherein denotes the received signal matrix under noiseless conditions, denote the ideal signal covariance matrix estimate and the noise covariance matrix estimate, respectively, denotes the conjugate transpose.

5. The denoising CNN and MUSIC based metasurface DOA estimation method according to claim 1, characterized in that, The denoising CNN network learns a mapping relationship between through residual learning f .

6. The denoising CNN and MUSIC based metasurface DOA estimation method according to claim 5, characterized in that, The denoising CNN network comprises: Input layer: the real part and the imaginary part of the noisy covariance matrix estimate are taken as double-channel input; Feature extraction layer: comprising a plurality of series modules comprising convolution layer, batch normalization layer and activation function; Output layer: one convolution layer, the output channel number is 2, corresponding to the real part and the imaginary part of the output matrix; Residual connection: taking the network output as the estimation of the noise covariance matrix, and obtaining the preliminary denoising result by subtracting the estimation from the input; Hermitian layer: receiving the preliminary denoising result, and outputting the final denoised covariance matrix estimate satisfying the Hermitian property through operation.

7. The denoising CNN and MUSIC based metasurface DOA estimation method according to any one of claims 1-6, characterized in that, The DOA estimation specifically comprises: The range of the incident angle sine value is evenly divided into P search grids; The denoised covariance matrix estimate is subjected to eigenvalue decomposition, and based on the final... N K Each feature vector forms a noise subspace; According to the MUSIC algorithm, calculate the spatial spectrum value corresponding to each search grid; Obtain the DOA estimation result by spectral peak search.

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