A robust doa estimation method based on admm-net

Abstract

The application discloses a kind of robust direction of arrival estimation method based on ADMM-Net, by expanding ADMM algorithm into model-driven deep network ADMM-Net to improve DOA estimation accuracy, speed up DOA estimation speed and have robustness to array disturbance.Firstly, the sparse transformation of source and array received multi-shot data is carried out by space over-complete dictionary, and the DOA estimation is converted into compressed sensing sparse recovery problem;Then, ADMM algorithm is expanded, and model-driven deep network ADMM-Net with explainability is formed;ADMM-Net is used to reconstruct source power spectrum and carry out DOA estimation.The present application can learn the hyperparameters in iterative algorithm and array disturbance, solve the problem that existing compressed sensing DOA estimation method based on calculation speed is slow, and fails under the condition of array disturbance, realize fast, accurate, explainable and robust DOA estimation.

Description

Technical Field

[0001] This invention belongs to the fields of array signal processing technology and deep learning technology, and specifically relates to a robust direction-of-arrival estimation method based on ADMM-Net. Background Technology

[0002] Direction of Arrival (DOA) estimation refers to estimating the direction of arrival of a signal from observations from multiple array receiving antennas. DOA estimation is a major problem in array signal processing and has wide applications in various fields such as radar, sonar, and wireless communication.

[0003] Over the decades, scholars have proposed various methods to improve the accuracy of DOA estimation, which can be mainly divided into three categories: 1) Subspace-based algorithms; 2) Compressed Sensing (CS) methods; and 3) Deep Learning (DL) methods. Subspace-based DOA estimation methods can achieve super-resolution estimation under high signal-to-noise ratio (SNR) conditions; however, they require a sufficient number of snapshots to approximate the covariance matrix, and are sensitive to angle separation. Compressed Sensing-based DOA estimation methods can accurately reconstruct sparse signals under certain conditions, but the reconstruction error increases as the SNR decreases. However, this method typically requires solving a complex optimization problem with high computational complexity, often requiring hundreds or thousands of iterations, and its estimation performance is highly sensitive to hyperparameters during the optimization process. Furthermore, these model-driven methods require accurate array information, and will fail when the array is perturbed. Deep learning methods can adaptively learn array information; however, most current deep learning-based DOA estimation methods are purely data-driven, and their "black box" network mechanisms are difficult to interpret. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the present invention aims to provide a robust DOA estimation method based on ADMM-Net, which can learn the hyperparameters and array perturbations in the iterative algorithm to achieve fast, accurate, interpretable and robust DOA estimation.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A robust direction-of-arrival estimation method based on ADMM-Net includes the following steps:

[0007] Step 1: Given a specified number of grid divisions, perform a sparse transformation on the source power and the covariance matrix of the array received data to convert DOA estimation into a compressed sensing sparse recovery problem.

[0008] Step 2: Expand the Alternating Direction Method of Multipliers (ADMM) algorithm to obtain the model-driven deep network ADMM-Net. Preprocess the data after sparse transformation, and represent the complex tensor as a stack of its real and imaginary parts. All operations on complex numbers in the deep network are redefined according to the rules of complex number operations.

[0009] Step 3: Generate data with a fixed signal-to-noise ratio, and train the ADMM-Net obtained in Step 2 using the data processed by the sparse transformation in Step 1;

[0010] Step 4: Using the array received data after the sparse transformation in Step 1 as input, reconstruct the source power spectrum using the ADMM-Net trained in Step 3;

[0011] Step 5: For the source power spectrum reconstructed in Step 4, search for the support set corresponding to the peak value of the power spectrum to complete the DOA estimation.

[0012] This invention also provides a robust direction-of-arrival estimation system based on ADMM-Net, comprising:

[0013] The receiving module receives source power and multiple beat signals from multiple array receiving antennas;

[0014] The processing module executes the robust direction-of-arrival estimation method based on ADMM-Net to achieve DOA estimation;

[0015] The display module presents the DOA estimation results.

[0016] The present invention also provides an apparatus comprising:

[0017] A processor and a memory, wherein the memory is used to store computer programs, and the processor is used to call and run the computer programs stored in the memory to execute the robust direction-of-arrival estimation method based on ADMM-Net.

[0018] The present invention also provides a computer-readable storage medium for storing a computer program that causes a computer to execute the robust direction-of-arrival estimation method based on ADMM-Net.

[0019] Compared with the prior art, the beneficial effects of the present invention are:

[0020] This invention proposes a model-driven deep network-based DOA estimation method, transforming DOA estimation into a compressed sensing sparse recovery problem. The model-driven deep network ADMM-Net can adaptively learn array perturbations and hyperparameters during iteration, and possesses interpretability. Under a fixed signal-to-noise ratio of 10 dB, the network is trained using sample covariance matrices with different snapshot numbers. The trained ADMM-Net network is then used to reconstruct the source power spectrum for DOA estimation.

[0021] Furthermore, the model-driven deep network ADMM-Net, designed based on the ADMM algorithm, only requires dozens of iterations, significantly improving the speed of DOA estimation.

[0022] Furthermore, the model-driven deep network ADMM-Net can learn hyperparameters in iterative algorithms, improving the performance of DOA estimation.

[0023] Furthermore, the model-driven deep network ADMM-Net can adaptively learn array perturbations, enabling it to handle array adaptation scenarios in real-world applications.

[0024] Furthermore, the training dataset contains samples with different numbers of snapshots, which gives the network a stronger generalization ability. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the DOA estimation method of the present invention.

[0026] Figure 2 This is a schematic diagram of the model-driven deep network ADMM-Net.

[0027] Figure 3 This is a performance comparison chart of the original ADMM algorithm and ADMM-Net under the condition of signal-to-noise ratio (SNR) = 10dB and different number of snapshots.

[0028] Figure 4 This is a performance comparison chart of the original ADMM algorithm, the Atomic Norm Minimization (ANM) method, and ADMM-Net under different signal-to-noise ratios.

[0029] Figure 5 In the case of array mismatch, the estimation performance of ADMM-Net under different signal-to-noise ratios was tested using 20, 30, 40, and 50 snapshots respectively.

[0030] Figure 6 The figure shows the estimation results of this invention and other algorithms, based on a randomly selected sample with a signal-to-noise ratio (SNR) of 10dB and 25 snapshots, given a known array.

[0031] Figure 7The figure shows the estimation results of this invention and other algorithms under the condition of array mismatch, where a sample with a signal-to-noise ratio (SNR) of 10dB and 25 snapshots is randomly selected. Detailed Implementation

[0032] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0033] This invention discloses a Direction of Arrival (DOA) estimation method based on a model-driven deep network. By expanding the Alternating Direction Method of Multipliers (ADMM) algorithm into a model-driven deep network ADMM-Net, the accuracy and speed of DOA estimation are improved, and the method is robust to array perturbations.

[0034] The core elements of this invention include:

[0035] This paper transforms DOA estimation into a sparse recovery problem and expands the Alternating Direction Multiplier Method (ADMM) to design an interpretable model-driven deep network, ADMM-Net. Specifically, ADMM-Net contains a fixed number of iterative blocks, each corresponding to one iteration of the ADMM algorithm. The network can learn the hyperparameters and array perturbations in the iterative algorithm, solving the problems of slow computation and failure under array perturbations in existing compressed sensing-based DOA estimation methods. This achieves fast, accurate, interpretable, and robust DOA estimation.

[0036] First, a sparse transformation is performed on the source and array-received multi-shot data using a spatially overcomplete dictionary, transforming DOA estimation into a compressed sensing sparse recovery problem. Then, the ADMM algorithm is expanded to form an interpretable model-driven deep network, ADMM-Net. ADMM-Net is used to reconstruct the source power spectrum and perform DOA estimation.

[0037] Figure 1 This is a flowchart illustrating a specific embodiment of the present invention, such as... Figure 1 As shown, the present invention provides a robust direction-of-arrival estimation method based on ADMM-Net, comprising the following steps:

[0038] Step 1: Establish a spatial discrete sparse representation model of the covariance matrix of the received data.

[0039] The purpose of this model, which is also the objective of this step, is to perform a sparse transformation on the source power and the covariance matrix of the array received data, given a specified number of grid divisions, thereby transforming the DOA estimation into a compressed sensing sparse recovery problem.

[0040] Suppose that K far-field narrowband signals are incident on a uniform linear array containing M sensors, the received signal of the array can be expressed as:

[0041] x(t)=A(θ)s(t)+n(t)

[0042] Assuming a continuous domain of origin (DOA) can be represented by a given set of grid points, and if these grid points are divided into G equal parts, this means the DOA can only take G values ​​at each grid point. Therefore, the array-received signal can be represented in the following overcomplete form:

[0043]

[0044] The array collects data from L snapshots. The received signal from the array can be equivalently represented in the following matrix form:

[0045]

[0046] Wherein, the received signal X = [x(1),x(2),...,x(t),...,x(L)], and the source signal is... Noise N = [n(1),n(2),…,n(t),…,n(L)], where L is the number of snapshots collected. It can be recovered from X. To solve the DOA estimation problem, The position corresponding to the peak value in the graph indicates the direction of the information source.

[0047] Among them, the gridded array guide vector matrix It is an M×G dictionary matrix, where G is the number of meshes, and A(θ) is the original / unmeshable array steering vector matrix; the k-th column vector of the dictionary matrix. The specific form of the m-th element (corresponding to the (m+1)-th array element) is: λ is the wavelength, and d is the element spacing. It is the direction of arrival of the k-th signal source; This represents a gridded signal source; n(t) represents a signal source with a mean of 0 and a variance of σ. 2 Additive white Gaussian noise. Specifically, the matrix The k-th column contains elements in each element. This parameter simply means that each element corresponds to a different array element; if the first array element is used as the reference for a uniform linear array, the distance between the m-th array element and the first array element is (m-1)d.

[0048] A sparse transformation is performed on the source power and the covariance matrix of the array received data, which is then expressed as the sample covariance matrix of the array received signal. This can be further expressed as:

[0049]

[0050] In this context, the superscript H indicates the conjugate transpose, and the notation E indicates the expected value. ⊙ denotes the Khatri-Rao product of a matrix; Power spectrum p = [p1, p2, ..., p n ,...,p G The nth term of the power spectrum p σ 2 This is the noise variance, also known as noise power; Representation matrix Vectorization, where I represents the identity matrix, vec(I) denotes the vectorization of the identity matrix; ε represents the sample covariance matrix of the finite snapshot data. The deviation from the true covariance matrix R. (Gridded signal source) It is an extension of s(t), specifically in the form of:

[0051]

[0052] In other words, when the DOA falls on a grid point, the value at that grid point is the value of the k-th source; otherwise, the value is 0.

[0053] s k (t) represents the k-th information source. express The conjugate transpose of; This represents the DOA value at the nth grid point after gridding.

[0054] The power spectrum p is non-zero only at the source location, meaning the spatial spectrum p is sparse. Therefore, it can be determined from the sample covariance matrix. The power spectrum p is recovered to solve the DOA estimation problem, and the position of the peak in p represents the source direction.

[0055] After being transformed into a sparse recovery problem, this problem becomes a typical sparse linear inverse problem, which can be solved by optimizing the following objective function:

[0056]

[0057] in, The vectorized sample covariance matrix, M represents the number of array elements.

[0058] The problem of DOA estimation is essentially about solving for θ. kThis invention discretizes the continuous DOA domain, that is, after gridding the matrix A(θ), the DOA estimation problem becomes a sparse recovery problem, which only requires knowing which grid points are not 0.

[0059] Step 2, Data Preprocessing: Complex Number Operations in Deep Networks.

[0060] This step combines compressed sensing-based DOA estimation methods with deep learning methods, often referred to as model-driven deep networks, fully leveraging the advantages of both model-driven and data-driven approaches.

[0061] Deep networks redefine operations on complex numbers as: for any complex number z, use the real part of the complex number... and the virtual part The complex number is represented by two real-valued entities, and complex number operations are simulated using real-valued arithmetic. The specifics of complex convolution are as follows:

[0062] For complex convolution kernels and complex tensors Complex convolution can be represented as real convolution as: The network input data is the aforementioned vectorized sample covariance matrix. Because deep networks cannot directly handle complex tensors, therefore... Preprocessing is performed, that is, the complex number is represented by two real-valued entities, the real part and the imaginary part. The transformed data dimensions are respectively in And A[0,:,:] is the real part. A[1,:,:] represents the imaginary part, and batch represents the batch size in a deep network.

[0063] The performance of model-driven methods depends heavily on the dictionary matrix. While achieving high accuracy is desirable, practical arrays suffer from various defects, such as sensor coupling, phase inconsistency, and sensor position errors. These array perturbations prevent the acquisition of an accurate dictionary matrix. Therefore, accurate DOA estimation cannot be achieved. With the development of deep learning, model-driven deep unfolding networks combine the advantages of model-driven algorithms utilizing known prior information and deep networks learning from data. Thus, they have both interpretability and robustness to array perturbations, and can effectively solve the DOA estimation problem.

[0064] Step 3: Build the model-driven deep network ADMM-Net.

[0065] Specifically, this step unfolds the ADMM algorithm to obtain the model-driven deep network ADMM-Net. All operations involving complex numbers in the deep network are redefined according to the rules of complex number operations. (Refer to...) Figure 2 The model-driven deep network ADMM-Net performs the following steps:

[0066] Step 3.1, the first step of the algorithm in the k-th iteration of the model-driven deep network ADMM-Net:

[0067]

[0068] p k This represents the result of the first step of the algorithm in the k-th iteration, where ρ is the learning parameter of the deep network, and z... k+1 β represents the result of the second step of the algorithm in the (k-1)th iteration. k-1 This represents the result of the third step of the algorithm in the (k-1)th iteration;

[0069] Step 3.2, the second step of the algorithm in the k-th iteration of the model-driven deep network ADMM-Net:

[0070]

[0071] Where z k This is the result of the second step of the algorithm in the k-th iteration, representing the estimated power spectrum obtained by the ADMM algorithm. Represents the soft thresholding operator, λ k and ρ k These are all learning parameters for deep networks;

[0072] Step 3.3, in the k-th iteration of the model-driven deep network ADMM-Net, the third step of the algorithm is the Lagrange multiplier β. k The update steps are as follows:

[0073] β k ←β k-1 +p k -z k

[0074] Step 3.4: Perform residual learning on the results obtained in Step 3.2 using the residual network;

[0075] Δz k ←ResCNN(z k )

[0076] The specific structure of the residual network is as follows: the first layer consists of 64 9×9 convolutional kernels and ReLU activation functions; the second layer consists of 32 1×1 convolutional kernels and ReLU activation functions; and the third layer consists of one 5×5 convolutional kernel and ReLU activation function.

[0077] Step 3.5: Add the results obtained in steps 3.2 and 3.4 to obtain the estimated value of the source power spectrum.

[0078]

[0079] Step 3.6: Repeat steps 3.1 to 3.5 T times to obtain the final result.

[0080] Step 4: Train the model to drive the deep network ADMM-Net.

[0081] The purpose of this step is to generate data with a fixed signal-to-noise ratio, and then use the data processed by the sparse transformation method in step 1 to train the ADMM-Net obtained by the method in step 2. The steps can be described as follows:

[0082] 1) Divide the data into training and testing sets. The training set contains data from different snapshots, with the same number of samples in each snapshot. Preprocess the data and represent the complex tensor as a stack of its real and imaginary parts.

[0083] 2) Use the mean squared error (MSE) as the loss function, and optimize the network parameters using the backpropagation algorithm and the stochastic gradient-based optimizer Adam;

[0084] 3) The network input is the array received data X after sparse transformation. The output is a gridded estimate of the source power spectrum. In the prediction phase, look for The predicted angle can be obtained by finding the support set corresponding to the peak value and converting it into the corresponding frequency or angle.

[0085] In one embodiment of the present invention, a fixed signal-to-noise ratio (SNR) of 10 dB is set. Assuming the receiving array is a uniform linear array of 8 elements with a spacing of half a wavelength between adjacent elements, and three signal sources, 50 snapshots of data are generated using additive white Gaussian noise, resulting in a total of 9000 samples. It is worth noting that since frequency and angle have a one-to-one correspondence, the signal frequency can be directly generated. The training set and the multiplication set are divided into two sets at an 8:1 ratio. The training set contains data at 15, 20, 25, 30, 35, 40, 45, and 50 snapshots, with 1000 samples per snapshot, for a total of 8000 samples. The data is preprocessed, representing complex tensors as a stack of their real and imaginary parts.

[0086] Step 5, Network Testing Phase: Reconstruct the power spectrum of the signal source.

[0087] In this step, the array received data after sparse transformation processing in step 1 is used as input, and the source power spectrum is reconstructed using the ADMM-Net trained in step 3. For the reconstructed source power spectrum, the support set corresponding to the power spectrum peak is searched to complete the DOA estimation.

[0088] This invention also provides a robust direction-of-arrival estimation system based on ADMM-Net, comprising:

[0089] The receiving module receives source power and multiple beat signals from multiple array receiving antennas;

[0090] The processing module executes the robust direction-of-arrival estimation method based on ADMM-Net to achieve DOA estimation;

[0091] The display module presents the DOA estimation results.

[0092] The receiving module of this invention can be a radar array antenna, a microphone array, a sonar array, etc.

[0093] The processing module of this invention can be a computer processor (CPU) or a GPU that excels at parallel computing.

[0094] The display module of the present invention can be a radar display screen, a microphone receiver display screen, etc.

[0095] Based on the data obtained from the above embodiments, under the conditions of signal-to-noise ratio (SNR) = 10dB and different snapshot numbers, the performance comparison between the original ADMM algorithm and ADMM-Net is as follows: Figure 3 As shown in the figure, the root mean square error of both ADMM and ADMM-Net estimations decreases significantly with increasing snapshot count, while the recovery rate increases significantly with increasing snapshot count. Furthermore, ADMM-Net's estimation performance is superior to ADMM.

[0096] Based on the data obtained from the above embodiments, the performance comparisons of the original ADMM algorithm, the Atomic Norm Minimization (ANM) method, and ADMM-Net under different signal-to-noise ratios are as follows: Figure 4 As shown in the figure, the root mean square error of ADMM-Net estimation decreases as the signal-to-noise ratio increases. In particular, ADMM-Net estimation is significantly better than ADMM and ANM methods under low signal-to-noise ratio conditions.

[0097] Based on the data obtained from the above embodiments, under the array mismatch scenario, the estimation performance of ADMM-Net at different signal-to-noise ratios was tested using 20, 30, 40, and 50 snapshots, respectively. Figure 5 As shown in the figure, the root mean square error of the estimation decreases significantly with the increase of signal-to-noise ratio and number of snapshots. This indicates that ADMM-Net can adaptively learn array perturbations and has robustness.

[0098] Based on the data obtained from the above embodiments, under the condition of a known array, a sample with a signal-to-noise ratio (SNR) of 10 dB and 25 snapshots is randomly selected. The estimation results of this invention and other algorithms are shown as follows. Figure 6 As shown in the figure, the method of the present invention can accurately estimate the direction of the signal source.

[0099] Based on the data obtained from the above embodiments, in the case of array mismatch, a sample with a signal-to-noise ratio (SNR) of 10 dB and 25 snapshots is randomly selected. The estimation results of this invention and other algorithms are shown as follows. Figure 7 As shown in the figure, when the array is mismatched, both the original ADMM algorithm and the Atomic Norm Minimization (ANM) method fail, while the ADMM-Net method of this invention can estimate the source direction.

[0100] In summary, it can be confirmed that the model-driven deep network proposed in this invention can learn hyperparameters and array perturbations in iterative algorithms, solving the problems of slow computation speed and failure in the presence of array perturbations in existing compressed sensing-based DOA estimation methods. It achieves fast, accurate, interpretable and robust DOA estimation, and can also perform DOA estimation when there are array defects.

Claims

1. A robust direction-of-arrival estimation method based on ADMM-Net, characterized in that, Includes the following steps: Step 1: Given a specified number of grid divisions, perform a sparse transformation on the source power and the covariance matrix of the array received data to convert DOA estimation into a compressed sensing sparse recovery problem. Step 2: Unfold the ADMM algorithm to obtain the model-driven deep network ADMM-Net. Preprocess the data after sparse transformation, representing complex tensors as a stack of their real and imaginary parts. Redefine all operations involving complex numbers in the deep network according to the rules of complex number operations. The model-driven deep network ADMM-Net performs the following steps: Step 2.1: In the model-driven deep network ADMM-Net... In this iteration, the first step of the algorithm is: Indicates the first The result of the first step of the algorithm in this iteration. These are the learning parameters for deep networks. Indicates the first The result of the second step of the algorithm in the next iteration. Indicates the first The result of the third step of the algorithm in this iteration; This represents the gridded array guide vector matrix. express The conjugate transpose of . express The conjugate transpose of . yes and Khatri-Rao product, , Denotes the Khatri-Rao product of matrices. Represents the identity matrix. Represents the vectorized sample covariance matrix; Step 2.2: In the model-driven deep network ADMM-Net... k In this iteration, the second step of the algorithm is: in It is the first The result of the second step of the algorithm in this iteration represents the estimated power spectrum obtained by the model-driven deep network ADMM-Net. Represents the soft threshold operator. and These are all learning parameters for deep networks; Step 2.3: In the model-driven deep network ADMM-Net... In this iteration, the third step of the algorithm involves the Lagrange multipliers. The update steps are as follows: Step 2.4: Perform residual learning on the results obtained in Step 2.2 using a residual network; Step 2.5: Add the results obtained in Step 2.2 and Step 2.4 to obtain the estimated value of the source power spectrum. ; Step 2.6: Repeat steps 2.1 to 2.

5. This time, the final result is obtained; Step 3: Generate data with a fixed signal-to-noise ratio, and train the ADMM-Net obtained in Step 2 using the data processed by the sparse transformation in Step 1; Step 4: Using the array received data after the sparse transformation in Step 1 as input, reconstruct the source power spectrum using the ADMM-Net trained in Step 3; Step 5: For the source power spectrum reconstructed in Step 4, search for the support set corresponding to the peak value of the power spectrum to complete the DOA estimation.

2. The robust direction-of-arrival estimation method based on ADMM-Net according to claim 1, characterized in that, Step 1 involves performing a sparse transformation on the source power and the covariance matrix of the array received data, expressed as follows: in It is the sample covariance matrix. ; The gridded array is guided by a vector matrix, i.e., a dictionary matrix. The column vectors are , of which column vectors The The elements are , It is the number of grid divisions; It's the wavelength. It is the spacing between array elements. It is the first The direction of the incoming wave from each signal source; For the power spectrum, non-zero elements only exist at the source location, i.e. It is sparse. , In the formula, Power spectrum The item, This indicates the calculation of the expected value. Indicates the first One source, This represents the number of snapshots collected. express The conjugate transpose of; Indicates the first after gridding n DOA values ​​at each grid point; This represents the noise power, also known as the noise variance. Represents the vectorization of the identity matrix. for With the true covariance matrix Deviation between; After transforming it into a sparse recovery problem, it can be solved by optimizing the following objective function: Thus, it can be obtained from Mid-recovery power spectrum Solving the DOA estimation problem The position corresponding to the peak value in the graph indicates the direction of the information source. , , , The number of array elements.

3. The robust direction-of-arrival estimation method based on ADMM-Net according to claim 2, characterized in that, In step 2, the network input data is... ,right Preprocessing is performed, that is, the complex number is represented by two real-valued entities, the real part and the imaginary part. The transformed data dimensions are respectively , ,in and For the real part, and The virtual part, This indicates the batch size in a deep network.

4. The robust direction-of-arrival estimation method based on ADMM-Net according to claim 1, characterized in that, In step 2.4, the structure of the residual network is as follows: The first layer consists of 64 9×9 convolutional kernels and ReLU activation functions; the second layer consists of 32 1×1 convolutional kernels and ReLU activation functions; and the third layer consists of one 5×5 convolutional kernel and ReLU activation function.

5. The robust direction-of-arrival estimation method based on ADMM-Net according to claim 1, characterized in that, In step 3, data is generated with a fixed signal-to-noise ratio, and ADMM-Net is trained through the following steps: 1) Divide the data into training and testing sets. The training set contains data from different snapshots, with the same number of samples in each snapshot. Preprocess the data and represent the complex tensor as a stack of its real and imaginary parts. 2) Use the mean squared error (MSE) as the loss function, and optimize the network parameters using the backpropagation algorithm and the stochastic gradient-based optimizer Adam; 3) The network input is the covariance matrix of the array received data after sparse transformation. The output is a gridded estimate of the source power spectrum. In the prediction phase, searching The predicted angle can be obtained by finding the support set corresponding to the peak value and converting it into the corresponding frequency or angle.

6. The robust direction-of-arrival estimation method based on ADMM-Net according to claim 5, characterized in that, The fixed signal-to-noise ratio is set to SNR=10dB.

7. A robust direction-of-arrival estimation system based on ADMM-Net, characterized in that, include: The receiving module receives source power and multiple block signals from multiple array receiving antennas; The processing module executes the robust direction-of-arrival estimation method based on ADMM-Net as described in any one of claims 1 to 6 to achieve DOA estimation; The display module presents the DOA estimation results.

8. A device, characterized in that, include: A processor and a memory, the memory being used to store a computer program, the processor being used to invoke and run the computer program stored in the memory to perform the method of any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, Used to store a computer program that causes a computer to perform the method according to any one of claims 1-6.

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