Single-snapshot direction finding method for reconstructing structured covariance matrix based on deep learning

Abstract

The invention discloses a single-snapshot direction finding method for reconstructing a structured covariance matrix based on deep learning. The method comprises the following steps: modeling an array covariance matrix; generating a deep learning training data set; deep learning network input and output; designing a network training loss function based on a structured covariance matrix; carrying out neural network architecture design and network training; and reconstructing a positive semidefinite toeplitz covariance matrix and estimating the direction of arrival. Compared with a method for constructing a covariance matrix by directly using network output, the method provided by the invention has the advantages that positive semidefinite and Toeplitz properties of the covariance matrix are simultaneously maintained in a network training process, and whitening decorrelation processing is carried out, so that high-precision and high-resolution direction finding performance can be obtained.

Description

Technical Field

[0001] The present invention belongs to the field of electronic information technology, especially the field of array signal processing technology, and particularly relates to the problem of using deep learning methods to process signal processing of uniform arrays of receivers such as radar, sonar, and communication, and is specifically a single-snapshot direction finding method based on deep learning. Background Art

[0002] Array signal processing is widely used in military and civilian technology fields, and has important applications in radar, communication, navigation and other technical fields. In recent years, millimeter wave radar has been widely used in autonomous driving systems due to its advantages of all-weather, strong anti-interference ability and low cost. However, after the radar is processed in the distance dimension and speed dimension, only single snapshot data can be used for array signal processing. The traditional Bartlett beamformer has low computational complexity, especially when the fast Fourier transform (FFT) is used to transform the steering into the frequency domain, the detection resolution is low. Since the rank of the array covariance matrix is ​​one in the single snapshot case, only a single target can be estimated when the subspace method is used. For multi-target situations, it is necessary to use the spatial smoothing method (see reference 1: Liu CL, Vaidyanathan P P. Remarks on the spatial smoothing step incoarray MUSIC [J]. IEEE Signal Processing Letters, 2015, 22 (9): 1438-1442.) to restore the rank of the covariance matrix. However, spatial smoothing will reduce the array aperture, thereby reducing the resolution and the estimated angle accuracy.

[0003] Traditional DOA estimation methods all rely on modeling. However, for many problems, it is difficult to find an accurate model. Traditional methods make assumptions and approximations based on experience during the modeling process, which may lead to the loss of some features, and then lead to insufficient utilization of observation data. To this end, researchers have begun to use deep learning for parameter estimation to solve these problems. Deep learning roughly transforms the DOA estimation problem into a classification problem and a regression problem. The gridded DOA estimation method implemented by the classification problem converts the continuous angle interval into a discrete angle grid. When the actual wave arrival angle is not on the discrete grid points, there will always be errors in the prediction results of the gridded method. Optimizing the DOA estimation problem into a deep learning regression problem to achieve gridless estimation will avoid the above problems. For example, in reference 2 (Barthelme A, Utschick W. DOA estimation using neural network-based covariance matrix reconstruction [J]. IEEE Signal Processing Letters, 2021, 28: 783-787.), the sample covariance matrix is ​​used as the input value, and a semi-positive prior neural network is used to reconstruct the sample covariance matrix into a theoretical covariance matrix with semi-positive properties. Then, the DOA estimation is derived from the estimated covariance matrix by multiple signal classification (MUSIC). Reference 3 (Wu X, Yang X, Jia X, et al. Agridless DOA estimation method based on convolutional neural network with Toeplitz prior [J]. IEEE Signal Processing Letters, 2022, 29: 1247-1251.) is similar to Reference 2, except that the neural network with Toeplitz prior is used to reconstruct the sample covariance matrix into a theoretical covariance matrix with Toeplitz property. However, the theoretical covariance matrix is ​​a matrix with both semi-positive definite and Toeplitz properties. Both References 2 and 3 can only use part of its properties, and some properties are still not fully utilized. Summary of the invention

[0004] The purpose of the present invention is to provide a single-snapshot direction finding method based on deep learning to reconstruct a structured covariance matrix in view of the above-mentioned deficiencies in the prior art. This method can simultaneously ensure that the covariance matrix output by the network has semi-positive definite and Toeplitz properties, which is more in line with the signal processing model of a general uniform array, thereby obtaining a direction finding result with higher accuracy and higher resolution.

[0005] The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix provided by the present invention comprises the following steps:

[0006] Step 1: array covariance matrix modeling;

[0007] Step 2: deep learning training data set generation;

[0008] Step 3: Deep learning neural network input and output design;

[0009] Step 4: Design of network training loss function based on structured covariance matrix;

[0010] Step 5: Deep learning neural network architecture design and network training;

[0011] Step 6: Reconstruct the semi-positive definite Toeplitz covariance matrix and estimate the direction of arrival.

[0012] Furthermore, step 1 specifically includes: in the target number range [1,K MAX ] randomly selects a target number K, where K MAX is the maximum number of targets to be processed for direction finding; set the number of array elements to be M, the set of multiple angle grid points to be Ω, the number of angles in the set to be L, θ∈Ω, and randomly select K different angles θ1,θ2,...,θ K , calculate the steering vector The array flow pattern A(θ)=[a(θ1),a(θ2),...,a(θ K )],in(·) T represents transpose, d represents the array element spacing, λ represents the signal wavelength, and j represents the imaginary unit;

[0013] Construct the array output x = A(θ)s + η, where s∈CN(0,R s ) represents a K-dimensional random signal vector, CN(·,·) represents a complex Gaussian distribution, the first parameter position represents the mean vector, and the second parameter position represents the covariance matrix; the covariance matrix R s The calculation formula is: Where diag(·) represents the generation of a diagonal matrix with corresponding elements as diagonal elements, and the power ratio ξ1,ξ2,...,ξ K-1 From the signal power ratio range [0,ξ MAX ] is randomly selected, ξ MAX is the maximum signal power ratio that needs to be processed for direction finding, in dB; η∈CN(0,σ 2 I M ) represents the M-dimensional noise vector, σ 2 represents the noise power, I M represents the M-dimensional identity matrix, where σ 2The calculation formula is σ 2 =10 -SNR / 10 , SNR is the signal-to-noise ratio, which needs to be calculated from the signal-to-noise ratio range [SNR min ,SNR max ] randomly selected, SNR min and SNR max are the minimum and maximum signal-to-noise ratios, respectively, in dB;

[0014] Compute array covariance matrix (·) H represents the conjugate transpose; then the theoretical covariance matrix for deep learning labels is generated The theoretical covariance matrix The calculation formula is:

[0015] Furthermore, step 2 specifically includes: setting K MAX , MAX 、SNR min 、SNR max The numerical and angle sets Ω, perform Q Monte Carlo experiments on step 1, and obtain Q pairs of array output covariance matrices And the theoretical covariance matrix R i ;right and After normalization, we get and in ||·|| F Indicates the Frobenius norm of the vector; the final training data set has a total of Q samples, each sample is and constitute;

[0016] Furthermore, step three specifically includes: taking the normalized array output covariance matrix The upper triangle of is column-vectorized Each The real part, imaginary part and The diagonal elements of are concatenated to form the eigenvector As the input of the deep learning neural network; the neural network is represented by The output of the neural network is represented as in Contains the estimated angle information, β i Expressed as represents the estimated angle, contains the estimated signal power, contains the estimated noise power;

[0017] Furthermore, step 4 specifically includes: the loss function of training the neural network is set to Where k is the regularization parameter, ||·||1 means to find the 1-norm of the vector, vec(·) means the matrix is ​​vectorized by columns, and ∑ -1 / 2 represents whitening decorrelation, and ∑ is expressed as:

[0018]

[0019] in Representation Matrix and Kronecker product; Reason Reconstructed semi-positive definite, Toeplitz covariance matrix, construction It includes the following sub-steps: constructing a matrix vector Construct a diagonal adjuvant matrix Semi-positive definite and Toeplitz covariance matrices for network reconstruction

[0020] Furthermore, step five specifically includes: the input layer dimension M of the neural network 2 , the output layer dimension is 2M+1, containing n hidden layers, each hidden layer contains m neurons, and there is an activation function between each hidden layer; the training data obtained in step 2 constitutes the feature vector z, which is input into the neural network g(z) to obtain the network output Then by Reconstructing the semi-positive definite, Toeplitz covariance matrix The construction of is as described in step 4;

[0021] The training of the neural network uses the back propagation algorithm, and the trained neural network is represented as

[0022] Furthermore, step six specifically includes: forming a new vector z′ from the test data and inputting it into the neural network In the network output Then by Reconstructing the semi-positive definite, Toeplitz covariance matrix Set the number of test data signal sources K′, and reconstruct the semi-positive definite Toeplitz covariance matrix Perform eigendecomposition and obtain the eigenvalues ​​v1≤v2≤2≤v arranged from small to large M′-1 ≤v M ; Take the eigenvectors corresponding to the MK′ smallest eigenvalues ​​to form the noise subspace E n ; Construct spectral function The angle corresponding to the peak of the spectrum function is the direction of the wave arrival angle, where θ′ is the search angle and a(θ′) is the search guidance vector, expressed as a(θ′)=[1,e -j2πd(sinθ′) / λ ,...,e -j2πd(M-1)(sinθ′) / λ ] T .

[0023] Furthermore, the deep learning neural network architecture of step five is set to a fully connected network, a residual network or a convolutional neural network.

[0024] Furthermore, the direction finding method in step six is ​​replaced by the Root-MUSIC algorithm to avoid spectrum peak searching and reduce the computational time complexity.

[0025] The beneficial effects of the present invention are:

[0026] 1. In the method proposed in the present invention, the covariance matrix for DOA estimation is constructed by using the network output auxiliary matrix. Compared with the method of directly using the network output to construct the covariance matrix, the semi-positive definiteness and Toeplitz properties of the constructed covariance matrix are guaranteed at the same time, making it more in line with

[0027] The signal processing model of a general uniform array can obtain high-precision and high-resolution direction finding results.

[0028] 2. The method of the present invention performs whitening decorrelation processing in the deep learning network model to reduce the correlation between noise components, thereby improving the accuracy of wave direction estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 The overall flow chart of the method of the present invention is

[0030] Figure 2 This is the overall structure diagram of the neural network of the present invention

[0031] Figure 3 The DOA estimation result of the present invention under different signal-to-noise ratios is

[0032] Figure 4 The estimation result of the direction of arrival of the present invention at different angle intervals is DETAILED DESCRIPTION

[0033] The technical solution of the present invention is further described in detail below through specific embodiments in conjunction with the accompanying drawings.

[0034] Embodiment 1:

[0035] Reference Figure 1 , is a flowchart of an optional example of a single-snapshot direction finding method based on deep learning to reconstruct a structured covariance matrix proposed in this application, and the method may include:

[0036] Step 1: Array covariance matrix modeling: In the target number range [1,K MAX ] randomly selects a target number K, where K MAX is the maximum number of targets to be processed for direction finding; set the number of array elements to be M, the set of multiple angle grid points to be Ω, the number of angles in the set to be L, θ∈Ω, and randomly select K different angles θ1,θ2,...,θ K , calculate the steering vector The array flow pattern A(θ)=[a(θ1),a(θ2),...,a(θ K )],in(·) T represents transpose, d represents the array element spacing, λ represents the signal wavelength, and j represents the imaginary unit;

[0037] Construct the array output x = A(θ)s + η, where s∈CN(0,R s ) represents a K-dimensional random signal vector, CN(·,·) represents a complex Gaussian distribution, the first parameter position represents the mean vector, and the second parameter position represents the covariance matrix; the covariance matrix R s The calculation formula is: Where diag(·) represents the generation of a diagonal matrix with corresponding elements as diagonal elements, and the power ratio ξ1,ξ2,...,ξ K-1 From the signal power ratio range [0,ξ MAX ] is randomly selected, ξ MAX is the maximum signal power ratio that needs to be processed for direction finding, in dB; η∈CN(0,σ 2 I M ) represents the M-dimensional noise vector, σ 2 represents the noise power, I M represents the M-dimensional identity matrix, where σ 2 The calculation formula is σ 2 =10 -SNR / 10 , SNR is the signal-to-noise ratio, which needs to be calculated from the signal-to-noise ratio range [SNR min ,SNR max ] randomly selected, SNR min and SNR max are the minimum and maximum signal-to-noise ratios, respectively, in dB;

[0038] Compute array covariance matrix (·) H represents the conjugate transpose; then the theoretical covariance matrix for deep learning labels is generated The theoretical covariance matrix The calculation formula is:

[0039] Step 2: Deep learning training data set generation: Set KMAX , MAX 、SNR min 、SNR max The numerical and angle sets Ω, perform Q Monte Carlo experiments on step 1, and obtain Q pairs of array output covariance matrices And the theoretical covariance matrix R i ;right and After normalization, we get and in ||·‖ F Indicates the Frobenius norm of the vector; the final training data set has a total of Q samples, each sample is and constitute;

[0040] Step 3: Deep learning neural network input and output design: Take the normalized array output covariance matrix The upper triangle of is column-vectorized Each The real part, imaginary part and The diagonal elements of are concatenated to form the eigenvector As the input of the deep learning neural network; the neural network is represented by The output of the neural network is represented as in Contains the estimated angle information, β i Expressed as represents the estimated angle, contains the estimated signal power, contains the estimated noise power;

[0041] Step 4: Design of network training loss function based on structured covariance matrix: The loss function for training the neural network is set as Where k is the regularization parameter, ‖·‖1 means to find the 1-norm of the vector, vec(·) means the matrix is ​​vectorized by columns, and the left multiplication ∑ -1 / 2 represents whitening decorrelation, and ∑ is expressed as:

[0042]

[0043] in Representation Matrix and Kronecker product; Reason Reconstructed semi-positive definite, Toeplitz covariance matrix, construction It includes the following sub-steps: constructing a matrix vector Construct a diagonal adjuvant matrix Semi-positive definite and Toeplitz covariance matrices for network reconstruction

[0044] Step 5: Neural network architecture design and network training: The input layer dimension M of the neural network 2 , the output layer dimension is 2M+1, containing n hidden layers, each hidden layer contains m neurons, and there is an activation function between each hidden layer; the training data obtained in step 2 constitutes the feature vector z, which is input into the neural network g(z) to obtain the network output Then by Reconstructing the semi-positive definite, Toeplitz covariance matrix The construction of is as described in step 4;

[0045] The training of the neural network uses the back propagation algorithm, and the trained neural network is represented as

[0046] Step 6: Reconstruct the semi-positive Toeplitz covariance matrix and estimate the direction of arrival; construct the new vector z′ from the test data and input it into the neural network In the network output Then by Reconstructing the semi-positive definite, Toeplitz covariance matrix Set the number of test data signal sources K′, and reconstruct the semi-positive definite Toeplitz covariance matrix Perform eigendecomposition and obtain the eigenvalues ​​v1≤v2≤2≤v arranged from small to large M′-1 ≤v M ; Take the eigenvectors corresponding to the MK′ smallest eigenvalues ​​to form the noise subspace E n ; Construct spectral function The angle corresponding to the peak of the spectrum function is the direction of the wave arrival angle, where θ′ is the search angle and a(θ′) is the search guidance vector, expressed as a(θ′)=[1,e -j2πd(sinθ′) / λ ,...,e -j2πd(M-1)(sinθ′) / λ ] T ;

[0047] In some embodiments, the deep learning neural network architecture in step five can be replaced with a convolutional network to reduce the number of training parameters and improve computational efficiency.

[0048] In other embodiments, the deep learning neural network architecture in step five can be replaced by a residual network to extract deep features and enhance the generalization ability of the model.

[0049] Embodiment 2:

[0050] On the basis of the first embodiment, the direction finding method in step six is ​​replaced by the Root-MUSIC algorithm, which can avoid the spectrum peak search and reduce the computational time complexity.

[0051] In order to verify the performance of the present invention, the following simulation examples are used for verification, and the experimental results are compared with those of spatial smoothing, semi-positive definite networks (see Patent 1: Pan Yujian, Hu Xingyu, Xu Xin, et al. Coprime array direction of arrival estimation method based on deep learning to reconstruct covariance matrix [P]. China: CN202210661582.2, 2022-08-09.), and Toeplitz network (see Patent 2: Pan Yujian, Zhao Zewei, Xu Xin, et al. A single-snapshot direction finding method for non-ideal non-uniform array based on deep learning [P]. China: CN202211515822.4, 2023-03-07.).

[0052] The array is set to a 7-element uniform linear array, and the angle range of the signal source is set to a uniform angle grid point within [-60°, 60°] with an interval of 2°. In the step of constructing training data, the signal-to-noise ratio is set to [10, 15, 20, 25] in dB. The target number range is 2. In the case of 2 targets, the maximum signal power ratio ξ MAX =0.3. A total of 219,600 training data were generated using the above method. The specific network structure of the deep learning network is as follows Figure 2 As shown: the input layer dimension of the deep learning network is 49, the output layer dimension is 15, and it contains 6 hidden layers. Each hidden layer contains 2048 neurons. There is an activation function between each hidden layer, and the activation function uses the ReLu function. The optimizer uses Adam, the maximum epoch number is set to 200, the batch size is set to 1024, and the initial learning rate is 0.001. The regularization parameter k=5. The simulation results of the method of the present invention are compared with those of the spatial smoothing method, the semi-positive definite network method and the Toeplitz network method. The latter two methods perform spatial smoothing on two identical subarrays in the 7 array elements so that they can estimate two signal sources. The comparison index is the root mean square error (RMSE) of the direction finding result.

[0053] Simulation Example 1: Select [-5°, 1°] as the signal incident angle of the test data set, select the signal-to-noise ratio from -5dB to 35dB to add noise to generate test data, and generate a total of 3000 test data for testing the direction of arrival estimation performance. The comparison results are as follows Figure 3 shown.

[0054] Simulation Example 2: Select [θ,θ+△θ] as the signal incident angle of the test data set, where θ is set to -5, and △θ is set to increase from 2 to 20 with a step size of 2. The signal-to-noise ratio is selected to be 30dB and noise is added to generate test data. A total of 3000 test data are generated to test the direction of arrival estimation performance. The comparison results are shown in the figure below. Figure 4 shown.

[0055] It can be seen that the direction finding performance of the method proposed in the present invention is significantly better than that of the comparison method, and the method has better denoising and resolution capabilities at a lower signal-to-noise ratio.

[0056] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A single-snapshot direction finding method based on deep learning to reconstruct a structured covariance matrix, characterized in that: The following steps are involved: Step 1: array covariance matrix modeling; Step 2: Generate deep learning training data set; Step 3: Deep learning neural network input and output design; Step 4: Design of network training loss function based on structured covariance matrix; Step 5: Deep learning neural network architecture design and network training; Step 6: Reconstruct the semi-positive definite Toeplitz covariance matrix and estimate the direction of arrival.

2. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 1, wherein The step 1 specifically includes: In the target number range [1,K MAX ] randomly selects the target number K, where K MAX is the maximum number of targets that need to be processed for direction finding; set the number of array elements to M, the set of multiple angle grid points to Ω, the number of angles in the set to L, θ∈Ω, and randomly select K different angles θ1,θ2,...,θ in Ω K , calculate the steering vector The array flow pattern A(θ)=[a(θ1),a(θ2),...,a(θ K )],in(·) T represents transpose, d represents the array element spacing, λ represents the signal wavelength, and j represents the imaginary unit; Construct array output x=A(θ)s+η, where s∈CN(0,R s ) represents a K-dimensional random signal vector, CN(·,·) represents a complex Gaussian distribution, the first parameter position represents the mean vector, and the second parameter position represents the covariance matrix; the covariance matrix R s The calculation formula is: Where diag(·) represents the generation of a diagonal matrix with the corresponding elements as diagonal elements, and the power ratio ξ1,ξ2,...,ξ K-1 From the signal power ratio range [0,ξ MAX ] is randomly selected, ξ MAX is the maximum signal power ratio that needs to be processed for direction finding, in dB; η∈CN(0,σ 2 I M ) represents the M-dimensional noise vector, σ 2 represents the noise power, I M represents the M-dimensional identity matrix, where σ 2 The calculation formula is σ 2 =10 -SNR / 10 , SNR is the signal-to-noise ratio, which needs to be calculated from the signal-to-noise ratio range [SNR min ,SNR max ] randomly selected, SNR min and SNR max are the minimum and maximum signal-to-noise ratios, respectively, in dB; Compute array covariance matrix (·) H represents the conjugate transpose; then generates the theoretical covariance matrix for deep learning labels The theoretical covariance matrix The calculation formula is:

3. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 1, wherein The second step specifically includes: Set K MAX ,ξ MAX , SNR min , SNR max The numerical and angle sets Ω, perform Q Monte Carlo experiments on step 1, and obtain Q pairs of array output covariance matrices And the theoretical covariance matrix R i ;right and Normalization is performed to obtain and in ||·|| F Indicates the Frobenius norm of the vector; the final training data set has a total of Q samples, each sample is and constitute.

4. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 1, wherein The step three specifically includes: Take the normalized array output covariance matrix The upper triangle of Each The real part, imaginary part and The diagonal elements of are concatenated to form the eigenvector As the input of the deep learning neural network; the neural network is represented by The output of the neural network is represented as in Contains the estimated angle information, β i Expressed as represents the estimated angle, contains the estimated signal power, Contains the estimated noise power.

5. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 1, wherein The step 4 specifically includes: The loss function for training the neural network is set to Where k is the regularization parameter, ||·||1 means finding the 1-norm of the vector, vec(·) means the matrix is ​​vectorized by columns, and multiplying ∑ -1 / 2 represents whitening decorrelation, and ∑ is expressed as: in Representation matrix and Kronecker product; for the reason Reconstructed semi-positive definite, Toeplitz covariance matrix, construction It includes the following sub-steps: constructing matrix vector Construct a diagonal adjuvant matrix Semi-positive definite and Toeplitz covariance matrices for network reconstruction 6. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 1, wherein The step five specifically includes: The input layer dimension of the neural network is M 2 , the output layer dimension is 2M+1, containing n hidden layers, each hidden layer contains m neurons, and there is an activation function between each hidden layer; the training data obtained in step 2 constitutes the feature vector z, which is input into the neural network g(z) to obtain the network output Then by Reconstructing the semi-positive definite and Toeplitz covariance matrices The construction is as described in step 4; The neural network is trained using the back propagation algorithm, and the trained neural network is represented as 7. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 1, characterized in that The step six specifically includes: The test data is formed into a new vector z′ and input into the neural network In the network, we get the output Then by Reconstructing the semi-positive definite and Toeplitz covariance matrices Set the number of test data signal sources K′, and reconstruct the semi-positive definite Toeplitz covariance matrix Perform eigendecomposition and obtain the eigenvalues ​​v1≤v2≤...≤v arranged from small to large M′-1 ≤v M ; Take the eigenvectors corresponding to the MK′ minimum eigenvalues ​​to form the noise subspace E n ; Construct spectral function The angle corresponding to the peak of the spectrum function is the direction of the arrival angle, where θ′ is the search angle and a(θ′) is the search steering vector, which is expressed as 8. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 6, characterized in that: The deep learning neural network architecture in step 5 can be set to a fully connected network, a residual network or a convolutional neural network.

9. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 7, characterized in that: The direction finding method in step 6 is replaced by the Root-MUSIC algorithm.

Images