Single snapshot direction finding method based on deep learning reconstruction of structured covariance matrix

Abstract

The application discloses a single-shot direction finding method based on deep learning and reconstruction of a structured covariance matrix, comprising array covariance matrix modeling, deep learning training data set generation, deep learning network input and output, network training loss function design based on a structured covariance matrix, neural network architecture design and network training, semi-positive definite Toeplitz covariance matrix reconstruction and direction of arrival estimation. Compared with a method of directly constructing a covariance matrix by using a network output, the semi-positive definite and Toeplitz properties of the covariance matrix are maintained during network training, and whitening and decorrelation processing are performed, so that the method can obtain high-precision and high-resolution direction finding performance.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of electronic information technology, especially the field of array signal processing technology, and particularly relates to a signal processing problem of using a deep learning method to process a uniform array of a radar, a sonar, a communication receiver and the like, in particular to a single-snapshot direction finding method based on deep learning. BACKGROUND

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

[0003] Traditional DOA estimation methods all rely on modeling. However, for many problems, it is difficult to find an accurate model. The traditional method makes assumptions and approximations based on experience in the modeling process, which may lead to the lack of some features, and thus the underutilization of observed data. For this reason, researchers have begun to use deep learning for parameter estimation to solve these problems. Deep learning roughly converts the DOA estimation problem into a classification problem and a regression problem. The classification problem realizes the grid DOA estimation method, which converts the continuous angle interval into a discrete angle grid. When the actual DOA is not on the discrete grid point, the prediction result of the grid method always has an error. Optimizing the DOA estimation problem as a deep learning regression problem realizes the gridless estimation, which avoids the above problems. As in document 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 the semi-definite prior neural network is used to reconstruct the theoretical covariance matrix with semi-definite properties. Then the DOA estimation is derived from the estimated covariance matrix by multiple signal classification (MUSIC). Document 3 (Wu X, Yang X, Jia X, et al. A gridless DOA estimation method based on convolutional neural network with Toeplitz prior [J]. IEEE Signal Processing Letters, 2022, 29: 1247-1251.) is similar to document 2, the difference is that the neural network with Toeplitz prior is used to reconstruct the theoretical covariance matrix with Toeplitz properties. However, the theoretical covariance matrix is a matrix with semi-definite and Toeplitz properties, and documents 2 and 3 can only use part of its properties, and part of the properties has not been fully utilized. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide a reconstruction structured covariance matrix single-shot direction finding method based on deep learning. This method can ensure that the covariance matrix output by the network has semi-definite and Toeplitz properties at the same time, and is more consistent with the general uniform array signal processing model, thereby obtaining higher precision and higher resolution direction finding results.

[0005] The application provides a single-shot direction finding method based on deep learning reconstruction of a structured covariance matrix, and comprises the following steps:

[0006] Step one, array covariance matrix modeling;

[0007] Step two, deep learning training data set generation;

[0008] Step three, deep learning neural network input and output design;

[0009] Step four, structured covariance matrix-based network training loss function design;

[0010] Step five, deep learning neural network architecture design and network training;

[0011] Step six, semi-definite Toeplitz covariance matrix reconstruction and direction of arrival estimation.

[0012] Further, step one specifically comprises: randomly selecting a target number K in a target number range [1, K MAX ], wherein K MAX is the maximum target number to be processed for direction finding; setting the number of array elements as M, a set composed of a plurality of angle grid points as Ω, the number of angle grid points in the set as L, θ∈Ω, randomly selecting K different angles θ1, θ2,..., θ K in Ω, and calculating a steering vector An array flow pattern A(θ)=[a(θ1),a(θ2),...,a(θ K )] is formed, wherein (·) T represents transposition, d represents the array element spacing, λ represents the signal wavelength, and j represents the imaginary unit;

[0013] An array output x=A(θ)s+η is constructed, wherein 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 calculation formula of the covariance matrix R s is as follows: wherein diag(·) represents a diagonal matrix with corresponding elements as diagonal elements, and power ratios ξ1, ξ2,..., ξ K-1 are randomly selected in a signal power ratio range [0, ξ MAX ], wherein ξ MAX is the maximum signal power ratio to be processed for direction finding, and the unit is dB; η∈CN(0,σ 2 I M ) represents an M-dimensional noise vector, σ 2 represents the noise power, and I M represents an M-dimensional unit matrix, wherein 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 generates the theoretical covariance matrix for deep learning labels The theoretical covariance matrix The calculation formula is:

[0015] Furthermore, step 2 specifically includes: setting 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;

[0016] Furthermore, step three specifically includes: taking 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;

[0017] Further, step four specifically includes: the loss function of the neural network is set as where k is a regularization parameter, ||·||1 represents the 1-norm of a vector, vec(·) represents the column-wise vectorization of a matrix, and ∑ -1 / 2 represents the whitening decorrelation, and ∑ represents

[0018]

[0019] where represents the matrix and the Kronecker product of is a semi-positive definite, Toeplitz covariance matrix reconstructed by , and the matrix is constructed The diagonal auxiliary matrix is constructed

[0020] Further, step five specifically includes: the input layer dimension M of the neural network is set as 2 , the output layer dimension is 2M+1, there are 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 two is constructed into the feature vector z, which is input into the neural network g(z) to obtain the network output The semi-positive definite, Toeplitz covariance matrix is reconstructed by , and the construction is as described in step four;

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

[0022] Further, step six specifically includes: the test data is constructed into a new vector z', which is input into the neural network to obtain the network output The semi-positive definite, Toeplitz covariance matrix is reconstructed by The number K' of test data signal sources is set, and the reconstructed semi-positive definite, Toeplitz covariance matrix is subjected to eigenvalue decomposition to obtain eigenvalues v1≤v2≤2≤v M′-1 ≤v M ; the noise subspace E is constructed by taking the eigenvectors corresponding to the M-K' smallest eigenvalues n ; and the spectral function ​The angle corresponding to the peak of the spectrum function is the direction of arrival, wherein θ' is a search angle, a(θ') is a search steering vector, and is expressed as a(θ')=[1,e -j2πd(sinθ′) / λ ,...,e -j2πd(M-1)(sinθ′) / λ ] T .

[0023] Further, the deep learning neural network architecture of step five is set as a full connection network, a residual network or a convolutional neural network.

[0024] Further, the direction finding method in step six is replaced by Root-MUSIC algorithm to avoid spectrum peak search and reduce the time complexity of calculation.

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

[0026] 1. In the method proposed in the present application, the covariance matrix for direction of arrival estimation is constructed by the network output auxiliary matrix, which, compared with the method of directly constructing the covariance matrix with the network output, ensures the semi-positive definite and Toeplitz properties of the constructed covariance matrix, making it more consistent with the signal processing model of the general uniform array.

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

[0028] 2. The method of the present application performs whitening decorrelation processing in the deep learning network model, reduces the correlation between noise components, and thus improves the accuracy of direction of arrival estimation. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is the overall flowchart of the method of the present application

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

[0031] Figure 3 is the direction of arrival estimation result of the present application under different signal-to-noise ratios

[0032] Figure 4 is the direction of arrival estimation result of the present application under different angle intervals DETAILED DESCRIPTION

[0033] The technical solutions of the present application will be further specifically described below by means of specific embodiments and in combination with the drawings.

[0034] Example 1

[0035] Referring to Figure 1 , the flowchart of an optional example of the single-shot direction finding method based on deep learning reconstruction structured covariance matrix proposed in the present application, the method can include:

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

[0037] The array output x = A(θ)s + η is constructed, 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 calculation formula of the covariance matrix R s is as follows: where diag(·) represents generating a diagonal matrix with corresponding elements as diagonal elements, and power ratios ξ1, ξ2,..., ξ K-1 are randomly selected in the signal power ratio range [0, ξ MAX ], and ξ MAX is the maximum signal power ratio to be processed, with a unit of dB; η ∈ CN(0, σ 2 I M ) represents an M-dimensional noise vector, σ 2 represents the noise power, and I M represents an M-dimensional unit matrix, where the calculation formula of σ 2 is σ 2 = 10 -SNR / 10 , SNR is the signal-to-noise ratio, which is randomly selected from the signal-to-noise ratio range [SNR min , SNR max ], SNR min and SNR max are the minimum and maximum signal-to-noise ratios, respectively, with a unit of dB;

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

[0039] Step two, deep learning training data set generation: set KMAX , ξ MAX , SNR min , SNR max The set of values and angles Ω, Q times of Monte Carlo experiments are performed on step one to obtain Q pairs of array output covariance matrices and theoretical covariance matrices R i ; and and are normalized to obtain and where ||·‖ F represents the Frobenius norm of the vector; the final training data set has a total of Q samples, each sample is composed of and ;

[0040] Step three, input and output design of deep learning neural network: taking the upper triangular of the normalized array output covariance matrix by column vectorization The real part and imaginary part of each and the diagonal element of are spliced to form a feature vector as the input of the deep learning neural network; the neural network is represented as The output of the neural network is represented as where contains the estimated angle information, β i is represented as represents the estimated angle, contains the estimated signal power, contains the estimated noise power;

[0041] Step four, network training loss function design based on structured covariance matrix: the loss function of the neural network is set as where k is the regularization parameter, ||·||1 represents the 1-norm of the vector, vec(·) represents the column vectorization of the matrix, and left multiplication ∑ -1 / 2 represents white decorrelation, and ∑ is represented as:

[0042]

[0043] where represents the Kronecker product of the matrix and ; is a semi-positive definite, Toeplitz covariance matrix reconstructed by , construct includes the following sub-steps: construct matrix vector construct diagonal auxiliary matrix Reconstruction of semi-positive, Toeplitz covariance matrix

[0044] Step five, 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 containing m neurons, and there is an activation function between each hidden layer; the training data obtained in step two is used to form the feature vector z, which is input into the neural network g(z) to obtain the network output Reconstruction of semi-positive, Toeplitz covariance matrix Reconstruction of semi-positive, Toeplitz covariance matrix The construction is as described in step four;

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

[0046] Step six, reconstruction of semi-positive, Toeplitz covariance matrix and DOA estimation; the test data is used to form a new vector z', which is input into the neural network to obtain the network output Reconstruction of semi-positive, Toeplitz covariance matrix Reconstruction of semi-positive, Toeplitz covariance matrix Set the number of test data signal sources K', and perform eigenvalue decomposition on the reconstructed semi-positive, Toeplitz covariance matrix to obtain eigenvalues v1≤v2≤2≤v M′-1 ≤v M ; take the M-K' smallest eigenvalues corresponding to the eigenvectors to form the noise subspace E n ; construct the spectral function The peak value of the spectral function corresponds to the angle of the DOA, where θ' is the search angle, a(θ') is the search steering vector, and is represented 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 by 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 two:

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

[0051] In order to verify the performance of the application, the following simulation examples are verified, and the experimental results are compared with spatial smoothing, semi-definite network (see patent 1: Pan Yujian, Xu Xin, et al. Intersecting array direction of arrival estimation method based on deep learning reconstruction covariance matrix [P]. China: CN202210661582.2, 2022-08-09.), topliz network (see patent 2: Pan Yujian, Zhao Zewei, Xu Xin, et al. A non-ideal non-uniform array single snapshot direction finding method based on deep learning [P]. China: CN202211515822.4, 2023-03-07.) are compared.

[0052] The array is set to a 7-element uniform linear array, and the angle range of the 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] dB. The target number range is 2, and the maximum signal power ratio ξ MAX = 0.3. A total of 219600 training data are generated by using the foregoing method. The specific network structure of the deep learning network is set as shown in Figure 2 The input layer dimension of the deep learning network is 49, the output layer dimension is 15, it contains 6 hidden layers, each hidden layer contains 2048 neurons, and there is an activation function between each hidden layer. The activation function uses ReLu function. The optimizer is Adam, the maximum epoch number is set to 200, the Batch size is set to 1024, the initial learning rate is 0.001. The regularization parameter k = 5. The simulation results of the method of the application and the spatial smoothing method, the semi-definite network method and the topliz network method are compared. The latter two methods perform spatial smoothing on two same sub-arrays in 7 elements to 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 incidence angle of the test data set, select the signal-to-noise ratio from -5dB to 35dB to add noise to generate test data, a total of 3000 test data are generated for testing the direction of arrival estimation performance. The comparison results are shown in Figure 3

[0054] ​Simulation example 2: the signal incident angle of the test data set is selected as [θ, θ+△θ], wherein θ is set as-5, and △θ is set to increase from 2 to 20 with a step of 2. The signal-to-noise ratio is selected as 30dB to add noise to generate test data, and a total of 3000 test data are generated for testing the direction-of-arrival estimation performance. The comparison result is as shown in the following table. Figure 4

[0055] It can be seen that the direction finding performance of the method is obviously better than that of the comparative method, and the method has better denoising ability and resolution ability at a lower signal-to-noise ratio.

[0056] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.​

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: semi-positive definite Toeplitz covariance matrix reconstruction and direction of arrival estimation; in, The second step specifically includes: setting 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; The step three specifically includes: taking 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; The fourth step specifically includes: setting the loss function of the neural network training 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 multiplied by Σ on the left. -1 / 2 represents whitening decorrelation, ∑ is represented by in Representation matrix and Kronecker product; for the 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 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 the array output x = A (θ) s + η, where represents a K-dimensional random signal vector, 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 The maximum signal power ratio that needs to be processed for direction finding is in dB; 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 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 4. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 1, wherein 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 5. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 3, wherein The deep learning neural network architecture in step five can be set to a fully connected network, a residual network or a convolutional neural network.

6. The single-snapshot direction finding method based on deep learning and reconstructing structured covariance matrix according to claim 4, wherein The direction finding method in step 6 is replaced by the Root-MUSIC algorithm.

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