Coherent signal arrival direction estimation method and device based on deep convolutional network

Abstract

The invention provides a coherent signal arrival direction estimation method and device based on a deep convolutional network, and belongs to the field of array signal processing. The method comprises the following steps: receiving a to-be-detected signal containing a coherent signal by using a uniform linear array antenna to obtain an array receiving data matrix and extract a covariance matrix; forming an input feature vector by right upper triangular elements divided from a diagonal line in the covariance matrix, inputting the input feature vector into a covariance estimation model formed by a deep convolutional network, obtaining an estimation value of the right upper triangular elements under an ideal incoherent condition, and reconstructing the estimation value to obtain a covariance matrix estimation value; and performing characteristic decomposition on the covariance matrix estimation value, and generating a spatial spectrum by using a MUSIC algorithm to obtain an estimation result of the signal arrival direction. According to the method, the noise-containing mixed signal covariance matrix is mapped into the ideal incoherent noise-free signal covariance matrix through a physical constraint supervised learning framework, so that the estimation precision and robustness of the MUSIC algorithm in a coherent scene are improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of array signal processing and deep learning, and particularly relates to a coherent signal direction of arrival estimation method and device based on a deep convolutional network. BACKGROUND

[0002] In the field of array signal processing, the estimation of the direction of arrival (DOA) of signals is one of the key technologies for determining the spatial position of targets or signal sources. Classic high-resolution DOA estimation algorithms, such as the multiple signal classification (MUSIC) algorithm and the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, can achieve good estimation performance when the incident signals are mutually independent (non-coherent). However, when there are multiple signal sources with high correlation or even complete coherence, the performance of traditional algorithms will decrease sharply or even fail, which is manifested as a lack of rank in the covariance matrix, making it difficult to decompose the subspaces and accurately distinguish multiple coherent signal sources, and thus causing the DOA estimation results to deviate or be unable to be estimated. In order to solve the problem of DOA estimation of coherent signal sources, de-coherent techniques such as spatial smoothing are usually used, but such methods will sacrifice the array aperture and resolution capability, making it difficult to effectively handle completely coherent signals while ensuring high precision.

[0003] The forward-backward spatial smoothing (FBSS) method constructs a full-rank matrix by respectively performing spatial smoothing on the original snapshot and the reverse snapshot, and then weighting and merging the covariance matrices of the two to construct a full-rank matrix; however, the effective degrees of freedom of this method are only 2 / 3 of the number of sensors, and the performance is limited when the number of array elements is small or the number of snapshots is limited.

[0004] The kernel spectrum estimation (KS) method maps the array observation data to a high-dimensional kernel space, uses a kernel function to convert the autocorrelation and cross-correlation information of coherent signals into virtual independent signals, and performs subspace decomposition in the kernel space to achieve DOA estimation; however, this method has extremely high computational complexity, making it difficult to meet real-time processing requirements.

[0005] The reconstruction based on Toeplitz structure (RCRT) method is proposed in the literature, which uses the 2M+1 elements contained in each row of the original covariance matrix to construct an MxM matrix with Toeplitz characteristics to restore the full rank; where M represents the number of array elements in a uniform linear array, but this method only uses about half of the information in the covariance matrix, which has the risk of information loss.

[0006] The minimum Toeplitz operator (MTOEP) method reconstructs the covariance matrix by defining a Toeplitz rectifier operator to fully utilize all covariance information; however, the number of estimable signals is still limited to half of the number of sensors, which cannot effectively handle scenarios where the number of signal sources is more than half.

[0007] Forward-backward linear prediction (FBLP) method de-correlates in the DOA estimation process by constructing a set of high-order linear prediction equations; but the method is extremely sensitive to the estimated parameters in the equation, and any small error can cause the final angle estimation to deviate significantly and unpredictably.

[0008] Forward-backward convolution kernel (FBCK) algorithm is proposed in the literature, which simultaneously applies forward and backward convolution kernel operations to the signal space matrix at a given time to restore the matrix rank equal to the number of signal sources and reconstruct the signal covariance matrix while keeping the array aperture unchanged; but this method relies on the moving array technology and the quasi-stationary assumption of the signal, and the computational complexity is higher than that of the traditional spatial smoothing method, and when the number of signal sources is high, the performance will decrease significantly.

[0009] In recent years, typical neural network DOA estimation methods have their own advantages and disadvantages: convolutional neural network CNN is good at extracting spatial patterns from two-dimensional features, but needs to assume that the signal is independent, and needs additional decorrelation processing if coherent sources are encountered, and the output is limited to grid resolution; fully connected deep neural network DNN provides end-to-end approximation, but lacks endogenous processing capability for coherent signals and unknown source numbers; the self-encoder introduces automatic denoising and decorrelation methods, which can solve the problem of coherent sources to some extent, but the method relies on sufficient training and the process is complex. SUMMARY

[0010] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide a coherent signal direction of arrival estimation method and device based on a deep convolutional network. Through a physically constrained supervised learning framework, the noisy mixed signal covariance matrix is mapped to an ideal non-coherent noise-free signal covariance matrix, and the Toeplitz structure is restored, thereby improving the estimation accuracy and robustness of the MUSIC algorithm in the coherent scene.

[0011] The first aspect of the present application provides a coherent signal direction of arrival estimation method based on a deep convolutional network, comprising:

[0012] A uniform linear array antenna is used to receive a to-be-measured signal to obtain an array received data matrix, wherein the to-be-measured signal contains coherent signals;

[0013] The covariance matrix of the array received data matrix is calculated, and the upper right triangular elements divided from the diagonal line in the covariance matrix are extracted to form an input feature vector;

[0014] The input feature vector is input into a preset covariance estimation model to obtain an estimated value of the upper right triangular element under ideal non-coherent conditions; wherein the model uses a deep convolutional neural network; and the estimated value of the upper right triangular element is reconstructed to generate a covariance matrix estimate under ideal non-coherent conditions;

[0015] The covariance matrix estimate is subjected to eigendecomposition, and a spatial spectrum is generated using a MUSIC algorithm to obtain an estimation result of the signal arrival direction.

[0016] In a specific embodiment of the present invention, before inputting the input feature vector into a preset covariance estimation model, the method further includes:

[0017] training the covariance estimation model;

[0018] The training of the covariance estimation model comprises:

[0019] 1) Use the same uniform linear array antenna as that used to obtain the signal to be tested to perform actual sampling or simulated sampling to obtain multiple sets of training signal data, each set of training signal data contains a mixed signal data matrix composed of coherent signals and incoherent signals and the corresponding ideal data matrix consisting of ideal incoherent signals

[0020] 2) Based on the result of step 1), extract the covariance matrix corresponding to the training signal data;

[0021] Among them, in each set of training signal data, The corresponding covariance matrix is ​​denoted as R train , The corresponding covariance matrix is ​​denoted as R ideal ;

[0022] 3) extracting the upper right triangular elements of the covariance matrix obtained in step 2);

[0023] Among them, R train and R ideal Extract the upper right triangle elements divided from the diagonal line respectively and get R train The corresponding upper right triangular elements are recorded as and R ideal The corresponding upper right triangular elements are recorded as

[0024] 4) The obtained As the input data of a single sample, the corresponding As the label of the sample, a data sample is formed, and all data samples constitute a sample set;

[0025] Divide the sample set according to the preset ratio to obtain the training set and the validation set;

[0026] 5) Constructing a covariance estimation model, using the training set obtained in step 4) to train the covariance estimation model and using the validation set to test it, and obtaining a trained covariance estimation model after the test passes.

[0027] In one specific embodiment of the present application, the covariance matrix acquisition method comprises:

[0028] For any data matrix received by the uniform linear array antenna, the size of which is MxN, M is the number of elements of the uniform linear array antenna, and N is the number of snapshots; an Mx1 signal vector x(n) corresponding to each snapshot in the received data matrix is extracted column by column, n = 1, …, N, and a covariance matrix corresponding to the received data matrix is obtained according to a covariance calculation expression

[0029] In one specific embodiment of the present application, it further comprises:

[0030] When training the covariance estimation model, a composite loss function is used:

[0031]

[0032] Wherein:

[0033] denotes a Toeplitz rectifier operator; J is an anti-diagonal unit matrix; I M is an MxM unit matrix; λ is a weight coefficient for balancing the influence between the data fitting term and the Toeplitz structure constraint term; ⊙ is the Hadamard product of matrices; ||·||F F is the Frobenius norm of the matrix; m is the index of the diagonal line in the Toeplitz structure constraint.

[0034] In one specific embodiment of the present application, it further comprises:

[0035] When acquiring training signal data through simulation sampling, an array manifold matrix A is calculated according to the direction of arrival (DOA) angle of the signal, a(θ i ) is the array manifold vector, d is the element spacing, λ is the wavelength, j is the imaginary unit, and m is the mth element in the array antenna;

[0036] Two baseband signal matrices are respectively constructed: a matrix S simulates an actual scenario containing coherent signal sources and incoherent signal sources, wherein the coherent signals are generated by multiplying a common baseband signal by a random factor, and the incoherent signals are independently generated; a matrix S i corresponds to an ideal case where different direction signal sources are independent;

[0037] According to a preset signal-to-noise ratio, a complex Gaussian white noise matrix N(t) matching the number of elements and the number of snapshots is generated;

[0038] The mixed signal data matrix is synthesized ​and the corresponding ideal data matrix

[0039] The second aspect of the present application provides a coherent signal direction of arrival estimation device based on a deep convolutional network, comprising:

[0040] The signal acquisition module is configured to receive the to-be-tested signal by using the uniform linear array antenna to obtain an array receiving data matrix, wherein the to-be-tested signal contains coherent signals.

[0041] The input feature vector extraction module is configured to calculate the covariance matrix of the array receiving data matrix, and extract the upper right triangular elements divided from the diagonal line in the covariance matrix to form an input feature vector.

[0042] The covariance estimation module is configured to input the input feature vector into a preset covariance estimation model to obtain the estimated value of the upper right triangular element under ideal non-coherent conditions; wherein the model adopts a deep convolutional neural network; and the estimated value of the upper right triangular element is reconstructed to generate the covariance matrix estimation value under ideal non-coherent conditions.

[0043] The signal direction of arrival estimation module is configured to perform eigenvalue decomposition on the covariance matrix estimation value, generate a spatial spectrum by using the MUSIC algorithm, and obtain the estimation result of the signal direction of arrival.

[0044] In one specific embodiment of the present application, before the input feature vector is input into the preset covariance estimation model, the following steps are further included:

[0045] The covariance estimation model is trained.

[0046] The training of the covariance estimation model includes:

[0047] 1) The same uniform linear array antenna as that used to obtain the to-be-tested signal is used to perform actual sampling or simulation sampling to obtain a plurality of groups of training signal data, wherein each group of training signal data contains a mixed signal data matrix composed of coherent signals and non-coherent signals and the corresponding ideal data matrix composed of ideal non-coherent signals

[0048] 2) Based on the result of step 1), the covariance matrix corresponding to the training signal data is extracted.

[0049] In each group of training signal data, the corresponding covariance matrix is denoted as R train , the corresponding covariance matrix is denoted as R ideal .

[0050] 3) extracting right upper triangular elements of the covariance matrix obtained in step 2) respectively;

[0051] wherein, R train and R ideal extracting right upper triangular elements divided from the diagonal respectively, to obtain R train the corresponding right upper triangular element is denoted as and R ideal the corresponding right upper triangular element is denoted as

[0052] 4) taking R obtained in step 3) as input data of a single sample, taking the corresponding R as the label of the sample, to form a data sample, and all data samples constitute a sample set;

[0053] dividing the sample set according to a preset proportion to obtain a training set and a verification set;

[0054] 5) constructing a covariance estimation model, training the covariance estimation model by using the training set obtained in step 4) and verifying by using the verification set, and obtaining the trained covariance estimation model after the verification is passed.

[0055] In one specific embodiment of the present application, the covariance matrix acquisition method comprises:

[0056] For any data matrix received by the uniform linear array antenna, the size of which is MxN, M is the number of elements of the uniform linear array antenna, and N is the number of snapshots; extracting an Mx1 signal vector x(n) corresponding to each snapshot in the received data matrix according to column, n = 1, …, N, and obtaining the covariance matrix corresponding to the received data matrix according to the covariance calculation expression .

[0057] In one specific embodiment of the present application, it further comprises:

[0058] When training the covariance estimation model, a compound loss function is used:

[0059]

[0060] wherein:

[0061] denotes a Toeplitz rectifier operator; J is an inverse diagonal unit matrix; I M is an MxM unit matrix; λ is a weight coefficient for balancing the influence between the data fitting term and the Toeplitz structure constraint term; and is the Hadamard product of matrices; and is the Frobenius norm of matrices. Fis the Frobenius norm of matrix; m is the index of diagonal line in Toeplitz structure constraint.

[0062] In one specific embodiment of the present application, further comprising:

[0063] When acquiring training signal data by simulation sampling, an array manifold matrix A is calculated according to a signal direction of arrival (DOA) angle, a(θ i is an array manifold vector, d is an element spacing, λ is a wavelength, j is an imaginary unit, and m is the mth element in the array antenna;

[0064] Two baseband signal matrices are respectively constructed: a matrix S simulates an actual scene containing coherent signal sources and incoherent signal sources, wherein the coherent signals are generated by multiplying a common baseband signal by a random factor, and the incoherent signals are independently generated; and a matrix S i Corresponding to the ideal case of independent signal sources in different directions;

[0065] According to a preset signal-to-noise ratio, a complex Gaussian white noise matrix N(t) matching the number of elements and the number of shots is generated;

[0066] The mixed signal data matrix is synthesized and the corresponding ideal data matrix

[0067] The third aspect of the present application provides an electronic device, comprising:

[0068] At least one processor; and a memory connected in communication with the at least one processor;

[0069] The memory stores instructions executable by the at least one processor, and the instructions are configured to execute the above-mentioned coherent signal direction of arrival estimation method based on a deep convolutional network.

[0070] The fourth aspect of the present application provides a computer readable storage medium, which stores computer instructions for causing the computer to execute the above-mentioned coherent signal direction of arrival estimation method based on a deep convolutional network.

[0071] The present application has the characteristics and advantages of:

[0072] The application fuses the prior knowledge of array signal processing into the network through a Toeplitz constraint term, avoids the uncertainty of a black box model, layer normalization and a composite loss function design significantly improve the estimation accuracy under a low signal-to-noise ratio and improve the robustness, the full rank characteristic of the reconstructed covariance matrix is restored, the MUSIC is directly applied, and no additional de-coherent preprocessing is required, the network inference time is fast, and is suitable for real-time processing scenes. The application can realize high-precision and low-delay angle estimation of multiple targets under a multipath and coherent scattering environment, and improve the target tracking and identification performance. The application has significant application value in key fields such as wireless communication, radar detection, sonar positioning and the like: in a 5G / 6G base station array, high-precision positioning of high-density user equipment can be realized, and the positioning error caused by the multipath effect is reduced; in an airborne radar system, coherent interference and target echoes can be effectively distinguished, and the target detection capability in a complex electromagnetic environment is improved; in the field of marine sonar detection, the resolution limit of a traditional method on a coherent sound source is broken through, and more accurate azimuth information is provided for submarine target identification and tracking. BRIEF DESCRIPTION OF DRAWINGS

[0073] Figure 1 A flowchart of a coherent signal direction of arrival estimation method based on a deep convolutional network according to an embodiment of the application.

[0074] Figure 2 A spatial spectrum estimation result graph in a coherent signal scenario according to an embodiment of the application.

[0075] Figure 3 A root mean square error comparison curve of the method and a traditional method under different signal-to-noise ratios according to an embodiment of the application.

[0076] Figure 4 A root mean square error comparison curve of the method and a traditional method under different snapshot numbers according to an embodiment of the application. DETAILED DESCRIPTION

[0077] The application provides a coherent signal direction of arrival estimation method and device based on a deep convolutional network, which is described in detail as follows in combination with the drawings and specific embodiments.

[0078] An embodiment of the first aspect of the application provides a coherent signal direction of arrival estimation method based on a deep convolutional network, which comprises:

[0079] A uniform linear array antenna is used to receive a to-be-measured signal to obtain an array receiving data matrix, wherein the to-be-measured signal contains a coherent signal;

[0080] A covariance matrix of the array receiving data matrix is calculated, and right upper triangular elements divided from the diagonal line in the covariance matrix are extracted to form an input feature vector.

[0081] inputting the input feature vector into a preset covariance estimation model to obtain an estimated value of an upper right triangular element under ideal non-coherent conditions, wherein the model adopts a deep convolutional neural network; and reconstructing the estimated value of the upper right triangular element to generate a covariance matrix estimation value under ideal non-coherent conditions;

[0082] performing eigenvalue decomposition on the covariance matrix estimation value and generating a spatial spectrum by using a MUSIC algorithm to obtain an estimation result of a signal direction of arrival.

[0083] In one specific embodiment of the present application, the coherent signal direction of arrival estimation method based on a deep convolutional network is divided into a training stage and a prediction stage, and the overall flow of the method is as shown in Figure 1 The method comprises the following steps:

[0084] 1) Training stage.

[0085] 1-1) Collecting training signal data used for constructing a training data set.

[0086] In the present embodiment, the training signal data can be obtained by actual sampling or simulation sampling, and preferably, the training signal data is obtained by simulation.

[0087] When the training signal data is obtained, it is assumed that a uniform linear array antenna is composed of M array elements, and there are K incident signal sources, wherein K is less than or equal to M. Some incident signal sources emit completely identical signals (i.e., the signal sources are coherent). In the present embodiment, the number C of coherent signal sources can be randomly selected, and C is less than or equal to K. In the present embodiment, the DOA angle corresponding to any signal source is:

[0088]

[0089] In one specific embodiment of the present application, the array manifold matrix A is calculated according to the DOA angle, a(θ i ) is the array manifold vector.

[0090] d is the array element spacing, λ is the wavelength, j is the imaginary unit, and m represents the mth array element in the array antenna.

[0091] The method further synthesizes an array received signal and estimates a covariance matrix thereof, and specifically comprises the following steps: first, two baseband signal matrices are constructed: a matrix S simulates an actual scene containing coherent signal sources and non-coherent signal sources, wherein the coherent signals are generated by multiplying a common baseband signal by a random factor, and the non-coherent signals are independently generated, and a matrix X is a matrix of the array received signal. iThe signal sources corresponding to different directions are independent ideal cases; then, according to a preset signal-to-noise ratio, a complex Gaussian white noise matrix N(t) matching the number of array elements and the number of snapshots is generated; subsequently, actual received signals, i.e. mixed signal data matrix and corresponding ideal incoherent signals, i.e. ideal data matrix When the signals arrive at the uniform linear array, M array elements receive signals with specific phase and amplitude responses, which together form an M*N-dimensional mixed signal data matrix where N is the number of snapshots, containing coherent and incoherent mixed signals, containing only incoherent signals, and are all M*N-dimensional, and corresponding form a set of training signal data.

[0092] In one specific embodiment of the present application, M=25 and K=16, wherein the array element spacing is half a wavelength d=λ / 2, θ i =-60°+(i-1)·8°, i=1, 2,..., 16, the signal-to-noise ratio (SNR) during data generation ranges from -20 to 20 dB, and the number of snapshots ranges from 50 to 500, thereby generating a 25*16-dimensional mixed signal data matrix composed of mixed signals received by 25 array elements In this embodiment, 10000 sets of mixed signal data matrixes containing coherent and incoherent mixed signals are collected Meanwhile, 10000 sets of 25*16-dimensional ideal data matrixes composed of ideal incoherent signals received by 25 array elements are generated

[0093] 1-2) Obtain the covariance matrix corresponding to the training signal data of step 1-1).

[0094] In this embodiment, for each M*N-dimensional matrix in each set of training signal data, an M*1-dimensional signal vector x(n) corresponding to each snapshot in the matrix is extracted by column, n=1,..., N, and then the covariance calculation expression is used to obtain the covariance matrix corresponding to the matrix, which has a size of M*M. In each set of training signal data, the covariance matrix corresponding thereto is denoted as R train , the covariance matrix corresponding thereto is denoted as R ideal .

[0095] After processing all the training signal data, all the training sample covariance matrixes form a training sample covariance matrix set, and all the label sample covariance matrixes form a label sample covariance matrix set

[0096] In a specific embodiment of the present invention, after processing the 25×16 dimensional matrix in each set of training signal data, a 25×25 dimensional covariance matrix is ​​obtained.

[0097] 1-3) Extract the upper right triangular elements of the covariance matrix obtained in step 1-2).

[0098] In this embodiment, R train and R ideal Extract the upper right triangle elements (including the main diagonal elements) divided from the diagonal respectively to get R train The corresponding upper right triangular elements are recorded as and R ideal The corresponding upper right triangular elements are recorded as

[0099] 1-4) Use the results of step 1-3) to construct a training set and a validation set.

[0100] In this embodiment, the step 1-3) obtained As the input data of a single sample, the corresponding As the label of the sample, it is paired one by one with the input data to form a data sample, and all data samples constitute a sample set.

[0101] In this embodiment, 80% of the samples are randomly selected from the sample set to form a training set, and the remaining 20% ​​of the samples form a validation set.

[0102] 1-5) Construct a covariance estimation model, use the training set obtained in step 1-4) to train the covariance estimation model and use the validation set to test it, and obtain the trained covariance estimation model after the test passes.

[0103] In this embodiment, the covariance estimation model adopts a deep convolutional network, which may include multiple convolutional layers, pooling layers, and a fully connected output layer, for extracting spatial features from the input array signal feature matrix and outputting covariance estimation results.

[0104] In a specific embodiment of the present invention, the covariance estimation model includes an input layer, three convolutional layers, and an output layer connected in sequence; specifically, as follows:

[0105] Input layer:

[0106] The input data is a vector of dimension 650, which comes from the upper right triangular elements of the 25×25 covariance matrix The input shape is [batch_size,1,650].

[0107] Hidden layer:

[0108] 3 layers of convolutional layers, and the specific structure is as follows:

[0109] The first convolutional layer: the number of input channels is 1, the number of output channels is 64; the convolution kernel size is 9, the padding is 4; the activation function is ReLU; the normalization method is LayerNorm; and the Dropout probability is 0.3.

[0110] The second convolutional layer: the number of input channels is 64, the number of output channels is 32; the convolution kernel size is 7, the padding is 3; the activation function is ReLU; the normalization method is LayerNorm; and the Dropout probability is 0.3.

[0111] The third convolutional layer: the number of input channels is 32, the number of output channels is 16; the convolution kernel size is 5, the padding is 2; the activation function is ReLU; the normalization method is LayerNorm; and the Dropout probability is 0.3.

[0112] The output layer: one layer of convolutional layer is used as the output layer in the embodiment, the number of input channels is 16, the number of output channels is 1; the convolution kernel size is 3, and the padding is 1.

[0113] The estimation value of the model finally output in the embodiment is , the dimension of the output data is the same as that of the input data (650 dimensions), and the estimation value can be restored to a 25x25 covariance matrix after reconstruction.

[0114] The DOA estimation model is trained by using the training set obtained in steps 1-4), and in one specific embodiment of the application, the training process of the model is as follows:

[0115] The training data is input into the model in batches (batch_size=64), and the input dimension is [batch_size, 1, 650]. The network is trained by using an Adam optimizer, and the initial learning rate is 10 -3 -3, and the training period is 100 epochs.

[0116] During the training process, a compound loss function is used:

[0117]

[0118] The error between the network output and the ideal non-coherent covariance matrix is calculated, and then the network weight parameters are updated through back propagation.

[0119] Wherein:

[0120] indicates a Toeplitz rectifier operator, which is used to force the matrix to satisfy the diagonal consistency; J is an anti-diagonal unit matrix; and IM is an M×M dimensional identity matrix; λ is a weight coefficient used to weigh the influence between the data fitting term and the Toeplitz structure constraint term; ⊙ is the Hadamard product of the matrix (element-by-element multiplication); ||·|| F is the Frobenius norm of the matrix; m is the index of the diagonal in the Toeplitz structure constraint.

[0121] In this embodiment, the loss function is optimized through continuous iteration. The specific optimization process is as follows:

[0122] The network calculates the predicted output of the current batch of input samples through forward propagation; then, based on the above loss function, calculates the error between the predicted output and the ideal incoherent signal covariance matrix; then, through backpropagation of the error, the Adam optimizer is used to update the network parameters, and the optimization goal is to minimize the value of the loss function.

[0123] During training, the model is converged by monitoring the loss function values ​​on the training and validation sets. The model is considered converged when the validation set loss function no longer decreases significantly over multiple epochs, and the training and validation set loss functions tend to be stable. This completes the covariance estimation model.

[0124] The loss function designed in the method described in this embodiment has the following advantages: the mean squared error term ensures that the network output numerically approximates the ideal incoherent signal covariance matrix. Furthermore, the Toeplitz structural constraint term incorporates prior knowledge of array stationarity into training, effectively regularizing the output matrix to restore its Hermitian–Toeplitz properties. This design not only solves coherence and reconstructs the complete noise subspace to improve the accuracy of the MUSIC algorithm, but also suppresses overfitting and enhances robustness under low SNR and few-sample conditions. It also accelerates training convergence and flexibly balances fitting and constraints through the weight coefficient λ, ultimately resulting in a stable and highly accurate covariance estimation model.

[0125] 2) Estimation stage.

[0126] 2-1) Obtain array reception data of the signal to be tested.

[0127] In this embodiment, when the DOA of an unknown signal source needs to be estimated, a uniform linear array antenna composed of M array elements, the same as in the training phase, is used to receive the signal to be measured to obtain an array reception data matrix. The structure and spacing d of the array reception data matrix remain consistent with those in the training phase.

[0128] 2-2) Calculate the covariance matrix of the array received data obtained in step 2-1), and then extract the upper right triangular elements (including the main diagonal elements) of the covariance matrix divided from the diagonal, and splice the real parts and imaginary parts of these complex elements respectively in a fixed order to form an input eigenvector.

[0129] 2-3) Input the input eigenvector obtained in step 2-2) into the covariance estimation model trained in step 1), and the model outputs the estimated value of the upper right triangular element under ideal non-coherent conditions; and the estimated value is reconstructed to generate the covariance matrix estimation value under ideal non-coherent conditions

[0130] 2-4) Perform eigenvalue decomposition on , and generate a spatial spectrum by using the MUSIC algorithm to obtain the estimation result of the DOA.

[0131] Further, Figure 2 is a spatial spectrum estimation result diagram in a coherent signal scenario in one embodiment of the present application. Figure 2 In the diagram, the range of signal arrival angles is given on the horizontal axis, the solid line corresponds to the arrival angle of the coherent signal, and the specific arrival angles are [-60.0, -52.0, -12.0, -4.0, 4.0, 12.0, 52.0, 60.0], and the dashed line corresponds to the arrival angle of the non-coherent signal, and the specific arrival angles are [-44.0, -36.0, -28.0, -20.0, 20.0, 28.0, 36.0, 44.0]. The vertical axis is the normalized MUSIC spectrum value (dB). It can be seen that when the coherent source and the non-coherent source are mixed to be incident, the reconstructed covariance matrix by the method can form sharp spectral peaks at all real arrival angles after MUSIC processing, and the spectral peaks of the non-coherent source and the coherent source are accurately separated and positioned, indicating that the complete noise subspace is recovered after the matrix is reconstructed, and thus the accurate estimation of the coherent source is realized.

[0132] Figure 3 is a root mean square error comparison curve diagram of the method described in the embodiment and the traditional method under different signal-to-noise ratios in one embodiment of the present application. Figure 3In the figure, the horizontal axis is the signal-to-noise ratio (SNR) (unit: dB), from -20 dB to +20 dB; and each curve in the figure corresponds to the DCN (i.e., the method described in the embodiment), and the RCRT, FBSS, FBLP, FBCK, MTOEP, KS and several other typical traditional de-coherent or Toeplitz reconstruction methods. As the SNR changes from low to high, it can be seen that the curve of the method described in the embodiment is almost close to the horizontal axis, and the RMSE is extremely low in the entire SNR range; while the RMSE of the traditional method rises sharply at low SNR (<0 dB), and only improves at high SNR. Therefore, it is shown that the method described in the embodiment can stably and accurately estimate the DOA of the coherent signal under the condition of low signal-to-noise ratio, and the robustness is significantly better than that of the existing method.

[0133] Figure 4 For the root mean square error comparison curve of the method described in the embodiment and the traditional method under different snapshot quantities in one specific embodiment of the application. Figure 4 In the figure, the horizontal axis is the number of snapshots (the number of snapshots, i.e., the number of time samples), from 0 to 500; and the vertical axis is also the RMSE (degree) of DOA estimation. The meaning of each curve is the same as Figure 3 With the increase of the number of snapshots, the RMSE of all methods decreases, but the curve of the application (DCN) is extremely low and reaches the convergence level after about 100 snapshots, while the traditional method still maintains a high error even at 500 snapshots. The result shows that the method of reconstructing the covariance matrix of the application requires less number of samples, i.e., can restore a full rank matrix and realize high-precision DOA estimation, and is more suitable for real-time application scenarios with limited snapshots.

[0134] To realize the above-mentioned embodiment, the second aspect embodiment of the application provides a coherent signal direction of arrival estimation device based on a deep convolutional network, comprising:

[0135] A to-be-measured signal acquisition module is configured to receive a to-be-measured signal by using a uniform linear array antenna to obtain an array receiving data matrix, wherein the to-be-measured signal contains a coherent signal;

[0136] An input feature vector extraction module is configured to calculate a covariance matrix of the array receiving data matrix, and extract upper right triangular elements divided from the diagonal line in the covariance matrix to form an input feature vector;

[0137] A covariance estimation module is configured to input the input feature vector into a preset covariance estimation model to obtain an estimated value of the upper right triangular element under ideal incoherent conditions; wherein the model adopts a deep convolutional neural network; and the estimated value of the upper right triangular element is reconstructed to generate a covariance matrix estimation value under ideal incoherent conditions;

[0138] The signal arrival direction estimation module is used to perform eigendecomposition on the covariance matrix estimation value and generate a spatial spectrum using a MUSIC algorithm to obtain an estimation result of the signal arrival direction.

[0139] In a specific embodiment of the present invention, before inputting the input feature vector into a preset covariance estimation model, the method further includes:

[0140] training the covariance estimation model;

[0141] The training of the covariance estimation model comprises:

[0142] 1) Use the same uniform linear array antenna as that used to obtain the signal to be tested to perform actual sampling or simulated sampling to obtain multiple sets of training signal data, each set of training signal data contains a mixed signal data matrix composed of coherent signals and incoherent signals and the corresponding ideal data matrix consisting of ideal incoherent signals

[0143] 2) Based on the result of step 1), extract the covariance matrix corresponding to the training signal data;

[0144] Among them, in each set of training signal data, The corresponding covariance matrix is ​​recorded as R train , The corresponding covariance matrix is ​​recorded as R ideal ;

[0145] 3) extracting the upper right triangular elements of the covariance matrix obtained in step 2);

[0146] Among them, R train and R ideal Extract the upper right triangle elements divided from the diagonal line respectively and get R train The corresponding upper right triangular elements are recorded as and R ideal The corresponding upper right triangular elements are recorded as

[0147] 4) The obtained step 3) As the input data of a single sample, the corresponding As the label of the sample, a data sample is formed, and all data samples constitute a sample set;

[0148] Divide the sample set according to the preset ratio to obtain the training set and the validation set;

[0149] 5) Constructing a covariance estimation model, using the training set obtained in step 4) to train the covariance estimation model and using the validation set to test it, and obtaining a trained covariance estimation model after the test passes.

[0150] In one specific embodiment of the present application, the covariance matrix acquisition method comprises:

[0151] For any data matrix received by the uniform linear array antenna, the size of which is MxN, M is the number of elements of the uniform linear array antenna, and N is the number of snapshots; extract the Mx1 signal vector x(n) corresponding to each snapshot in the received data matrix by column, n=1,…,N, and obtain the covariance matrix corresponding to the received data matrix according to the covariance calculation expression .

[0152] In one specific embodiment of the present application, it further comprises:

[0153] When training the covariance estimation model, a composite loss function is used:

[0154]

[0155] Wherein:

[0156] denotes a Toeplitz rectifier operator; J is an anti-diagonal unit matrix; I M is an MxM unit matrix; λ is a weight coefficient for balancing the influence between the data fitting term and the Toeplitz structure constraint term; ⊙ is the Hadamard product of matrices; ||·||F F is the Frobenius norm of the matrix; m is the index of the diagonal line in the Toeplitz structure constraint.

[0157] In one specific embodiment of the present application, it further comprises:

[0158] When acquiring training signal data by simulation sampling, the array manifold matrix A is calculated according to the signal direction of arrival (DOA) angle, a(θ i ) is the array manifold vector, d is the element spacing, λ is the wavelength, j is the imaginary unit, and m is the mth element in the array antenna;

[0159] Two baseband signal matrices are constructed respectively: matrix S simulates the actual scene containing coherent signal sources and incoherent signal sources, wherein the coherent signals are generated by multiplying a common baseband signal by a random factor, and the incoherent signals are independently generated; matrix S i corresponds to the ideal case of independent signal sources in different directions;

[0160] According to the preset signal-to-noise ratio, a complex Gaussian white noise matrix N(t) matching the number of elements and the number of snapshots is generated;

[0161] Synthesize the mixed signal data matrix and the corresponding ideal data matrix

[0162] Thus, the supervision learning framework through physical constraints can be realized to map the noisy mixed signal covariance matrix to an ideal incoherent noise-free signal covariance matrix, restore the Toeplitz structure, and thus improve the estimation accuracy and robustness of the MUSIC algorithm in a coherent scene. To implement the above embodiment, an electronic device is provided in a third aspect of the present application, comprising:

[0163] at least one processor; and a memory connected with the at least one processor in communication;

[0164] The memory stores instructions executable by the at least one processor, and the instructions are configured to perform the above-mentioned coherent signal direction of arrival estimation method based on a deep convolutional network.

[0165] To implement the above embodiment, a computer readable storage medium is provided in a fourth aspect of the present application, which stores computer instructions for causing the computer to perform the above-mentioned coherent signal direction of arrival estimation method based on a deep convolutional network.

[0166] It should be noted that the computer-readable medium in the above disclosure can be a computer-readable signal medium or a computer-readable storage medium or any combination of the two. The computer-readable storage medium may, for example, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or apparatus, or any combination of the above. More specific examples of a computer-readable storage medium can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device or apparatus. In the present disclosure, the computer-readable signal medium can include a data signal carried in a baseband or as a part of a carrier wave, which carries computer-readable program code. Such a propagated data signal can take many forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. The computer-readable signal medium can also be any computer-readable medium other than the computer-readable storage medium, which can send, propagate or transmit a program for use by or in conjunction with an instruction execution system, device or apparatus. The program code contained in the computer-readable medium can be transmitted by any suitable medium, including but not limited to a wire, a cable, an RF (radio frequency) or the like, or any suitable combination of the above.

[0167] The computer-readable medium described above can be contained in the electronic device described above; or can exist separately and not be assembled into the electronic device. The computer-readable medium described above carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the above-described embodiment of a coherent signal direction of arrival estimation method based on a deep convolutional network.

[0168] Computer program code for carrying out operations of the present disclosure can be written in any one or more programming languages or combinations of languages including object or visual programming languages such as Java, Smalltalk, C++ or conventional procedural programming languages such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0169] In the description of the specification, the description of the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Also, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in one or more embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the specification and the features of the different embodiments or examples, without contradiction.

[0170] In addition, the terms "first", "second", etc. are used only for the purpose of description and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first", "second" can explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "a plurality of" is at least two, for example, two, three, etc., unless otherwise specifically limited.

[0171] Any process or method descriptions or descriptions of the flow diagrams in the specification or otherwise described herein can be understood as representing code modules, segments, or portions of code which include one or more executable instructions for implementing specific logic functions (or steps) in the process, and the various embodiments of the application can include additional or fewer functions (or steps) in the process, and the functions (or steps) can be performed in the sequence shown or in other sequences, in an alternate order, or in parallel, depending on the implementation and the functions (or steps) involved.

[0172] The logic and / or steps represented in the flowcharts and / or described herein, for example, can be considered as a sequence of instructions to implement logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, apparatus, or device, such as a computer-based system, processor- based system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For purposes of this specification, a "computer-readable medium" can be any apparatus that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. The computer-readable medium can be a computer- readable storage medium or a computer-readable signal medium. The computer- readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium include the following: an electrical connection having one or more wires (electrical connections), a portable computer diskette (a magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium can even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, for example, via optical scanning of the paper or other medium, then compiled, interpreted, or otherwise processed in a suitable manner, if necessary, and stored in a computer memory.

[0173] It should be understood that aspects of the application can be implemented in hardware, software, firmware or combinations thereof. In the above embodiments, the various steps or methods can be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, and in another embodiment, any of the following technologies, known in the art, or their combinations can be used: discrete logic circuitry having logic gates for implementing logic functions on data signals, application specific integrated circuits having appropriate combinational logic gates, programmable gate arrays (PGA), field programmable gate arrays (FPGA), and the like.

[0174] Those skilled in the art can understand that all or part of the steps carried out by the above-mentioned embodiments can be completed by programs instructing related hardware, and the programs can be stored in a computer-readable storage medium. When the programs are executed, they include one or a combination of the steps of the method embodiments.

[0175] In addition, each of the functional units in the various embodiments of the present application can be integrated in one processing module, or each of the units can be physically present separately, or two or more units can be integrated in one module. The integrated module can be implemented in the form of hardware or in the form of a software functional module. When the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer readable storage medium.

[0176] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments within the scope of the present application.

Claims

1. A method for estimating the direction of arrival of coherent signals based on a deep convolutional network, characterized in that: include: Using a uniform linear array antenna to receive a signal to be measured, and obtaining an array receiving data matrix, wherein the signal to be measured includes a coherent signal; Calculating the covariance matrix of the array received data matrix, and extracting the upper right triangular elements of the covariance matrix divided from the diagonal to form an input eigenvector; Inputting the input feature vector into a preset covariance estimation model to obtain an estimated value of the upper right triangular element under ideal incoherent conditions; wherein the model adopts a deep convolutional neural network; reconstructing the estimated value of the upper right triangular element to generate an estimated value of the covariance matrix under ideal incoherent conditions; The covariance matrix estimate is subjected to eigendecomposition, and a spatial spectrum is generated using a MUSIC algorithm to obtain an estimation result of the signal arrival direction.

2. The method according to claim 1, characterized in that Before inputting the input feature vector into a preset covariance estimation model, the method further includes: training the covariance estimation model; The training of the covariance estimation model comprises: 1) Use the same uniform linear array antenna as that used to obtain the signal to be tested to perform actual sampling or simulated sampling to obtain multiple sets of training signal data, each set of training signal data contains a mixed signal data matrix composed of coherent signals and incoherent signals and the corresponding ideal data matrix consisting of ideal incoherent signals 2) Based on the result of step 1), extract the covariance matrix corresponding to the training signal data; Among them, in each set of training signal data, The corresponding covariance matrix is ​​denoted as R train , The corresponding covariance matrix is ​​denoted as R ideal ; 3) extracting the upper right triangular elements of the covariance matrix obtained in step 2); Among them, R train and R ideal Extract the upper right triangle elements starting from the diagonal line and get R train The corresponding upper right triangular elements are recorded as and R ideal The corresponding upper right triangular elements are recorded as 4) The obtained step 3) As the input data of a single sample, the corresponding As the label of the sample, a data sample is formed, and all data samples constitute a sample set; Divide the sample set according to the preset ratio to obtain the training set and the validation set; 5) Constructing a covariance estimation model, using the training set obtained in step 4) to train the covariance estimation model and using the validation set to test it, and obtaining a trained covariance estimation model after the test passes.

3. The method according to claim 2, characterized in that The covariance matrix is ​​obtained as follows: For any data matrix received by the uniform linear array antenna, the size of which is M×N, where M is the number of elements of the uniform linear array antenna and N is the number of snapshots; extract the M×1-dimensional signal vector x(n) corresponding to each snapshot in the received data matrix by column, where n=1,…,N, and calculate the covariance expression according to Obtain a covariance matrix corresponding to the received data matrix.

4. The method according to claim 2, characterized in that Also includes: When training the covariance estimation model, a composite loss function is used: in: represents the Toeplitz rectification operator; J is the anti-diagonal identity matrix; I M is the identity matrix of M×M dimensions; λ is the weight coefficient used to weigh the influence between the data fitting term and the Toeplitz structure constraint term; ⊙ is the Hadamard product of the matrix; ||·|| F is the Frobenius norm of the matrix; m is the index of the diagonal in the Toeplitz structure constraint.

5. The method according to claim 2, characterized in that Also includes: When obtaining training signal data through simulation sampling, the array flow matrix A is calculated according to the signal arrival direction DOA angle, A=[a(θ1)a(θ2)…a(θ k )], a(θ i ) is the array manifold vector, d is the array element spacing, λ is the wavelength, j is the imaginary unit, and m is the mth array element in the array antenna; Two baseband signal matrices are constructed separately: the matrix S simulates the actual scenario containing coherent signal sources and incoherent signal sources, where the coherent signal is generated by multiplying the common baseband signal by a random factor, and the incoherent signal is generated independently; the matrix S i This corresponds to the ideal situation where signal sources in different directions are independent; Generate a complex Gaussian white noise matrix N(t) that matches the number of array elements and the number of snapshots according to the preset signal-to-noise ratio; Synthetic Mixed-Signal Data Matrix and the corresponding ideal data matrix 6. A coherent signal arrival direction estimation device based on deep convolutional network, characterized in that: include: A signal acquisition module for testing, configured to receive the signal for testing using a uniform linear array antenna to obtain an array reception data matrix, wherein the signal for testing includes a coherent signal; An input eigenvector extraction module is used to calculate the covariance matrix of the array received data matrix and extract the upper right triangular elements divided from the diagonal line of the covariance matrix to form an input eigenvector; A covariance estimation module, configured to input the input feature vector into a preset covariance estimation model to obtain an estimated value of the upper right triangular element under ideal incoherence conditions; wherein the model adopts a deep convolutional neural network; Reconstructing the estimated values ​​of the upper right triangular elements to generate an estimated value of the covariance matrix under ideal incoherent conditions; The signal arrival direction estimation module is used to perform eigendecomposition on the covariance matrix estimation value and generate a spatial spectrum using a MUSIC algorithm to obtain an estimation result of the signal arrival direction.

7. The device according to claim 6, characterized in that Before inputting the input feature vector into a preset covariance estimation model, the method further includes: training the covariance estimation model; The training of the covariance estimation model comprises: 1) Use the same uniform linear array antenna as that used to obtain the signal to be tested to perform actual sampling or simulated sampling to obtain multiple sets of training signal data, each set of training signal data contains a mixed signal data matrix composed of coherent signals and incoherent signals and the corresponding ideal data matrix consisting of ideal incoherent signals 2) Based on the result of step 1), extract the covariance matrix corresponding to the training signal data; Among them, in each set of training signal data, The corresponding covariance matrix is ​​recorded as R train , The corresponding covariance matrix is ​​denoted as R ideal ; 3) extracting the upper right triangular elements of the covariance matrix obtained in step 2); Among them, R train and R ideal Extract the upper right triangle elements divided from the diagonal line respectively and get R train The corresponding upper right triangular elements are recorded as and R ideal The corresponding upper right triangular elements are recorded as 4) The obtained step 3) As the input data of a single sample, the corresponding As the label of the sample, a data sample is formed, and all data samples constitute a sample set; Divide the sample set according to the preset ratio to obtain the training set and the validation set; 5) Constructing a covariance estimation model, using the training set obtained in step 4) to train the covariance estimation model and using the validation set to test it, and obtaining a trained covariance estimation model after the test passes.

8. The device according to claim 7, characterized in that The covariance matrix acquisition method includes: For any data matrix received by the uniform linear array antenna, the size of which is M×N, where M is the number of elements of the uniform linear array antenna and N is the number of snapshots; extract the M×1-dimensional signal vector x(n) corresponding to each snapshot in the received data matrix by column, where n=1,…,N, and calculate the covariance expression according to Obtain a covariance matrix corresponding to the received data matrix.

9. The device according to claim 7, characterized in that Also includes: When training the covariance estimation model, a composite loss function is used: in: represents the Toeplitz rectification operator; J is the anti-diagonal identity matrix; I M is the identity matrix of M×M dimensions; λ is the weight coefficient used to weigh the influence between the data fitting term and the Toeplitz structure constraint term; ⊙ is the Hadamard product of the matrix; ||·|| F is the Frobenius norm of the matrix; m is the index of the diagonal in the Toeplitz structure constraint.

10. The device according to claim 7, characterized in that Also includes: When obtaining training signal data through simulation sampling, the array flow matrix A is calculated according to the signal arrival direction DOA angle, A=[a(θ1)a(θ2)…a(θ k )], a(θ i ) is the array manifold vector, d is the array element spacing, λ is the wavelength, j is the imaginary unit, and m is the mth array element in the array antenna; Two baseband signal matrices are constructed separately: the matrix S simulates the actual scenario containing coherent signal sources and incoherent signal sources, where the coherent signal is generated by multiplying the common baseband signal by a random factor, and the incoherent signal is generated independently; the matrix S i This corresponds to the ideal situation where signal sources in different directions are independent; Generate a complex Gaussian white noise matrix N(t) that matches the number of array elements and the number of snapshots according to the preset signal-to-noise ratio; Synthetic Mixed-Signal Data Matrix and the corresponding ideal data matrix

Images