A deep learning-based far-field signal source positioning method under unknown mutual coupling

Abstract

The application discloses a far-field signal source positioning method based on deep learning under unknown mutual coupling, comprising the following steps: acquiring far-field signal data to be positioned, constructing a feature extraction matrix, and inputting the feature extraction matrix into a signal source number detection network model to obtain a predicted signal source number; loading pre-training weight parameters for a covariance reconstruction network model according to the predicted signal source number; inputting the feature extraction matrix into the covariance reconstruction network model after the pre-training weight parameters are loaded, and reconstructing network output according to a toplyiz structure characteristic, and adopting a multiple signal classification algorithm to realize far-field signal source positioning. The application improves the accuracy of signal source number detection by at least 5 percentage points compared with other baseline algorithms when the signal-to-noise ratio is less than 15 dB, improves the positioning accuracy of far-field signal sources by nearly twice compared with other baseline algorithms when the number of signal sources is small, and significantly improves the positioning performance in various harsh environments.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, and specifically relates to a deep learning-based method for locating far-field signal sources under unknown mutual coupling. Background Technology

[0002] Far-field signal source localization is a crucial problem in array signal processing, with applications in radar, sonar, mobile, and wireless communications. Over the past few decades, numerous high-precision far-field signal source localization algorithms have emerged, such as multiple signal classification algorithms and rotation-invariant signal parameter estimation algorithms. However, the localization performance of these algorithms heavily relies on the accurate construction of the array model. In real-world applications, unpredictable couplings between array elements inevitably exist, which severely degrades the performance of these algorithms.

[0003] To reduce or even eliminate mutual coupling effects, scholars have proposed numerous classical algorithms, which can be broadly categorized into three types. The first type fully utilizes the symmetric Topplitz structure of the mutually coupled matrices in a uniform linear array. However, these algorithms only use information from the intermediate subarrays, reducing the array's aperture and limiting their universality. The second type is reduction-based algorithms, which utilize all the array's information, but in some cases, the appearance of spurious peaks in the spectrum significantly reduces the algorithm's localization accuracy. The last type is sparse reconstruction-based algorithms, which can achieve better performance, but this method typically requires the application of second-order or higher-order statistics, resulting in relatively high computational complexity. All of these traditional algorithms have their own inherent limitations. In contrast, deep learning algorithms have demonstrated outstanding localization advantages in many harsh environments. Currently, in the literature on array signal processing, deep learning algorithms have not been well studied for the localization of far-field signal sources under unknown mutual coupling. Summary of the Invention

[0004] To overcome the problems in the prior art, the purpose of this invention is to provide a deep learning-based method for locating far-field signal sources under unknown mutual coupling, which can significantly improve the accuracy of signal source number detection and the precision of direction of arrival estimation.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A deep learning-based method for locating far-field signal sources under unknown mutual coupling includes the following steps:

[0007] Acquire far-field signal data to be located, and obtain the feature extraction matrix based on the far-field signal data;

[0008] The feature extraction matrix is ​​input into the signal source detection network model to obtain the predicted number of signal sources;

[0009] Based on the predicted number of signal sources, load pre-trained weight parameters into the covariance reconstruction network model;

[0010] The feature extraction matrix is ​​input into the covariance reconstruction network model loaded with pre-trained weight parameters to obtain the first row of data information of the predicted ideal covariance matrix;

[0011] The first row of the predicted ideal covariance matrix is ​​reconstructed based on the Toplitz structure characteristics to obtain the complete ideal covariance matrix. Then, a multi-signal classification algorithm is applied to the complete ideal covariance matrix to achieve far-field signal source localization.

[0012] Furthermore, the far-field signal data to be located is acquired through acquisition or simulation, the covariance matrix of the array received data is calculated based on the far-field signal data, and the feature extraction matrix is ​​calculated based on the covariance matrix.

[0013] Furthermore, the covariance matrix R of the array received data C for:

[0014] R C =E{x(t)x H (t)}=CAR S A H C H +R N

[0015] Where C represents the unknown mutual coupling effect matrix, A is the manifold matrix of the uniform linear array, and R s Let R be the covariance matrix of the incident signal. N Let R be the covariance matrix of Gaussian white noise. S =E{s(t)s(t) H}, s(t) is the incident signal vector, R N =E{ω(t)ω(t) H}, ω(t) is the additive noise vector, E{×} denotes the expectation, (×) H Let x(t) represent the Hermitian transpose, and x(t) be the far-field signal data, where x(t) = [x1(t), x2(t), ..., x M (t)] T x1(t), x2(t) and x M (t) represents the data received on the 1st, 2nd and Mth array elements, respectively.

[0016] Furthermore, the incident signal vector s(t) is calculated using the following formula:

[0017]

[0018] In the formula, s1(t), s2(t), and sK (t) represents the signals emitted by the 1st, 2nd and Kth far-field signal sources, respectively.

[0019] Furthermore, the additive noise vector ω(t) is calculated using the following formula:

[0020]

[0021] In the formula, ω1(t), ω2(t) and ω M (t) represent the Gaussian white noise received by the 1st, 2nd and Mth sensor elements, respectively;

[0022] The feature extraction matrix X is of size M×M×2, where M is the total number of matrix elements, including the first two-dimensional matrix. Second two-dimensional matrix in, and These represent the real and imaginary parts of the complex value of the matrix, respectively.

[0023] Furthermore, the signal source detection network model includes an input layer, a two-dimensional convolutional layer, a batch normalization layer, a modified linear unit layer, a fully connected layer, and an output layer. There are four two-dimensional convolutional layers, each employing 128 2*2 filters with a stride of 1. Each two-dimensional convolutional layer is followed by a batch normalization layer and a modified linear unit layer. There are three fully connected layers, with 512, 256, and 128 neurons respectively. The output layer is a classification structure composed of a fully connected layer with M neurons and a Softmax activation function.

[0024] Furthermore, the loss function of the signal source detection network model. as follows:

[0025]

[0026] Where T is the total number of training samples; i is the training sample index; u j u(t) represents the j-th element of the actual signal source number of the t-th sample after one-hot encoding, where u(t) = [u1(t), u2(t), ..., u2(t)]. M [t], when the number of signal sources is k, u k (t) is 1, and all other elements are 0; This is the j-th element of the prediction result for the number of signal sources for the t-th sample.

[0027] Furthermore, the training sets for the signal source number detection network model and the covariance reconstruction network model were obtained through simulation.

[0028] Furthermore, the covariance reconstruction network model includes an input layer, a two-dimensional convolutional layer, a batch normalization layer, a modified linear unit layer, a fully connected layer, and an output layer. There are four two-dimensional convolutional layers, using 128 filters with a dimension of 2*2 and a stride of 1. Each convolutional layer is followed by a batch normalization layer and a modified linear unit layer. There are three fully connected layers, with 512, 256, and 128 neurons in each layer. The output layer is a regression structure composed of 2M neurons.

[0029] Furthermore, the loss function of the covariance-reconstructed network model is... for:

[0030]

[0031] Where T is the total number of training samples; This represents the first row of data information for the ideal covariance matrix of the t-th sample. This represents the network prediction output for the t-th sample.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] The deep learning-based far-field signal source localization method under unknown coupling conditions of this invention, compared to the poor localization performance of traditional model-based far-field signal source localization algorithms under unknown coupling conditions, introduces a signal source number detection network model and a covariance reconstruction network model. On the one hand, the signal source number detection network model can achieve end-to-end output by learning the source number information in the covariance matrix of real samples, and its detection accuracy is significantly better than other source number detectors. For example, when the signal-to-noise ratio is less than 15dB, the accuracy of signal source number detection is improved by at least 5 percentage points compared with other baseline algorithms. On the other hand, the covariance reconstruction network model is designed based on the Toplitz structure characteristics, which can reduce the complexity of the algorithm and effectively solve the problem of reduced array aperture caused by traditional algorithms. Overall, under different signal source number localization conditions in the experimental settings, the method of this invention can achieve the best localization accuracy performance compared with other traditional model-based localization algorithms.

[0034] Furthermore, this invention has experimentally determined an optimal number of two-dimensional convolutional layers, which can simultaneously achieve high positioning accuracy and low computational complexity, thus reducing unnecessary time costs. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art are briefly introduced below; obviously, the drawings described below are some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0036] Figure 1 This is a schematic diagram of a deep learning-based far-field signal source localization architecture under unknown mutual coupling, according to an embodiment of the present invention.

[0037] Figure 2 This is a schematic diagram of the Signal Source Detection Network (SNDN) and Covariance Reconstruction Network (ICRN) models, where each two-dimensional convolutional layer is followed by a batch normalization layer and a correction linear unit layer.

[0038] Figure 3 This is a schematic diagram illustrating the performance of the far-field signal source localization method as a function of different numbers of two-dimensional convolutional layers in an embodiment of the present invention. The horizontal axis represents the signal-to-noise ratio (SNR), and the vertical axis represents the root mean square error (RMSE) of the far-field signal direction of arrival estimation.

[0039] Figure 4 This is a magnified view of a local area near a signal-to-noise ratio (SNR) of 10 dB, illustrating how the performance of the far-field signal source localization method varies with different numbers of two-dimensional convolutional layers in this embodiment of the invention. The horizontal axis represents the signal-to-noise ratio (SNR), and the vertical axis represents the root mean square error (RMSE) of the far-field signal direction of arrival estimation.

[0040] Figure 5 This is a schematic diagram showing the change in the accuracy of signal source detection as a function of the signal-to-noise ratio (SNR). The horizontal axis represents the SNR, and the vertical axis represents the detection accuracy.

[0041] Figure 6 This diagram illustrates the variation of root mean square error (RMSE) of far-field signal direction-of-arrival (DOA) estimation with signal-to-noise ratio (SNR) for different numbers of signal sources. The horizontal axis of each diagram represents the SNR, and the vertical axis represents the RMSE. Specifically, (a) shows the DOA estimation performance with one signal source; (b) shows the DOA estimation performance with two signal sources; (c) shows the DOA estimation performance with three signal sources; and (d) shows the DOA estimation performance with four signal sources.

[0042] Figure 7This is a schematic diagram showing the change of the root mean square error (RMSE) of the direction of arrival estimation of a far-field signal source with the number of snapshots. The horizontal axis represents the number of snapshots, and the vertical axis represents the root mean square error (RMSE) of the direction of arrival estimation.

[0043] Figure 8 This is a schematic diagram showing the change of the root mean square error (RMSE) of the direction of arrival estimation of a far-field signal source with the angular separation of the signal direction. The horizontal axis represents the angular separation of the signal direction, and the vertical axis represents the root mean square error (RMSE) of the direction of arrival estimation. Detailed Implementation

[0044] To make the objectives, technical effects, and technical solutions of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention. Based on the embodiments disclosed in the present invention, other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0045] The present invention provides a deep learning-based method for locating far-field signal sources under unknown mutual coupling, comprising the following steps:

[0046] Step 1: Acquire or simulate far-field signal data to be located, and obtain the feature extraction matrix based on the far-field signal data; specifically, this includes the following steps:

[0047] Acquire or simulate far-field signal data to be located, calculate the covariance matrix of the array received data based on the far-field signal data, and calculate the feature extraction matrix based on the covariance matrix.

[0048] The covariance matrix R of the array received data C for:

[0049] R C =E{x(t)x H (t)}=CAR S A H C H +R N

[0050] R = AR S A H

[0051] Where C represents the unknown mutual coupling effect matrix, A is the manifold matrix of the uniform linear array, and R s Let R be the covariance matrix of the incident signal. N Let R be the covariance matrix of Gaussian white noise. S=E{s(t)s(t) H}, s(t) is the incident signal vector, R N =E{ω(t)ω(t) H}, ω(t) is the additive noise vector, E{×} denotes the expectation, (×) H Let x(t) represent the Hermitian transpose, and x(t) be the far-field signal data, where x(t) = [x1(t), x2(t), ..., x...]. M (t)] T x1(t), x2(t) and x M (t) represents the data received on the 1st, 2nd and Mth array elements respectively, and R represents the ideal covariance matrix without mutual coupling effect and noise information.

[0052] The incident signal vector s(t) is calculated by the following formula:

[0053]

[0054] In the formula, s1(t), s2(t), and s K (t) represents the signals emitted by the 1st, 2nd and Kth far-field signal sources, respectively.

[0055] The additive noise vector ω(t) is calculated using the following formula:

[0056]

[0057] In the formula, ω1(t), ω2(t) and ω M (t) represents the Gaussian white noise received by the 1st, 2nd and Mth sensor elements, respectively.

[0058] The feature extraction matrix X is of size M×M×2, where M is the total number of matrix elements, including the first two-dimensional matrix. Second two-dimensional matrix in, and These represent the real and imaginary parts of the complex value of the matrix, respectively.

[0059] Step 2: Input the feature extraction matrix obtained in Step 1 into the signal source detection network model to obtain the predicted number of signal sources;

[0060] The signal source number detection network model includes an input layer, a two-dimensional convolutional layer, a batch normalization layer, a modified linear unit layer, a fully connected layer, and an output layer. The signal source number detection network model has four two-dimensional convolutional layers, which use 128 2*2 filters with a stride of 1. Each convolutional layer is followed by a batch normalization layer and a modified linear unit layer. The number of fully connected layers is three, with 512, 256, and 128 neurons respectively. The output layer is a classification structure composed of a fully connected layer with M neurons and a Softmax activation function.

[0061] Specifically, the signal source detection network model consists of nine substructures. The first substructure is the input layer, i.e., the receiving layer for the feature extraction matrix. The second to fifth substructures all share the same architecture: each consists of a 2D convolutional layer, a batch normalization layer, and a calibrated linear unit layer. For each 2D convolutional layer, 128 filters of size 2×2 and the same padding strategy are used to achieve multi-dimensional feature acquisition while avoiding the loss of edge information. The sixth, seventh, and eighth substructures represent fully connected layers containing 512, 256, and 128 neurons, respectively. Finally, the ninth substructure is a classification structure with M neurons, which treats signal source detection as a multi-class classification problem with M categories, outputting the signal source detection result after one-hot encoding.

[0062] The loss function of the signal source detection network model is the category cross-entropy function.

[0063]

[0064] Where T is the total number of training samples; i is the training sample index; u j u(t) is the j-th element of the actual signal source number of the t-th sample after one-hot encoding, i.e., u(t) = [u1(t), u2(t), ... u2(t)]. M [t], when the number of signal sources is k, u k (t) is 1, and all other elements are 0; This is the j-th element of the prediction result for the number of signal sources for the t-th sample.

[0065] The training set for the signal source detection network model generated through simulation specifically includes: the number of signal sources is randomly generated 100,000 times within the range of [1, 4], and the direction of arrival (DOA) of each signal source is randomly generated between [-60°, 60°]. Ten samples are set for each signal source generation result, with their signal-to-noise ratios randomly distributed within [-10dB, 15dB], and the number of snapshots is fixed at 200. Therefore, the dataset of the signal source detection network model contains a total of 1 million samples, of which training data and validation data account for 80% and 20%, respectively.

[0066] Step 3: Based on the number of signal sources predicted in Step 2, load the pre-trained weight parameters from the corresponding database into the covariance reconstruction network model.

[0067] The covariance reconstruction network model includes an input layer, a two-dimensional convolutional layer, a batch normalization layer, a modified linear unit layer, a fully connected layer, and an output layer. The covariance reconstruction network model has four two-dimensional convolutional layers, using 128 2*2 filters with a stride of 1. Each convolutional layer is followed by a batch normalization layer and a modified linear unit layer. The fully connected layer has three layers with 512, 256, and 128 neurons, respectively. The output layer is a regression structure composed of 2M neurons.

[0068] The loss function for the covariance reconstruction network model is:

[0069]

[0070] Where T is the total number of training samples; This represents the data information of the first row of the ideal covariance matrix for the t-th sample, specifically in the form of... Right now It contains the first row of data (r1(t) ~ r M The real part (Re) and imaginary part (Im) of (t). Similarly, This represents the network prediction output for the t-th sample.

[0071] The covariance reconstruction network model also consists of nine substructures, the first eight of which are the same as the first eight substructures of the signal source number detection network model. The only difference is that the ninth substructure of the covariance reconstruction network model is a regression structure composed of 2M neurons, which outputs the first row of data information of the ideal covariance matrix.

[0072] A database is established to store the pre-trained network parameters of the covariance reconstruction network under different numbers of signal sources. More importantly, it also stores the mapping relationship between different numbers of signal sources and the corresponding pre-trained network parameters. Specifically, by inputting the prediction results of the signal source detection network model with respect to the number of sources into the database, the pre-trained parameters of the covariance reconstruction network model with the corresponding number of sources can be matched.

[0073] Step 4: Input the feature extraction matrix obtained in Step 1 into the covariance reconstruction network model after loading the weight parameters in Step 3 to obtain the first row of data information of the predicted ideal covariance matrix.

[0074] To obtain pre-training parameters for the covariance reconstruction network model with different source numbers, training sets were established for four different source number scenarios. For the k-th source number scenario, it was assumed that k sources were randomly distributed within the spatial range of [-60°, 60°], where 1 ≤ k ≤ 4. For each source number scenario, 60,000 data points were randomly generated for the direction of arrival (DOA) of the signal sources. Then, 30 samples were set for each signal source generation result, with the signal-to-noise ratio (SNR) of the samples randomly distributed between -10dB and 15dB, and the number of snapshots fixed at 200. Therefore, 1.8 million samples were generated for the training dataset for each source number scenario. Furthermore, the training data and validation data accounted for 80% and 20%, respectively. It is important to note that the covariance reconstruction network model was trained separately for each source number scenario, and its corresponding pre-training parameters were stored in a database.

[0075] Step 5: Using the first row of data information of the predicted ideal covariance matrix obtained in Step 4, the matrix is ​​reconstructed according to the Toplitz structure characteristics to obtain the complete ideal covariance matrix. Then, a multi-signal classification algorithm is used to locate the far-field signal source.

[0076] Example 1

[0077] This invention discloses a deep learning-based method for locating far-field signal sources under unknown mutual coupling, which is a method for locating multiple far-field signal sources. The method flow is as follows: Figure 1 As shown, it includes the following steps:

[0078] Consider K far-field narrowband incoherent signals {s} k The (t)} impacts a uniform linear array of M sensor elements spaced d apart, and it is assumed that there is an unknown mutual coupling effect between these sensors.

[0079] If we define the first element of the array as the phase reference point, then the noisy signal x(t) received by the entire array can be expressed as:

[0080] x(t)=CAs(t)+ω(t) (1)

[0081] in, x1(t), x2(t) and x M s(t) represents the signals received on the 1st, 2nd and Mth sensor elements, respectively; s(t) and ω(t) are the given incident signal vector and additive noise vector, respectively.

[0082]

[0083]

[0084] Wherein, s1(t), s2(t) and s K(t) represent the signals emitted by the 1st, 2nd, and Kth far-field signal sources, respectively; ω1(t), ω2(t), and ω M (t) represents the Gaussian white noise received on the 1st, 2nd and Mth sensor elements, respectively.

[0085] Matrix C represents the unknown mutual coupling effect, which has a band-symmetric Toeplitz structure and can be represented as C = toeplitz(c), where c represents the mutual coupling coefficient vector and can be represented as c = [1, c1, c2, ..., c]. P [,0,L,0], each mutual coupling coefficient c p The absolute value of is between 0 and 1. The array manifold matrix A of a uniform linear array can be represented as A=[a(θ1),a(θ2),L,a(θ) K )], where a(θ k ) is the direction vector of a uniform linear array, which can be represented as θ k This represents the position parameter (i.e., direction of arrival) of the k-th signal source.

[0086] In this invention, it is assumed that the incident signal {s} k Let {(t)} be a generalized, zero-mean static random process with additive noise {ω}. m {(t)} is Gaussian white noise, and is related to the signal {s} k (t)} is unrelated.

[0087] (1) Acquire or simulate the far-field signal data to be located, and calculate the covariance matrix R of the array received data based on the far-field signal data. C According to the covariance matrix R C Calculate and obtain the feature extraction matrix X;

[0088] In step (1), the feature extraction matrix X of the network input is calculated:

[0089] From far-field signal data First, the covariance matrix R of the array received data is calculated. C ;

[0090] R C =E{x(t)x H (t)}=CAR S A H C H +R N

[0091] R = AR S A H

[0092] Where matrix C represents the unknown mutual coupling effect, A is the array manifold matrix of the uniform linear array, and RS Let R be the covariance matrix of the incident signal. S =E{s(t)s(t) H}, s(t) is the incident signal vector, R N Let R be the covariance matrix of Gaussian white noise. N =E{ω(t)ω(t) H}, where ω(t) is the additive noise vector. E{×} represents the expectation, (×) H Let x(t) represent the Hermitian transpose, x1(t), x2(t), and x2(t) represent the far-field signal data. M (t) represents the data received on the 1st, 2nd and Mth array elements respectively, and R represents the ideal covariance matrix without mutual coupling effect and noise information.

[0093] Generally, the covariance matrix R of the array received data C It can be approximated by averaging the time term t. This invention retains some information from the covariance matrix, including its real and imaginary parts. The specific content of the feature extraction matrix X proposed in this invention is described below:

[0094] The feature extraction matrix X is of size M×M×2, where M is the total number of matrix elements, including the first two-dimensional matrix. Second two-dimensional matrix in, and Let R represent the real and imaginary parts of the complex value of the matrix, respectively; C This is the covariance matrix of the data received by the array.

[0095] (2) Construct a signal source detection network model (SNDN); the signal source detection network model takes the feature extraction matrix X obtained in step (1) as input and estimates the number of far-field sources through convolutional layers, fully connected layers and classification structures;

[0096] For details, see Figure 2 The signal source detection network model constructed in this invention consists of nine substructures, including one input layer, four substructures composed of two-dimensional convolutional layers (Conv2D layers), batch normalization layers (BN layers) and rectified linear unit layers (ReLU layers), three fully connected layers (FC layers) and one output layer.

[0097] The feature extraction matrix X obtained in step (1) is used as the input information of the input layer of the signal source detection network model;

[0098] The following are four identical substructures, each consisting of a 2D convolutional layer (Conv2DLayer), a batch normalization layer (BN Layer), and a rectified linear unit layer (ReLU Layer). The 2D convolutional layer extracts source information from the input data; each layer uses 128 2x2 filters with a stride of 1 to perform convolution operations on the input data. Then, a batch normalization layer (BN Layer) is used to normalize the information transmitted in the network, making network training easier to optimize. Finally, a rectified linear unit layer (ReLU Layer) enhances the network's expressive power through non-linear mapping.

[0099] The sixth, seventh, and eighth substructures are represented as fully connected layers (FC layers) consisting of 512, 256, and 128 neurons, respectively. Finally, the ninth substructure is a classification structure with M neurons, which treats signal source detection as a multi-class classification problem with M categories, and outputs the encoded signal source detection result.

[0100] Finally, there is the Output Layer, which is used to output the predicted number of far-field signal sources.

[0101] (3) Establish a database to store the pre-trained network parameters of the covariance reconstruction network under different numbers of signal sources. More importantly, it also stores the mapping relationship between different numbers of signal sources and the corresponding pre-trained network parameters. Specifically, by inputting the prediction results of the signal source detection network model with respect to the number of sources into the database, the pre-trained parameters of the covariance reconstruction network model with the corresponding number of sources can be matched.

[0102] (4) Construct the Covariance Reconstruction Network (ICRN); such as Figure 2 As shown, the covariance reconstruction network model also consists of nine substructures, the first eight of which are the same as the first eight substructures of the signal source number detection network model described in step (2). The only difference is that the ninth substructure of the covariance reconstruction network model is a regression structure composed of 2M neurons, which outputs the first row of data information of the predicted ideal covariance matrix.

[0103] (5) By simulation, training sets are generated for the signal source number detection network constructed in step (2) and the covariance reconstruction network constructed in step (4). The two neural network models are pre-trained using the training sets, and the parameters required for the pre-trained neural network models are determined. The pre-training parameters of the covariance reconstruction network are saved to the database constructed in step (3).

[0104] Specifically, the parameters required for training the two network models should be set according to the following conditions:

[0105] 1) The loss function of the signal source number detection network is the category cross-entropy:

[0106]

[0107] Here, one-hot encoding is performed for each possible number of signal sources, T is the total number of training samples, and u j u(t) is the j-th element of the actual signal source number of the t-th sample after one-hot encoding, i.e., u(t) = [u1(t), u2(t), ... u2(t)]. M [t], when the number of signal sources is k, u k (t) is 1, and all other elements are 0; This is the j-th element of the prediction result for the number of signal sources for the t-th sample.

[0108] 2) The loss function of the covariance reconstruction network model is:

[0109]

[0110] in, This represents the data information of the first row of the ideal covariance matrix for the t-th sample, specifically in the form of... Right now It contains the first row of data (r1(t) ~ r M The real part (Re) and imaginary part (Im) of (t). Similarly, This represents the network prediction output for the t-th sample, where T is the total number of training samples.

[0111] 3) Both of the above network models are trained by the Adaptive Moment Estimation Optimizer with an initial learning rate of 0.001. In order to prevent the training from getting stuck in local optimization or diverging, the learning rate will be halved every 10 training cycles.

[0112] 4) The maximum number of training cycles is set to 30;

[0113] 5) The mini-batch size used in the training iteration is 64, and the data order of the training set is shuffled before each training iteration.

[0114] (6) Input the feature extraction matrix X obtained in step (1) into the signal source detection network model that has been trained in step (5), and output the predicted number of signal sources through the signal source detection network model; extract the corresponding pre-training parameters of the covariance reconstruction network from the database constructed in step (5) according to the prediction result of the number of sources; input the feature extraction matrix X into the covariance reconstruction network model that has been loaded with the pre-training parameters obtained in step (5), and output the first row of data information of the ideal covariance matrix; then reconstruct the complete ideal covariance matrix using the Toplitz structure characteristics, and finally use the multi-signal classification algorithm to realize the far-field signal source localization.

[0115] The effectiveness of the method of the present invention is verified by numerical simulation below:

[0116] The method proposed in this embodiment of the invention is verified on a uniform linear array consisting of 7 sensor elements, with the spacing between the sensors being half the wavelength. The mutual coupling coefficients are 2, specifically c1 = 0.5663 + 0.4114i and c2 = 0.2898 - 0.0776i. Theoretically, the method of this invention can simultaneously train any number of far-field signal sources and estimate their number and direction of arrival. For simplicity, this invention only lists four scenarios for the number of signal sources, i.e., 1 to 4 signal sources. The direction of arrival of each signal source is randomly generated between [-60°, 60°]. The signal-to-noise ratio of the received signal is randomly distributed between -10dB and 15dB, and the number of snapshots of the received signal is fixed at 200.

[0117] Correspondingly, the training set of the signal source number detection network model in this invention specifically includes: the number of signal sources is randomly generated 100,000 times within the range of [1, 4], and the direction of arrival of each signal source is randomly generated between [-60°, 60°]. Ten samples are set for each signal source generation result, with their signal-to-noise ratios randomly distributed within [-10dB, 15dB], and the number of snapshots is fixed at 200. Therefore, the dataset of the signal source number detection network model contains a total of 1 million samples, of which training data and validation data account for 80% and 20%, respectively.

[0118] Furthermore, the training set for the covariance reconstruction network model in this invention specifically includes training sets established for four different source number scenarios. For the k-th source number scenario, it is assumed that k sources are randomly distributed within the spatial range, where 1 ≤ k ≤ 4. For each source number scenario, 60,000 data points are randomly generated for the direction of arrival of the signal source. Then, 30 samples are set for each signal source generation result, where the signal-to-noise ratio of the samples is randomly distributed between -10dB and 15dB, and the number of snapshots is fixed at 200. Therefore, 1.8 million samples are generated for the training dataset for each source number scenario, where training data and validation data account for 80% and 20%, respectively.

[0119] After training the entire localization method using the training set described above, comparative experiments can be conducted for verification. First, this invention investigates the impact of the number of two-dimensional convolutional layers on the localization performance of far-field signal sources. For comparison, different network models are composed of 1 to 5 two-dimensional convolutional layers. Figure 3 This diagram illustrates how the performance of the far-field signal source localization method varies with the number of two-dimensional convolutional layers. The figure shows that at low signal-to-noise ratios, the performance of the localization method improves as the number of convolutional layers increases from one to five, due to the enhanced expressive power of the network model. However, as... Figure 4 As shown, when the signal-to-noise ratio is around 10dB, it is noteworthy that the localization performance of the network model consisting of four convolutional layers is better than that of the network model consisting of five convolutional layers. This may be due to overfitting caused by too many network parameters. Therefore, the network model with four convolutional layers proposed in this invention is based on a comprehensive trade-off between expressive power and the risk of overfitting.

[0120] Figure 5 The figure illustrates the trend of source number detection accuracy as a function of signal-to-noise ratio (SNR). For the source number detection problem, four different traditional estimators are used for comparison, with the number of sources in the test dataset distributed in the range [1,4]. As can be seen from the figure, the source number detection performance of the method presented in this invention is significantly better than all other estimators, especially in the low SNR region. Furthermore, even at an SNR of 15 dB, the accuracy of traditional source number estimators only reaches 95%. This may be because these estimators are based on the eigenvalues ​​of the covariance matrix, which have mutual coupling effects, and they do not eliminate the influence of mutual coupling on the estimator.

[0121] Figure 6 The trend of root mean square error (RMSE) of direction-of-arrival estimation for far-field signals with signal-to-noise ratio is shown for different numbers of signal sources. Figure 6 (a) is a schematic diagram of the direction of arrival estimation performance when there is only one signal source; Figure 6 (b) is a schematic diagram of the direction of arrival estimation performance when there are 2 signal sources; Figure 6 (c) is a schematic diagram of the direction of arrival estimation performance when there are 3 signal sources; Figure 6Figure (d) illustrates the direction-of-arrival (DOA) estimation performance when there are 4 signal sources. To verify the superiority of the method of this invention, experimental results were compared with those of the recursive reduced-order localization algorithm (R-RARE), reduced-order localization algorithm (RARE), MID-ARRAY algorithm, MUSIC algorithm, and Cramérault lower bound (CRB). For fairness, it was assumed that the number of signal sources was known in advance, and the DOA estimation of all algorithms was based on spectral peak search, where the grid spacing of the spectral peak search was fixed at 0.1°. It should be noted that, because the MID-ARRAY algorithm reduces the array aperture, it can locate a maximum of 2 signal sources under the conditions of the verification experiment. Figure 6 Its positioning performance is not shown in (c) and (d). From Figure 6 As can be seen from the four sub-figures (a) to (d), regardless of the number of signal sources, the method proposed in this invention exhibits the best positioning performance among all algorithms, and it does not suffer from the problem of reduced array aperture. It is worth noting that in... Figure 6 In (a) and (b), when the signal-to-noise ratio is low, the localization performance of the method proposed in this invention even breaks through the Cramer-Rao lower bound (CRB). This is likely because the Cramer-Rao lower bound (CRB) represents the optimal accuracy of an unbiased estimator, while the method proposed in this invention uses a biased estimator and is therefore not constrained by the CRB.

[0122] Figure 7 The trend of the root mean square error (RMSE) for far-field signal source direction-of-arrival estimation with the number of snapshots is shown. It is important to note that... Figure 7 The simulation settings are as follows: two signal sources are generated within the range of [-60°, 60°], the signal-to-noise ratio is set to 10dB, and the number of snapshots varies from 10 to 1000. Figure 7 As can be seen, the proposed method generally outperforms other algorithms regardless of the number of snapshots. It is noteworthy that even without training on different numbers of snapshots, the method still exhibits good performance compared to other model-based algorithms. This demonstrates that the method in this invention has good generalization performance across various snapshot counts.

[0123] at last, Figure 8A schematic diagram illustrating the variation of the root mean square error (RMSE) for far-field signal source direction-of-arrival (DOA) estimation with the angular separation of the signal direction is presented. The simulation settings are as follows: two signal sources are located at -20.65° and -20.65° + Δθ, respectively, where the angular separation Δθ ranges from 2° to 22°, the step size is 2°, the signal-to-noise ratio is fixed at 10 dB, and the number of snapshots is set to 200. As can be seen from the figure, regardless of the angular spacing, the DOA estimation accuracy of the method of this invention is consistently higher than that of other algorithms. Furthermore, it is worth noting that the method of this invention has advantages in localization under some small angular spacing conditions.

[0124] This invention proposes a deep learning-based method for far-field signal source localization under unknown mutual coupling conditions. The method mainly consists of a signal source number detection network responsible for source count detection and a covariance reconstruction network responsible for ideal covariance matrix recovery. The signal source number detection network achieves end-to-end output by learning the source number information from the covariance matrix of real samples. The covariance reconstruction network is designed based on the Toplitz matrix structure and is used to recover the first row data information of the ideal covariance matrix, free from mutual coupling effects and noise information. Furthermore, its parameters are loaded from a database containing pre-trained parameters for different source counts. Simulation results show that, compared with existing traditional far-field signal source localization algorithms, the proposed method maintains high performance under various conditions, including low snapshot number, low signal-to-noise ratio, and small separation angles of multiple signal sources' directions of arrival. Overall, the proposed method can significantly improve the source count detection accuracy and direction-of-arrival estimation accuracy of far-field signal sources under unknown mutual coupling conditions.

[0125] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still make modifications or equivalent substitutions to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention are within the protection scope of the claims of the present invention pending approval.

Claims

1. A deep learning-based method for locating far-field signal sources under unknown mutual coupling, characterized in that, Includes the following steps: Acquire far-field signal data to be located, and obtain the feature extraction matrix based on the far-field signal data; The feature extraction matrix is ​​input into the signal source detection network model to obtain the predicted number of signal sources. The signal source detection network model includes an input layer, two-dimensional convolutional layers, batch normalization layers, rectified linear unit layers, fully connected layers, and an output layer. There are four two-dimensional convolutional layers, each using 128 2*2 filters with a stride of 1. Each two-dimensional convolutional layer is followed by a batch normalization layer and a rectified linear unit layer. There are three fully connected layers, with 512, 256, and 128 neurons respectively. The output layer consists of... The classification structure, composed of a fully connected layer of 100 neurons and a Softmax activation function, represents the loss function of the signal source detection network model. as follows: in, It is the total number of training samples; i It is the training sample number; For the first t The actual signal source number of the sample after one-hot encoding is the first j One element, When the number of signal sources is k hour, The value is 1, and all other elements are 0; For the first t The prediction result of the number of signal sources for the nth sample j One element; Based on the predicted number of signal sources, pre-trained weight parameters are loaded into the covariance reconstruction network model. The covariance reconstruction network model includes an input layer, a two-dimensional convolutional layer, a batch normalization layer, a rectified linear unit layer, a fully connected layer, and an output layer. There are four two-dimensional convolutional layers, employing 128 2*2 filters with a stride of 1. Each convolutional layer is followed by a batch normalization layer and a rectified linear unit layer. There are three fully connected layers with 512, 256, and 128 neurons respectively. The output layer consists of two... M A regression structure composed of neurons; The feature extraction matrix is ​​input into the covariance reconstruction network model loaded with pre-trained weight parameters to obtain the first row of data information of the predicted ideal covariance matrix; The first row of the predicted ideal covariance matrix is ​​reconstructed based on the Toplitz structure characteristics to obtain the complete ideal covariance matrix. Then, a multi-signal classification algorithm is applied to the complete ideal covariance matrix to achieve far-field signal source localization.

2. The method for locating far-field signal sources based on deep learning under unknown mutual coupling as described in claim 1, characterized in that, Acquire or simulate far-field signal data to be located, calculate the covariance matrix of the array received data based on the far-field signal data, and calculate the feature extraction matrix based on the covariance matrix.

3. The method for locating far-field signal sources based on deep learning under unknown mutual coupling as described in claim 1, characterized in that, Covariance matrix of array received data for: in, Represents the unknown mutual coupling effect matrix. The manifold matrix of a uniform linear array, Let be the covariance matrix of the incident signal. The covariance matrix of Gaussian white noise is... , Let be the incident signal vector. , It is an additive noise vector. Indicates the expectation. Indicates Hermite transpose. For far-field signal data, far-field signal data , , and They represent the 1st, 2nd and 3rd respectively. Data received on each array element.

4. The method for locating far-field signal sources based on deep learning under unknown mutual coupling as described in claim 3, characterized in that, Incident signal vector Calculated using the following formula: In the formula, , and They represent the 1st, 2nd and... K The signal is emitted by a far-field signal source.

5. The method for locating far-field signal sources based on deep learning under unknown mutual coupling as described in claim 3, characterized in that, Additive noise vector Calculated using the following formula: In the formula, , and They represent the 1st, 2nd and... M Gaussian white noise received by each sensor element; Feature extraction matrix Size is , The total number of array elements, including the first two-dimensional matrix. Second two-dimensional matrix ,in, and These represent the real and imaginary parts of the complex value of the matrix, respectively.

6. The method for locating far-field signal sources based on deep learning under unknown mutual coupling as described in claim 1, characterized in that, The training sets for the signal source number detection network model and the covariance reconstruction network model were obtained through simulation.

7. The method for locating far-field signal sources based on deep learning under unknown mutual coupling as described in claim 1, characterized in that, Loss function of covariance reconstructing network model for: in, T It is the total number of training samples; Indicates that for the first t The first row of data information for the ideal covariance matrix of each sample. , Indicates that for the first t The network prediction output for each sample.

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