A neural network-based covariance matrix optimization method

Abstract

A neural network-based covariance matrix optimization method, the implementation steps are: (1) constructing an array antenna received signal model x(k); (2) according to the signals received by the array in different directions of arrival, signal-to-noise ratio and reflection coefficient, a received signal set X is obtained; (3) for each received signal x (k), the estimated covariance matrix R is calculated q q , and the covariance matrix under the condition of no multipath q ; (4) the amplitude-phase information of each element of the upper triangular matrix of the covariance matrix R and R is extracted respectively, and the vectorization is carried out to obtain the amplitude-phase vector r q ; (5) a CNN-LSTM network model is designed; (6) the CNN-LSTM network model is trained using the data set D; (7) the trained CNN-LSTM network is used to optimize the input covariance matrix. The advantage of the present application is that the neural network optimization method can eliminate the influence of the multipath signal in the space on the estimation of the covariance matrix. The present application can be applied to the field of array signal processing.​

Description

Technical Field

[0001] This invention relates to the field of array signal processing, and specifically to a method for optimizing the covariance matrix based on neural networks. Background Technology

[0002] In the field of array signal processing, the covariance matrix of the array signal is a crucial basis for signal sensing. It is essential for sensing the direction of arrival and polarization information of electromagnetic waves. To estimate the covariance matrix, the raw signal received by the array antenna is typically processed directly. However, this method is susceptible to multipath interference, resulting in a highly variable estimated covariance matrix that negatively impacts subsequent signal processing and the accuracy of signal sensing. Summary of the Invention

[0003] The problem this invention aims to solve is: given the original signal received by the array, how to obtain a covariance matrix unaffected by multipath interference in the environment. The solution is a covariance matrix optimization method based on neural networks, the implementation steps of which are:

[0004] (1) Define a uniform linear array with M array elements and an element spacing of d = λ / 2, where λ is the wavelength corresponding to the signal center frequency; the signal received by the array antenna includes three parts: direct path, multipath, and noise, represented as follows: The received signal is an M×1 dimensional column vector, where the sampling sequence number k = 1, ..., K, K is the number of sampling snapshots, s(k) is the complex baseband signal, and n(k) is a signal with zero mean and variance. The additive white Gaussian noise column vector, where I is the number of multipath signals, ηi is the reflection coefficient of the i-th multipath, and a(θ) is the M×1 dimensional direction vector corresponding to the signal with incident angle θ. d θ represents the incident direction along the direct path. i Indicates the i-th multipath incident direction;

[0005] (2) The range of incident angles for the direct and reflected paths of the array antenna is defined as [θ]. start θ end The step size is θ. step Reflection coefficient η i The distribution interval is (0, 1), and the step size is η. step The signal-to-noise ratio (SNR) range corresponding to the complex baseband signal s(k) is [SNR start SNR end The step size is SNR. step Then the number of signal types received by the array is Q, forming a set of received signals X = {x} q (k)|q=1,2,...,Q};

[0006] (3) For each signal in the signal set X, calculate its estimated covariance matrix and theoretical covariance matrix; for the q-th received signal x q (k), q=1,2,...,Q, and the incident angle of its direct path is θ. dq Complex baseband signal s q (k) Signal-to-noise ratio is SNR q The covariance matrix is ​​estimated and calculated. The dimension is M×M; and the ideal covariance matrix under the condition of no multipath is required. Where E represents an identity matrix of dimension M×M;

[0007] (4) Extract the covariance matrix respectively and R q The amplitude and phase information of each element in the upper triangle are used to obtain an amplitude-phase vector with M×M elements. and r q The correspondence between the covariance matrix and its magnitude and phase vectors is as follows:

[0008]

[0009] r = [A 11 A 12 A 1M A 22 A 2M A MM φ 12 φ 13 , ..., φ 1M φ 23 , ..., φ 2M , ..., φ M-1，M ]

[0010] Further build the dataset

[0011] (5) Design a CNN-LSTM network model, which consists of a convolutional neural network (CNN) and a long short-term memory (LSTM) neural network model connected in series. The entire network model includes two hidden layers and a multi-layer stacked LSTM. Each hidden layer contains a convolutional layer, a normalization layer and an activation layer. The network input layer size is (M×M)×1, the kernel size of each convolutional layer is 1×3, and the number of convolutional kernels is 64. The multi-layer stacked LSTM network includes two LSTM layers with a hidden parameter of 120. The input of the network is the magnitude and phase vector r of the original covariance matrix. qThe output is the magnitude and phase vector q of the optimized covariance matrix.

[0012] (6) Use dataset D and CNN-LSTM network to train network parameters; the network training process is based on Adam optimizer, the initial learning rate is 0.001, the maximum batch size is defined as 300, the batch size is 256, the training objective is to minimize the L2 loss function, and the updated network parameters are obtained through error inverse propagation.

[0013] (7) Input the amplitude and phase vectors of the covariance matrix of the actual received signal of the array to be optimized into the trained CNN-LSTM network. The output of the network is the amplitude and phase vectors of the optimized covariance matrix. Then, according to the definition of amplitude and phase vectors, the optimized covariance matrix is ​​recovered.

[0014] The beneficial effect of this invention is that, by employing a neural network optimization method, the influence of multipath signals in space on covariance matrix estimation can be eliminated. This invention can be applied to the field of array signal processing. Attached Figure Description

[0015] Figure 1 This is a system block diagram of a covariance optimization method based on neural networks. Detailed Implementation

[0016] First, a multipath signal reception model for an array antenna is constructed. Then, the received signal covariance and ideal covariance are calculated to establish a dataset. A CNN-LSTM optimization network model is designed and its parameters are trained using the dataset. Finally, the trained network is used to optimize the original signal covariance matrix. The overall steps are as follows: Figure 1 As shown. The specific implementation steps are as follows:

[0017] (1) Define a uniform linear array with M array elements and an element spacing of d = λ / 2, where λ is the wavelength corresponding to the signal center frequency; the signal received by the array antenna includes three parts: direct path, multipath, and noise, represented as follows: The received signal is an M×1 dimensional column vector, where the sampling sequence number k = 1, ..., K, K is the number of sampling snapshots, s(k) is the complex baseband signal, and n(k) is a signal with zero mean and variance. The additive white Gaussian noise column vector, where I is the number of multipath signals, ηi is the reflection coefficient of the i-th multipath, and a(θ) is the M×1 dimensional direction vector corresponding to the signal with incident angle θ. d θ represents the incident direction along the direct path. i Indicates the i-th multipath incident direction;

[0018] (2) The range of incident angles for the direct and reflected paths of the array antenna is defined as [θ]. start θ endThe step size is θ. step Reflection coefficient η i The distribution interval is (0, 1), and the step size is η. step The signal-to-noise ratio (SNR) range corresponding to the complex baseband signal s(k) is [SNR start SNR end The step size is SNR. step Then the number of signal types received by the array is Q, forming a set of received signals X = {x} q (k)|q=1,2,...,Q};

[0019] (3) For each signal in the signal set X, calculate its estimated covariance matrix and theoretical covariance matrix; for the q-th received signal x q (k), q=1,2,...,Q, and the incident angle of its direct path is θ. dq Complex baseband signal s q (k) Signal-to-noise ratio is SNR q The covariance matrix is ​​estimated and calculated. The dimension is M×M; and the ideal covariance matrix under the condition of no multipath is required. Where E represents an identity matrix of dimension M×M;

[0020] (4) Extract the covariance matrix respectively and R q The amplitude and phase information of each element in the upper triangle are used to obtain an amplitude-phase vector with M×M elements. and r q The correspondence between the covariance matrix and its magnitude and phase vectors is as follows:

[0021]

[0022] r = [A 11 A 12 A 1M A 22 A 2M A MM φ 12 φ 13 , ..., φ 1M φ 23 , ..., φ 2M , ..., φ M-1，M ]

[0023] Further build the dataset

[0024] (5) Design a CNN-LSTM network model, which consists of a convolutional neural network (CNN) and a long short-term memory (LSTM) neural network model connected in series. The entire network model includes two hidden layers and a multi-layer stacked LSTM. Each hidden layer contains a convolutional layer, a normalization layer and an activation layer. The network input layer size is (M×M)×1, the kernel size of each convolutional layer is 1×3, and the number of convolutional kernels is 64. The multi-layer stacked LSTM network includes two LSTM layers with a hidden parameter of 120. The input of the network is the magnitude and phase vector r of the original covariance matrix. q The output is the magnitude and phase vector q of the optimized covariance matrix.

[0025] (6) Use dataset D and CNN-LSTM network to train network parameters; the network training process is based on Adam optimizer, the initial learning rate is 0.001, the maximum batch size is defined as 300, the batch size is 256, the training objective is to minimize the L2 loss function, and the updated network parameters are obtained through error inverse propagation.

[0026] (7) Input the amplitude and phase vectors of the covariance matrix of the actual received signal of the array to be optimized into the trained CNN-LSTM network. The output of the network is the amplitude and phase vectors of the optimized covariance matrix. Then, according to the definition of amplitude and phase vectors, the optimized covariance matrix is ​​recovered.

Claims

1. A method for optimizing the covariance matrix based on neural networks, the implementation steps of which are: (1) Define a uniform linear array with M array elements and an element spacing of d = λ / 2, where λ is the wavelength corresponding to the signal center frequency; the signal received by the array antenna includes three parts: direct path, multipath, and noise, represented as follows: The received signal is an M×1 dimensional column vector, where the sampling sequence number k = 1, ..., K, K is the number of sampling snapshots, s(k) is the complex baseband signal, and n(k) is a signal with zero mean and variance. The additive white Gaussian noise column vector, where I is the number of multipath signals, η i Let θ be the multipath reflection coefficient of the i-th path, and a(θ) be the M×1 dimensional direction vector corresponding to the signal with incident angle θ. d θ represents the incident direction along the direct path. i Indicates the i-th multipath incident direction; (2) The range of incident angles for the direct and reflected paths of the array antenna is defined as [θ]. start ,θ end The step size is θ. step Reflection coefficient η i The distribution interval is (0,1), and the step size is η. step The signal-to-noise ratio (SNR) range corresponding to the complex baseband signal s(k) is [SNR start SNR end The step size is SNR. step Then the number of signal types received by the array is Q, forming a set of received signals X = {{x} q (k)|q=1,2,...,Q}; (3) For each signal in the signal set X, calculate its estimated covariance matrix and theoretical covariance matrix; for the q-th received signal x q (k), q=1,2,…,Q, and the incident angle of its direct path is θ. dq Complex baseband signal s q (k) Signal-to-noise ratio is SNR q The covariance matrix is ​​estimated and calculated. The dimension is M×M; and the ideal covariance matrix under the condition of no multipath is required. Where E represents an identity matrix of dimension M×M; (4) Extract the covariance matrix R respectively q and By analyzing the amplitude and phase information of each element in the upper triangle, an amplitude-phase vector r with M×M elements is obtained. q and The correspondence between the covariance matrix and its magnitude and phase vectors is as follows: r=[A 11 ,A 12 ,...,A 1M ,A 22 ,...,A 2M ,...,A MM ,f 12 ,f 13 ,...,f 1M ,f 23 ,...,f 2M ,...,f M-1,M ] Further build the dataset (5) Design a CNN-LSTM network model, which consists of a convolutional neural network (CNN) and a long short-term memory (LSTM) neural network model connected in series. The entire network model includes two hidden layers and a multi-layer stacked LSTM. Each hidden layer contains a convolutional layer, a normalization layer and an activation layer. The network input layer size is (M×M)×1, the kernel size of each convolutional layer is 1×3, and the number of convolutional kernels is 64. The multi-layer stacked LSTM network includes two LSTM layers with a hidden parameter of 120. The input of the network is the magnitude and phase vector r of the original covariance matrix. q The output is the magnitude and phase vector of the optimized covariance matrix. (6) Use dataset D and CNN-LSTM network to train network parameters; the network training process is based on Adam optimizer, the initial learning rate is 0.001, the maximum batch size is defined as 300, the batch size is 256, the training objective is to minimize the L2 loss function, and the updated network parameters are obtained through error inverse propagation. (7) Input the amplitude and phase vectors of the covariance matrix of the actual received signal of the array to be optimized into the trained CNN-LSTM network. The output of the network is the amplitude and phase vectors of the optimized covariance matrix. Then, according to the definition of amplitude and phase vectors, the optimized covariance matrix is ​​recovered.

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