Plug-and-play single-bit sparse bipolar array direction-of-arrival estimation method based on noise reduction network

Abstract

The invention provides a plug-and-play single-bit sparse bipolar array DOA (direction of arrival) estimation method based on a noise reduction network. According to the method, in a maximum posterior probability direction of arrival estimation algorithm, a sparse reconstruction model based on a covariance matrix is described as the sum of a known sparse representation model and unknown noise, and the known model and the unknown noise are processed separately by using a plug-and-play technology. Specifically, a known model part obtains a closed-form solution through a least square method, and an unknown noise part is completed by a noise reduction network driven by data; the noise reduction network is suitable for one-dimensional sparse signals, only carries out sparse signal noise reduction work, does not contain model information of an array, only needs a small training data set, and is high in generalization. The training data required by the method is far lower than that of a typical deep convolution and deep expansion direction-of-arrival estimation network, and the robustness to the number of source signals is high.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing, and specifically relates to a plug-and-play single-bit sparse dipole array direction of arrival (DOA) estimation method based on a noise reduction network. Background Art

[0002] The dipole array has the ability to sense the polarization information of electromagnetic signals, and its output is the electric field strength of electromagnetic waves in different directions. These complete electric field strength information lay the foundation for improving the detection performance of the array. Compared with traditional scalar arrays, dipole arrays have more robust detection performance, stronger anti-interference ability, higher resolution, and polarization multiple access ability. However, with the same number of array elements, the number of channels required by the dipole array is twice that of the scalar sensor array. Its detection of signal polarization information is achieved by increasing the number of sensors, which in turn leads to a substantial increase in system cost and is not suitable for scenarios with large scale, low power supply capacity, or limited cost, such as large-scale multiple input multiple output (MIMO) systems, unmanned aerial vehicles, and vehicle-mounted communication systems.

[0003] To solve the problem of high hardware cost overhead in dipole arrays, some scholars have proposed single-bit sparse dipole arrays based on single-bit sampling technology and sparse array technology, reducing system overhead from the perspectives of measurement and array structure respectively. For single-bit sparse dipole arrays, the single-bit multiple signal classification (OB-MUSIC) algorithm is used to estimate the direction of arrival (DOA) of the array. However, this algorithm has limited accuracy and high computational complexity when the array scale is large and the number of snapshots is limited. Although there are already high-precision super-resolution algorithms, their computational complexity cannot meet the requirements of real-time tracking and monitoring of targets. Summary of the Invention

[0004] The purpose of the present invention is to propose a plug-and-play single-bit sparse dipole array direction of arrival estimation method based on a noise reduction network.

[0005] The technical solution for achieving the purpose of the present invention is as follows: A plug-and-play single-bit sparse dipole array direction of arrival estimation method based on a noise reduction network, including:

[0006] Step 1: Use virtual array signal processing technology and non-quantization technology to transform the direction of arrival estimation problem of a single-bit sparse dipole array into the direction of arrival estimation problem of the virtual signal of a differential array;

[0007] Step 2: Use plug-and-play technology to decompose the maximum a posteriori probability estimation algorithm for direction of arrival estimation into two parts: a known model and unknown noise, and iteratively solve the known model and unknown noise to obtain the beam arrival direction angle. The specific solution methods are as follows:

[0008] The least squares method is used to solve the known model part to obtain a closed-form solution, and a data-driven noise reduction network is used to solve the unknown noise part.

[0009] Compared with the prior art, the significant advantages of the present invention are as follows: The present invention utilizes the decoupling ability of the plug-and-play (PnP) technology for the known model and unknown noise, and decomposes the maximum a posteriori probability (MAP) estimation algorithm for DOA estimation into two parts: the known model and the sparse signal noise reduction network; the noise reduction network adopted in the present invention is only a standard sparse signal noise reduction network, which has nothing to do with the array model. Therefore, the network contains less information, requires less training data, and has strong generalization ability. The amount of training data required for the noise reduction network in the present invention is much lower than that of the deep convolutional network and the deep unfolding network, and it has strong robustness to the number of source signals.

[0010] The present invention will be further described in detail below with reference to the accompanying drawings. Description of the Drawings

[0011] Figure 1 It is a single-bit sparse dipole array diagram.

[0012] Figure 2 It is a schematic diagram of the PnP-MAP noise reduction network.

[0013] Figure 3 It is a comparison of the DOA estimation performance of the PnP-MAP algorithm and the least absolute shrinkage and selection operator (LASSO) algorithm at different signal-to-noise ratios. Detailed Embodiments

[0014] The present invention will be further elaborated below with reference to the accompanying drawings and examples.

[0015] A plug-and-play single-bit sparse dipole array direction-of-arrival estimation method based on a noise reduction network, which is used in the field of array signal processing technology. The present invention first uses virtual array signal processing technology and non-quantization technology to transform the direction-of-arrival estimation of the single-bit sparse dipole array into the direction-of-arrival estimation of the virtual signal of the differential array; then uses the plug-and-play technology to decompose the maximum a posteriori probability estimation algorithm for DOA estimation into two parts: the known model and the unknown noise. The known model part is obtained by the least squares method to obtain a closed-form solution, and the unknown noise part is completed by a data-driven noise reduction network; then a noise reduction network suitable for one-dimensional sparse signals is designed. Since this network only performs sparse signal noise reduction work and does not contain the model information of the array, the training of the network only requires a small data set; finally, the least squares method and the noise reduction network are alternately iteratively solved to obtain the DOA estimation.

[0016] In a specific embodiment, taking the nested dipole array as an example, the training set of the noise reduction network consists of 10 5 samples, and the test set consists of 2×10 4It consists of one sample, and the matrix dimensions of the input signal and the output signal are both 1×162. The Adam algorithm is used to optimize the network. The specific implementation steps of this method are as follows:

[0017] Step 1: Use virtual array signal processing technology and non-quantization technology to transform the problem of direction-of-arrival (DOA) estimation of a single-bit sparse dipole array into the problem of DOA estimation of virtual signals of a difference array.

[0018] The received signal of the sparse dipole array at time t has the following expression:

[0019]

[0020] where is the set of element positions in the array, called the element layout set. i = 1 represents the parallel direction of the x-axis, and i = 2 represents the parallel direction of the y-axis. represents the set of received signal sources. is the vector formed by the received signals of the array in the i direction. is the steering vector matrix, where is the response vector of the array. is the response of the l-th dipole element. is the normalized DOA of the m-th source signal, and θ m ∈[-π / 2,π / 2] is the actual DOA of the m-th source signal, and d is the element spacing. represents the response vector of the dipole vector sensor, and diag(·) represents constructing a diagonal matrix. is the response of the dipole vector sensor of the m-th source signal, and its expression is:

[0021]

[0022] is the source signal vector. represents the additive noise vector in the i direction of the array, and n l,i (t) represents the additive noise in the i direction of the l-th element.

[0023] Calculate the non-quantized covariance matrix as:

[0024]

[0025] where g m.i represents the energy of the m-th signal received in the i direction, σ 2 represents the noise energy, I represents the identity matrix, and (·)* denotes the adjoint of a matrix, (·) H denotes the conjugate transpose of a matrix.

[0026] For vectorize and multiply by the weight matrix W to combine terms at the same position, and the resulting differential array measurement vector That is:[[]]

[0027]

[0028] Wherein,[[]] denotes the set of arrangements of the differential array, n 1 , n 2 denotes the specific position in the set of element position arrangements,[[]] denotes the steering vector matrix of the differential array, and its specific form is similar to denotes the virtual measurement signal, <e 0 > m = δ m,0 , δ m,0 is the Kronecker function,[[]] denotes the pseudoinverse of a matrix, W denotes the weight matrix, and its ath column is denoted as <w> :,a = [vec(J(a))] T , where the element in the \(l\)th row and \(l\)th column of \(J(a)\) i row and \(l\)th j column Specifically expressed as:

[0029]

[0030] In addition, and have a similar structure, so can be regarded as the quantized measurement signal of the difference array with the steering vector matrix .

[0031] After single-bit sampling of the received signal of the sparse dipole array , its received signal The expression is:

[0032]

[0033] where signc(·) is the single-bit sampling operator, defined as c R and \(c\) I respectively represent the real and imaginary parts of the complex number \(c\), and sign(·) is the sign function, defined as:

[0034]

[0035] The single-bit sampling covariance matrix of is expressed as:

[0036]

[0037] After normalizing , the normalized covariance matrix is defined as:

[0038]

[0039] where \(N\) i is a diagonal matrix, represents the element in the \(n\)th row and \(n\)th column of the matrix.

[0040] When all source signals are independent and conform to the complex Gaussian distribution, the single-bit sampling covariance matrix and the normalized covariance matrix have a one-to-one correspondence, specifically:

[0041]

[0042] where the definition of the arcsine operator arcsine(·) is:

[0043] arcsine(c) = arcsin(c R ) + jarcsin(c I ) (11)

[0044] The normalized covariance matrix can be reconstructed from the single-bit sampled covariance matrix i.e.:

[0045]

[0046] where the definition of the sine operator sine(·) is:

[0047] sine(c) = sin(c R ) + jsin(c I ) (13)

[0048] where sin(·) is the sine function.

[0049] For independent source signals, the normalized covariance matrix and the unquantized covariance matrix R yL,i satisfy: where Therefore, the eigenvectors of these two covariance matrices span the same vector space, i.e., the DOA of the source signal can be estimated from According to Equation (10), the differential array measurement vector of the single-bit sparse dipole array can be written as:

[0050]

[0051] In a conventional dipole array, the data in different axis directions are jointly processed. However, after single-bit sampling, the reconstruction of the normalized covariance matrix is performed independently on each axis. For the signal energy received by the antenna dipoles in different axis directions, by adding the signal energies received in the two axis directions, we can obtain:

[0052]

[0053] Step 2: Use the plug-and-play technique to decompose the maximum a posteriori probability estimation algorithm for direction of arrival (DOA) estimation into a known model and an unknown noise part. The known model part obtains a closed-form solution by the least squares method, while the unknown noise part is handed over to a data-driven noise reduction network to complete.

[0054] As can be seen from Step 1, the expression of the quantized measurement signal of the array can be transformed into a problem of solving the DOA estimation of the single-bit sparse dipole array, and its expression is:

[0055]

[0056] wherein, is a virtual measurement signal, is the virtual measurement signal in the i direction, is the received signal energy in the i direction after dequantization of the m-th signal after single-bit sampling, is the noise power after single-bit sampling.

[0057] It can be seen that is similar in structure to the received signal of the sparse dipole array and can be regarded as the received signal of a differential array . Therefore, the direction of arrival (DOA) of the single-bit sparse dipole array can be estimated based on the output data of the differential array. After discretizing and gridding the entire spatial angle range,

[0058] it is sparse in the spatial domain, that is, the values corresponding to most grids are 0. Once is obtained, the DOA of the signal can be determined according to the positions corresponding to the grids with non-zero points. The value of and the positions corresponding to the grids with non-zero points can be obtained by solving the linear inverse problem of equation (16).

[0059] For equation (16), the maximum a posteriori probability estimation problem can be solved as follows to estimate

[0060]

[0061] wherein, represents any regression term, α is the regression coefficient, is the noise energy after dequantization after single-bit sampling. Equation (17) can be expressed by introducing an auxiliary variable z as:

[0062]

[0063] The Lagrange multiplier method is used to solve problem (18). Introduce the Lagrange multiplier μ, and its Lagrangian objective function is:

[0064]

[0065] According to the idea of alternating optimization, alternately optimize and z.

[0066] Fix z and update Problem (19) is transformed into:

[0067]

[0068] The closed - form solution of problem (20) is:

[0069]

[0070] where k represents the number of iterations.

[0071] Fix Update z, and problem (19) is transformed into:

[0072]

[0073] Thus, the known model information and unknown noise information are decoupled into two independent sub - problems of equations (21) and (22). The closed - form solution of equation (21) is obtained by the least - squares method, and equation (22) can be regarded as a noise reduction problem, expressed as:

[0074]

[0075] where is a sparse signal, which is non - zero only when the DOA is on the grid. Therefore, a denoising network can be used to solve this denoising problem, denoted as denoiseNet(·) in equation (23).

[0076] Specifically, the specific structure of the denoising network:

[0077] Its structure is as Figure 2 shown. This denoising network includes a residual module and a batch normalization module.

[0078] First, the real and imaginary parts of the input data are taken out and merged into the same channel. Assuming the number of grid points is D, the data dimension input to the network is Batchsize×1×D, where Batchsize is the batch size. The PnP - MAP denoising network consists of three parts:

[0079] 1) conv + relu

[0080] For the first part, a convolutional layer with a convolutional kernel size of L, a stride of 1, and padding of (L - 1) / 2 zeros at both ends is set, and then the relu function is used for non - linear processing. The role of this convolutional layer is to extract the local features of the input data, and the non - linear processing of relu can change the representation form of the input data. The specific parameter settings of this part are: it includes two convolutional layers. The number of convolutional kernels in convolutional layer 1 is 256, and the convolutional kernel size is 25; the number of convolutional kernels in convolutional layer 2 is 128, and the convolutional kernel size is 25.

[0081] 2) conv + bn + relu

[0082] For the second part, batch normalization is added between the convolutional layer and the ReLU function, which optimizes the data distribution through iterations during network training. This part enables the network to maintain a normal distribution during parameter updates, preventing the phenomenon of data being too large or too small due to parameter updates, and suppressing the vanishing gradient problem during training to a certain extent. The specific parameter settings for this part are as follows: it includes nine hidden layers and two convolutional layers. The number of convolutional kernels in convolutional layer 3 is 64, and the kernel size is 15. The number of convolutional kernels in hidden layers 4 - 12 is 32, and the kernel size is 5. The number of convolutional kernels in convolutional layer 13 is 16, and the kernel size is 7.

[0083] 3)conv

[0084] For the last part, a convolutional layer is used for output reconstruction, and the feature data with 16 channels is transformed into a single-channel output through a linear operation. This output reconstruction method can help simplify the model output and extract the most important feature information. The specific parameter settings for this part are as follows: it includes one convolutional layer. The number of convolutional kernels in convolutional layer 14 is 1, and the kernel size is 15.

[0085] Then, the training and testing of the network are completed. The specific steps are as follows:

[0086] First, generate network labels, and the labels are set as sparse signals in the case of no noise. As can be seen from step 1, the differential array received signal can be obtained through the virtual array signal processing technology:

[0087]

[0088] Among them, represents the received signal of the differential array in the network of, is the steering vector matrix of the differential array in the network, represents the sparse signal in the network in the case of no noise. The sparse signal can be obtained through the following formula:

[0089]

[0090] To make the sparse signal obtained by network training have a unique solution, it is required that the number of rows of the steering vector matrix of the differential array in the network is greater than the number of columns. Given that the length of the differential array is 111, so in the experiment, the spatial spectrum is divided into 81 grids, that is, the signal vector length is 81. For the complex number take out its real part and imaginary part and combine them into one channel, that is:

[0091]

[0092] Among them, (·) R is the real part extraction operation, and (·) I is the imaginary part extraction operation. is the real part of the sparse signal, is the imaginary part of the sparse signal. After the merging operation, the label is a one-dimensional vector of 1×162

[0093] The input data of the network is generated by the following formula:

[0094]

[0095] Among them, is the noise energy after dequantization of single-bit sampling in the network. The Lagrangian operator μ = 0.1, is obtained from Equation (24). For the complex input data , the processing is the same as the network label. The real part and the imaginary part are merged, and the input data is a one-dimensional vector of 1×162.

[0096] The training set of the network consists of 10 5 samples, and the test set consists of 2×10 4 samples. Let the training dataset be with a total of J samples; the network parameter set is Ξ; the network output is expressed as:

[0097]

[0098] The goal of the denoising network is to recover a clean signal from the noisy input data. Therefore, it is hoped that the output of the network is as close as possible to the true noise-free signal. Therefore, the network uses the mean square error as the loss function to measure the difference between the denoising network output and the true value, and improves the denoising effect of the network through the optimization process. Define the mean square error loss as:

[0099]

[0100] Among them, J is the number of samples, is the label of the jth sample, is the network output vector of the jth sample. Then, the process of network training can be expressed as the following optimization problem:

[0101]

[0102] In summary, the sparse signal can be iteratively solved through the following two steps:

[0103]

[0104] Insert the trained denoiser into the alternating iteration process to solve the sparse signal and obtain the direction of arrival angle.

[0105] Embodiment

[0106] Through actual network training, the specific implementation of the plug-and-play single-bit sparse dipole array DOA estimation method based on the noise reduction network of the present invention is further described.

[0107] 1) Array parameter setting

[0108] The 14-element single-bit sparse dipole array for simulation is a 7×7 nested array, denoted as:

[0109]

[0110] Array It is composed of two nested 7-element uniform linear arrays. In the experiment, the energy of all source signals is random, the polarization degree is a random variable uniformly distributed within (0, 1), the polarization parameter auxiliary polarization angle is a random variable uniformly distributed within [-π / 2, π / 2], and the auxiliary polarization phase is a random variable uniformly distributed within [-π, π].

[0111] 2) Training set parameter setting

[0112] In network training, the network label is set as:

[0113]

[0114] It is known that the differential array length is 111, and the spatial spectrum is divided into 81 grids, that is, the signal vector length is 81. For a complex number Take its real part and imaginary part and combine them into one channel, that is:

[0115]

[0116] After the merging operation, the label is a one-dimensional vector of 1×162.

[0117] The input data of the network is generated by the following formula:

[0118]

[0119] For the input data complex number The processing is the same as the network label. Combine the real part and the imaginary part, then the input data is a one-dimensional vector of 1×162. The training set of the network consists of 10 5 samples, and the test set consists of 2×10 4 It consists of [[1, 6]] random numbers for the number of signals, random numbers within (0, 1) for signal energy, random numbers within (0, 20) for signal-to-noise ratio, and 50 snapshots.

[0120] 3) Network training settings

[0121] The definition of the least mean square error loss is as follows:

[0122]

[0123] where J is the number of samples, is the label of the j-th sample, is the network output vector of the j-th sample. The purpose of network training is to minimize the loss function in the above formula, expressed as:

[0124]

[0125] This network is built using the PyTorch framework. The hyperparameters for network training and the simulation parameters for the dataset are shown in Table 1.

[0126] Table 1 Hyperparameters for PnP-MAP network training

[0127]

[0128] 4) Evaluation metrics

[0129] The present invention aims to perform direction-of-arrival (DOA) estimation for a single-bit sparse dipole array through a plug-and-play method based on a denoising network. The present invention uses the hit rate HitRate to measure the accuracy of DOA estimation. The definition of the hit rate is:

[0130]

[0131] where Q represents the number of Monte Carlo experiments, and M is the number of signal sources. represents the angle estimation of the m-th signal in the q-th experiment, represents the true angle value of the m-th signal in the q-th experiment, represents that it is equal to 1 when its parameter is 0, and 0 otherwise.

[0132] 5) Comparison of training data volume

[0133] The training data volume of the denoising network in the PnP-MAP method is compared with that of the deep convolutional network (DCN)-6 network and the deep unfolded iterative soft threshold algorithm (ISTA) network. The size of the training volume is measured by the number of training samples.

[0134] Table 2 Number of training samples required for different networks

[0135]

[0136]

[0137] The training set sizes in Table 2 are all the optimal training set sizes found after balancing the network training performance and computational resources. Among them, the PnP-MAP denoising network reduces the training amount by an order of magnitude compared with DCN-6 and Deep Unrolled ISTA. This is because for DCN-6 and Deep Unrolled ISTA networks, they learn the known model information, and when constructing the training set, they need to construct a training set that traverses all possible positions of the DOA of the source signals. The number of training set samples is a power function of the number of source signals. While the PnP-MAP method processes the known model information and unknown noise separately, and the denoising network contains less model information, resulting in less training data required. 4 9) Result analysis

[0138] 6) Result analysis

[0139] A total of 3 instance simulations were carried out in the present invention, Figure 3 which are the experimental verifications of the DOA estimation performance of the PnP-MAP method varying with the signal-to-noise ratio when the number of target sources is 3, 5, and 6 respectively.

[0140] Through observation and comparison, when the number of signal sources changes, the DOA estimation performance of the proposed PnP-MAP method in the present invention changes little, indicating that the PnP-MAP method is robust to the number of signal sources.

[0141] In summary, the proposed PnP-MAP method in the present invention processes the known model and unknown noise contained in the signal separately, making the required training data volume much lower than that of the deep convolutional network and the deep unrolled network, and having strong robustness to the number of source signals.< / w> ​

Claims

1. A plug-and-play single-bit sparse dipole array direction of arrival estimation method based on a noise reduction network, characterized in that: include: Step 1: Using virtual array signal processing technology and quantization-free technology, the DOA estimation problem of a single-bit sparse dipole array is transformed into a virtual signal DOA estimation problem of a differential array; Step 2: Use the plug-and-play technology to decompose the maximum a posteriori probability estimation algorithm for direction of arrival estimation into two parts: a known model and unknown noise. The known model and the unknown noise are iteratively solved to obtain the beam arrival direction angle. The specific solution methods are: The least squares method is used to solve the known model part to obtain a closed-form solution, and a data-driven denoising network is used to solve the unknown noise part.

2. The plug-and-play single-bit sparse dipole array direction of arrival estimation method based on noise reduction network according to claim 1, characterized in that: The specific method of using virtual array signal processing technology and quantization-free technology to transform the DOA estimation problem of a single-bit sparse dipole array into a virtual signal DOA estimation problem of a differential array is as follows: Calculate the received signal of the sparse dipole array at time t The unquantized covariance matrix of For the unquantized covariance matrix Vectorize and multiply by the weight matrix W to merge items at the same position, and the resulting differential array measurement vector Receiving signals from a sparse dipole array Perform single-bit sampling to obtain the received signal after single sampling Calculate the single-bit sampling covariance matrix of the received signal after single sampling For the unquantized covariance matrix Normalize to get the normalized covariance matrix By sampling the covariance matrix of a single bit Reconstruct the normalized covariance matrix The differential array measurement vector of the single-bit sparse dipole array is constructed according to the normalized covariance matrix.

3. The plug-and-play single-bit sparse dipole array direction of arrival estimation method based on noise reduction network according to claim 1, characterized in that: Calculate the received signal of the sparse dipole array at time t The unquantized covariance matrix of The specific formula is: in, g m.i represents the energy of the mth signal received in the i direction, is the response of the dipole vector sensor to the mth source signal, σ 2 represents the noise energy, I represents the identity matrix, (·) * represents the adjoint of the matrix, (·) H represents the conjugate transpose of a matrix, is the array element position set; is the steering vector matrix, where for The response vector of the array, is the response of the lth dipole element, is the normalized direction of arrival of the mth source signal.

4. The plug-and-play single-bit sparse dipole array direction of arrival estimation method based on noise reduction network according to claim 3, characterized in that: Differential array measurement vector Specifically: In the formula, represents the pseudo-inverse of the matrix, W represents the weight matrix, represents the steering vector matrix of the difference array, g i represents a virtual measurement signal, e0 is a vector, where the mth element <e0> m =δ m,0 , δ m,0 is the Kronecker function.

5. The plug-and-play single-bit sparse dipole array direction of arrival estimation method based on noise reduction network according to claim 2, characterized in that: By sampling the covariance matrix of a single bit Reconstruct the normalized covariance matrix Specifically: In the formula, <·> p,q Represents the element in the p-th row and q-th column of the matrix.

6. The plug-and-play single-bit sparse dipole array direction of arrival estimation method based on noise reduction network according to claim 4, characterized in that: The differential array measurement vector of the single-bit sparse dipole array is specifically:

7. The plug-and-play single-bit sparse dipole array direction of arrival estimation method based on noise reduction network according to claim 1, characterized in that: The specific method of using plug-and-play technology to decompose the maximum a posteriori probability estimation algorithm for direction of arrival estimation into two parts: a known model and unknown noise is as follows: The differential array measurement vector for solving the single-bit sparse dipole array is transformed into the angle of arrival problem for solving the single-bit sparse dipole array. The expression is: in, is a virtual measurement signal, is the virtual measurement signal in the i direction, is the signal energy received in the i direction of the mth signal after single-bit sampling and quantization, is the noise power after single-bit sampling, is the response of the dipole vector sensor to the mth source signal, is the normalized direction of arrival of the mth source signal; We estimate by solving the following maximum a posteriori probability estimation problem in, represents any regression term, α is the regression coefficient, is the noise energy after dequantization of single-bit sampling; By introducing the auxiliary variable z, the above formula can be expressed as: The Lagrange multiplier method is used to solve the above equation, which is: Introducing the Lagrangian multiplier μ, the Lagrangian objective function is: According to the idea of ​​alternating optimization, alternating optimization and z; Fixed z, Update The maximum a posteriori probability estimation problem is transformed into: The closed-form solution is: Where k represents the number of iterations; fixed Update z, and the maximum a posteriori probability estimation problem is transformed into: are the known model and the unknown noise respectively.

8. The plug-and-play single-bit sparse dipole array direction of arrival estimation method based on noise reduction network according to claim 1, characterized in that: The specific structure of the noise reduction network includes: The first part contains two convolutional layers. Each convolutional layer uses the relu function for nonlinear processing. The function of this convolutional layer is to extract the local features of the input data. The second part contains nine hidden layers and two convolutional layers. Batch normalization is added between each convolutional layer and the relu function to optimize the distribution of data through iterations in network training. The third part includes a convolution layer, and the activation function is still the relu function, which converts the feature data of 16 channels into a single-channel output through linear operation; The three parts are connected in sequence.

9. The plug-and-play single-bit sparse dipole array direction of arrival estimation method based on noise reduction network according to claim 1, characterized in that: The specific process of training the denoising network is as follows: Generate network labels, and set the labels to be sparse signals in the absence of noise The differential array receiving signal can be obtained through virtual array signal processing technology: in, Representing differential arrays in a network The received signal, is the steering vector matrix of the differential array in the network, Represented as a sparse signal in the absence of noise in the network; Sparse signal Obtained by the following formula: Steering vector matrix for differential arrays in a network The number of rows is greater than the number of columns; For plural Take out its real part and imaginary part and merge them into one channel, that is: in,(·) R To take the real part, (·) I To take the imaginary part operation, is the real part of the sparse signal, is the imaginary part of the sparse signal. After the merging operation, the label is a one-dimensional vector of 1×162 The input data of the network is generated by: in, is the noise energy after single-bit sampling in the network and quantization, and the Lagrangian operator μ = 0.1; Complexify the input data The processing is consistent with the network label, and the real part and the imaginary part are merged; Assume that the training dataset is There are J samples in total; the network parameter set is Ξ; the network output It is expressed as: The goal of the denoising network is to recover a clean signal from noisy input data. The minimum mean square error is used as the loss function to measure the difference between the denoising network output and the true value, and the denoising effect of the network is improved through the optimization process.

10. The plug-and-play single-bit sparse dipole array direction of arrival estimation method based on noise reduction network according to claim 9, characterized in that: The minimum mean square error loss function is: Where J is the number of samples, is the label of the jth sample, is the network output vector of the jth sample; The network training process is expressed as the following optimization problem:

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