DOA estimation method based on double-channel complex convolutional neural network

Abstract

This invention discloses a DOA estimation method based on a dual-channel complex convolutional neural network. The method first formulates the DOA estimation problem as a multi-label classification task, using the complex covariance matrix of the array received signal as input. This input is fed into the first channel, composed of standard convolutional layers, and the second channel, composed of dilated convolutional layers and pooling layers. The dilated convolutional layers increase the receptive field of the feature map without losing angular information. The features extracted from the two channels are fused and then output through a fully connected layer and a sigmoid function to achieve angular classification results, thus realizing DOA estimation under multi-source input. This invention further improves the accuracy of DOA estimation. Simulation results show that the dual-channel complex neural network feature fusion method has a better convergence speed, and under conditions of low signal-to-noise ratio and few snapshots, this method has higher estimation accuracy.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing, specifically involving a DOA (Driection of Arrival) estimation method. Background Technology

[0002] Array signal processing, also known as spatial domain signal processing, is an important branch of signal processing. Direction of arrival (DOA) estimation, a key research area in array signal processing, is widely used in radar, sonar, electronic reconnaissance, and radio communications. DOA estimation, also known as spatial spectrum estimation, processes the signals received by the array to estimate the direction angle of the spatial signal reaching the array reference element. In the late 1970s and early 1980s, the development of subspace algorithms elevated DOA estimation to super-resolution levels. Feature subspace algorithms are divided into two categories: noise subspace algorithms, represented by MUSIC (Multiple Signal Classification), and signal subspace algorithms, represented by ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique). These methods are based on covariance techniques, requiring a sufficient number of snapshots to accurately estimate DOA, especially under low signal-to-noise ratio (SNR) conditions.

[0003] In recent years, compressed sensing (CS) methods have also been used for DOA estimation, leveraging the sparsity of the signal source in the spatial domain (angle). DOA estimation is obtained after solving a sparse minimization task, and there are two main methods:

[0004] 1) Greedy method based on pseudonorm;

[0005] 2) Norm-based convex relaxation methods. Additionally, the more unique approach is l... 2,1 -SVD method. One of the main drawbacks of all these methods is that they require tuning one or more parameters (depending on the number of snapshots, SNR, or both) to ensure good performance, and DOA estimation is usually very sensitive to tuning of these parameters.

[0006] A recent approach involves estimating DOA using deep learning (DL). These methods do not require building a signal model; instead, they extract features from a large dataset and train the network to learn the nonlinear relationship between the array output and the direction of arrival, thus achieving DOA estimation. Numerous researchers have investigated this area and proposed several methods. For example, a deep neural network (DNN) with fully connected (FC) layers was used to classify the DOA of two targets using the signal covariance matrix. However, the results showed that the DOA estimation performance was not ideal. Another approach is a pseudospectral estimation method and an extended angle estimation method based on DL. However, these only demonstrated experimental results under high signal-to-noise ratio (SNR) conditions. Subsequent researchers used two-dimensional convolutional neural networks to estimate DOA under low SNR conditions, but the estimation accuracy needs further improvement due to the limitations of the single-channel real-valued network structure in signal feature extraction. Summary of the Invention

[0007] The technical problem this invention aims to solve is the insufficient feature extraction for direction-of-arrival (DOA) estimation using a single-channel real convolutional neural network array under low signal-to-noise ratio (SNR). This invention proposes an asymmetric dual-channel complex convolutional structure for DOA estimation under low SNR conditions. Dilated convolution is used to increase the receptive field and improve classification accuracy, and features extracted from the input data using standard convolution are fused. Furthermore, the complex convolutional neural network utilizes its unique complex convolution method to extract and fuse the amplitude and phase features of the signal, thereby achieving accurate DOA estimation for multiple objectives.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] The steps of the DOA estimation algorithm based on a dual-channel complex convolutional neural network are as follows:

[0010] Step 1: Determine the target spatial range. Two narrowband incoherent signals arrive at the linear array from different azimuth angles. At each input signal-to-noise ratio, arbitrarily select K training angles from the target spatial range G, set the resolution ρ = 1°, and calculate the corresponding complex covariance matrix. Then, convert the corresponding complex covariance matrix R... d X, as input data for a two-channel convolutional neural network d The input dataset can be defined as χ = {X} (1) ,X (2) ,...,X (D)};

[0011] Step 2: For the corresponding complex covariance matrix, convert its training angles in the target spatial domain into binary vectors Z, and use these binary vectors as the corresponding input labels to obtain the training dataset. The training dataset is represented as follows:

[0012]

[0013] Step 3: Use a dual-channel convolutional neural network to extract features separately, fuse the feature extraction results of the two channels through a fully connected layer, arrange the output feature maps of the two channels into an output vector, and calculate the category corresponding to the feature.

[0014] Step 4: When inputting test sample X d At that time, the output label of the dual-channel convolutional neural network is:

[0015]

[0016] Where f(·) represents the nonlinear function of the entire neural network structure, and the output value is...

[0017] Output value Corresponding to the input label, the K DOA estimates of the input source correspond to angles with a probability of 1 for the input label, and the output is the result of the DOA estimation.

[0018] Compared with the prior art, the present invention has the following technical effects:

[0019] 1. Using the complex covariance matrix as input, compared to separating the real and imaginary parts of the covariance matrix, makes better use of amplitude and phase features and has richer feature learning capabilities.

[0020] 2. The DOA estimation algorithm based on dual-channel complex convolutional neural networks has a faster convergence speed compared to single-channel real number network structures.

[0021] 3. Simulation results show that the DOA estimation algorithm based on dual-channel complex convolutional neural network has better estimation accuracy than the single-channel real network structure under low signal-to-noise ratio and relatively few snapshots. Attached Figure Description

[0022] Figure 1 This is a flowchart of the signal processing of the present invention.

[0023] Figure 2 This is a dual-channel complex convolutional neural network structure.

[0024] Figure 3 This is the accuracy curve.

[0025] Figure 4 This is the loss curve.

[0026] Figure 5 The root mean square error curves are shown for different SNR values.

[0027] Figure 6The root mean square error curves are shown for different snapshots.

[0028] Figure 7 The root mean square error curves are shown for different arrival angle differences. Detailed Implementation

[0029] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings:

[0030] This invention mainly studies a DOA estimation algorithm based on a dual-channel complex convolutional neural network. Figure 2 This is a schematic diagram of a two-channel complex convolutional neural network structure. Figure 1 This is the signal processing flow of this embodiment. Its main steps are as follows:

[0031] Step 1: Input the dataset, specifically:

[0032] For a uniform linear array (ULA) with N elements, the complex covariance matrix of the array output is R. d It can be seen that it is an N×N dimensional matrix, and each element can be represented using the real and imaginary part method as follows:

[0033]

[0034] Since a complex neural network is used, it is not necessary to store the real and imaginary parts of the covariance matrix in different channels; the complex covariance matrix R can be directly stored in the network. d As input to the neural network.

[0035] Step 2: Input data labels, specifically:

[0036] DOA estimation is modeled as a multi-label classification task. For the target spatial range G = [-60°, 60°], two narrowband incoherent signals arrive at the linear array from different azimuth angles. At each input signal-to-noise ratio (SNR), K = 2 angles are arbitrarily selected from the range G with a resolution of ρ = 1°, resulting in D = 7260 possibilities. The corresponding covariance matrix is ​​then calculated. The covariance matrix R for each possibility is... d X, as input data to the neural network (d) Therefore, the input dataset for a CNN can be defined as χ = {X} (1) ,X (2) ,...,X (D)}

[0037] Next, for each example X (d)The two training angles in G are converted into binary vectors with two 1s and the rest 0s. With a resolution of ρ = 1°, for a target spatial range G = [-60°, 60°], the grid will become M = [-60°, ..., -1°, 0°, 1°, ..., 60°], a total of 121 grid points; furthermore, the angle pair {59°, 60°} corresponds to a 121×1 binary vector. Used as the corresponding input labels. Therefore, the training dataset

[0038] Step 3: Extract and fuse features from both channels, specifically as follows:

[0039] In the dual-channel convolutional network structure proposed in this paper, the first channel consists of a standard convolutional layer, and the second channel consists of a dilated convolutional layer and a pooling layer. The two channels are used for feature extraction separately and then fused together.

[0040] (1) Standard convolutional layer

[0041] The dual-channel network structure consists of seven standard convolutional layers, C1 to C7, each with 128 convolutional kernels. Each convolutional layer is followed by a batch normalization layer and a ReLU nonlinear activation function. The kernel size is k×k, with k=3 for layer C1 and k=2 for layers C2-C7. The stride δ=2 during convolution in layer C1 and δ=1 during convolution in layers C2-C7. Layers C1-C7 have no padding.

[0042] For a complex input h = x + iy, where x is the real part, y is the imaginary part, both x and y are real vectors, and i is the imaginary unit. The complex convolution kernel W = A + iB, where A is the real matrix, B is the imaginary matrix, both A and B are real matrices, and i is the imaginary unit. The complex input and complex convolution are specifically represented as follows:

[0043] W*h=(A*xB*y)+i(B*x+A*y)

[0044] Represented in matrix form:

[0045]

[0046] in, Represents the real part of the variable. It represents the imaginary part of the variable.

[0047] The convolution operation of the q-th filter in the l-th complex convolutional layer is:

[0048]

[0049]

[0050] In the formula: m,n=1,2,...,M, X represents the output of the convolution operation of the q-th filter in the l-th convolutional layer, i.e., the q-th feature map of the l-th layer. [l-1] This represents the output of the (l-1)th layer, where M [l-1] This represents the kernel size of the (l-1)th layer. This represents the number of convolutional kernels in the (l-1)th layer. This represents the q-th complex weight matrix of the l-th convolutional layer. Indicates deviation. V represents the complex convolution weighted sum of the q-th filter in the l-th convolutional layer; the symbol * represents the convolution operation; f(·) represents the nonlinear activation function; V [l] O represents the weighted sum of complex convolutions in the l-th convolutional layer; [l] This represents the output data of the l-th layer.

[0051] (2) Void convolution layer

[0052] The dual-channel network structure contains nine dilated convolutional layers (D1-D9), each with 128 convolutional kernels. Each convolutional layer is followed by a batch normalization layer and the ReLU non-linear activation function. Dilated convolution injects holes into the standard convolutional kernel to increase the network's receptive field, effectively preventing feature loss and improving classification accuracy. To avoid grid artifacts, the dilation rate is 5 for D1, D4, and D7, 2 for D2, D5, and D8, and 1 for D3, D6, and D9. The kernel size is k×k, with k=3 for layers D1-D9, and a stride δ=1 during convolution. p represents the padding size, ensuring the output feature map size equals the input feature map size. For a convolution kernel of size k×k, r is the dilation rate when the kernel convolves with the input data. This is equivalent to inserting r-1 zero values ​​between two adjacent values ​​of the original filter to generate a new filter, and then convolving the input signal with the filter. The convolution kernel after injecting dilation is denoted as κ.

[0053] For a complex input s = u + iv, where u is the real part, v is the imaginary part, both u and v are real vectors, and i is the imaginary unit. The complex convolution kernel Z = E + iF, where E is the real matrix, F is the imaginary matrix, both E and F are real matrices, and i is the imaginary unit. The complex input and complex convolution are specifically represented as follows:

[0054] Z*s=(E*uF*v)+i(F*u+E*v)

[0055] Represented in matrix form:

[0056]

[0057] in, Represents the real part of the variable. It represents the imaginary part of the variable.

[0058] The convolution operation of the q-th filter in the l-th complex dilated convolutional layer is:

[0059]

[0060]

[0061] In the formula: m,n=1,2,...,Q, Y represents the output of the convolution operation of the q-th filter in the l-th convolutional layer, i.e., the q-th feature map of the l-th layer. [l-1] This represents the output of the (l-1)th layer, where Q [l-1] This represents the kernel size of the (l-1)th layer. This represents the number of convolutional kernels in the (l-1)th layer. This represents the q-th complex weight matrix of the l-th convolutional layer. Indicates deviation. This represents the complex convolution weighted sum of the q-th filters in the l-th dilated convolutional layer; the symbol * represents the convolution operation; f(·) represents the nonlinear activation function; This represents the weighted sum of complex convolutions in the l-th dilated convolutional layer; This represents the output data of the l-th layer.

[0062] To improve computational speed and the robustness of the extracted features, pooling layers, P1, P2, and P3, are added after D3, D6, and D9 respectively to perform downsampling operations. This operation is performed independently on the output feature maps of D3, D6, and D9, ensuring that the number of input and output feature maps for this layer is equal and corresponds one-to-one. A node in the output feature map is a function of multiple nodes within the corresponding local receptive field in the input feature map. Average pooling is used to calculate the average value of each node within the local receptive field, and a 2×2 filter is used.

[0063] (3) Fully connected layer

[0064] The first channel, composed of standard convolutional layers, and the second channel, composed of dilated convolutional layers and pooling layers, complete image feature extraction. The fully connected layer fuses the feature extraction results from both channels, arranges the output feature maps of the two channels into an output vector, and calculates the category corresponding to each feature. Each node in the input and each node in the output of the fully connected layer has a weighted link, expressed as follows:

[0065] In a fully connected layer, the product of complex weights W and complex data c is:

[0066] Wc = (Xa - Yb) + i(Ya + Xb)

[0067] Represented in matrix form

[0068]

[0069] The specific operations of the l-th complex fully connected layer are as follows:

[0070]

[0071]

[0072] Among them, W [l] c represents the weight of the l-th layer of the fully connected layer. [l-1] This represents the output of the (l-1)th layer of the fully connected layer. The symbol · represents the bias of the l-th layer; the symbol · represents the convolution operation in the fully connected layer; f(·) represents the non-linear activation function. This represents the weighted sum of complex convolutions in the l-th fully connected layer; This represents the output data of layer l. The fully connected layer FC1 has 1024 neurons, followed by ReLU and Dropout layers. The weights are randomly set to zero with a 30% probability to improve the generalization of the estimator and avoid overfitting. FC2, as the output layer, consists of a layer with 121 neurons and a sigmoid layer.

[0073] Step 4: Output the DOA estimation results, specifically:

[0074] The neural network was trained offline in a supervised manner on the training dataset D, with the input label set to 1 at the source DOA angle and 0 elsewhere. When the test sample X was input... d At that time, the output label of the dual-channel convolutional neural network is:

[0075]

[0076] Where f(·) represents the nonlinear function of the entire neural network structure, and the output value is...

[0077] The effectiveness of the method of this invention is verified by computer simulation below. The experiment selects the binary cross-entropy function as the loss function and the Adam function as the optimization function. The initial learning rate is 0.0001, β1 = 0.9, and β2 = 0.999. The batch size is set to 32, and the number of iterations is set to 80. When the validation loss reaches stability after 10 epochs, the learning rate is reduced by a factor of 0.7. During the training process, the input data is randomly allocated into a training set (90%) and a validation set (10%). Figure 3 , Figure 4 These figures represent the accuracy and loss curves of a single-channel real convolutional network, a single-channel complex convolutional network, and a dual-channel complex convolutional network, respectively, on the validation set during training. The maximum number of iterations for all three models is 80. Figure 3 and Figure 4 It can be seen that all three models tend to stabilize after a certain number of iterations. The single-channel complex network has a faster convergence speed than the single-channel real network, and the dual-channel complex network has a faster convergence speed than the single-channel complex network.

[0078] This invention uses root mean square error (RMSE) to measure DOA estimation performance. Experiments were conducted to analyze the effects of signal-to-noise ratio, number of snapshots, and angle of arrival difference on DOA estimation performance.

[0079] (1) The impact of signal-to-noise ratio (SNR) on DOA estimation performance:

[0080] In this experiment, the DOA estimation performance of the proposed dual-channel complex convolutional neural network and single-channel complex convolutional neural network was evaluated in two directions: θ1 = 34.13° and θ2 = 36.13°. The estimation performance was then compared with that of the single-channel real network at these two angles. Figure 5 The figures show the root mean square error curves under different SNRs. It can be seen that the proposed dual-channel complex network estimation performance is generally better than the single-channel real network estimation performance under low signal-to-noise conditions.

[0081] (2) The impact of snapshot number on DOA estimation performance:

[0082] In this experiment, the DOA of two sources at a signal-to-noise ratio of -10 dB was estimated, with the number of snapshots ranging from 100 to 10,000. For each value of snapshot T, the average RMSE exceeded 1,000 MC. The direction of the first source was -26.13°, and the direction of the second source was -24.13°. Figure 6 The root mean square error curves under different snapshots show that the estimation performance of the dual-channel complex convolutional neural network structure and the robustness performance of the single-channel real structure estimation are basically the same, but the structural angle estimation proposed in this paper has better performance.

[0083] (3) The impact of the angle of arrival difference on DOA estimation performance:

[0084] The first source angle θ1 = -11.8°, the second source angle θ2 = θ1 + Δθ, the signal-to-noise ratio is -10dB, and the number of snapshots is 500. For each Δθ value, 1000 Monte Carlo experiments are performed. Figure 7 The root mean square error curves for different arrival angle differences show that the performance of both the single-channel real number estimation and the proposed dual-channel complex network structure estimation are relatively stable, but the RMSE of the dual-channel complex network estimation is smaller than that of the single-channel real number network estimation.

[0085] Therefore, single-channel complex networks have a faster convergence speed than single-channel real networks, and dual-channel complex networks offer better feature extraction than single-channel complex networks, resulting in a faster convergence speed. Especially at low signal-to-noise ratios and with a relatively small number of snapshots, dual-channel complex networks exhibit higher estimation accuracy compared to single-channel real networks.

[0086] Although the above embodiments have described the present invention in detail, in actual implementation, details can still be supplemented and equivalent substitutions can be made according to actual operation. It should be noted that these technical solutions that supplement details and make equivalent substitutions to the claims of the present invention are all considered to be within the scope of protection of the present invention.

Claims

1. A DOA estimation method based on a dual-channel complex convolutional neural network, characterized in that, The steps include the following: Step 1: Determine the target spatial range. Two narrowband incoherent signals arrive at the linear array from different azimuth angles. At each input signal-to-noise ratio, arbitrarily select K training angles from the target spatial range G and set the resolution. And calculate the corresponding complex covariance matrix, and then... Input data for a two-channel convolutional neural network Define the input dataset as ; Step 2: For the corresponding complex covariance matrix, convert its training angles in the target spatial domain into binary vectors Z, and use these binary vectors as the corresponding input labels to obtain the training dataset. The training dataset is represented as follows: ； Step 3: Extract features using a dual-channel convolutional neural network. Fuse the feature extraction results of the two channels through a fully connected layer, arrange the output feature maps of the two channels into an output vector, and calculate the category corresponding to the feature. The first channel of the dual-channel convolutional neural network is a standard convolutional layer, and the second channel is a dilated convolutional layer and a pooling layer. The hollow convolutional layer consists of nine layers, represented as follows: Each convolutional layer contains 128 convolutional kernels, and each convolutional layer is followed by a batch normalization layer and a non-linear activation function. Dilated convolution injects holes into the standard convolution kernel; to avoid grid effects, The void ratio is 5. The void ratio is 2. The void ratio is 1 for all convolution kernel sizes. , Layer convolution kernel size , stride during the convolution process of a layer , The padding size is set to ensure that the output feature map size equals the input feature map size. For a size of... The convolution kernel is defined as follows: r is the dilation rate of the kernel when convolving the input data. This is equivalent to inserting r-1 zero values ​​between two adjacent values ​​of the original filter to generate a new filter. The input signal is then convolved with the filter, and the resulting kernel with the added dilation is denoted as . ; For complex number input ,in It is the real part. It is the virtual part. and They are all real number vectors. It is the imaginary unit; complex convolution kernel , It is a real part matrix. It is an imaginary matrix. and They are all real number matrices. The imaginary unit is used to represent the complex input and complex convolution as follows: ； Represented in matrix form: ； in, Represents the real part of the variable. Represents the imaginary part of a variable; No. The first complex hollow convolutional layer The convolution operation of each filter is as follows: ； ； In the formula, , , Indicates the first The first convolutional layer The output of the convolution operation of the nth filter, i.e., the nth... The first layer Each feature map Indicates the first The output of the layer, where , Indicates the first kernel size of the layer Indicates the first The number of convolutional kernels in a layer Indicates the first The first convolutional layer A complex weight matrix, Indicates deviation, Indicates the first The first empty convolutional layer A complex convolution weighted sum of filters; symbol This represents the convolution operation; Represents a non-linear activation function; Indicates the first A complex convolution weighted sum of dilated convolutional layers; Indicates the first Layer output data; exist A pooling layer is then added to perform downsampling operations, denoted as... This operation is in The output feature maps are processed independently, so the number of input and output feature maps of this layer are equal and correspond one-to-one. A node in the output feature map is a function of multiple nodes in the corresponding local receptive field of the corresponding feature map in the input. Average pooling is selected to take the average value of each node in the local receptive field, and the size of the filter used is 2×2. Step 4: When inputting test samples At that time, the output label of the dual-channel convolutional neural network is: ； in The output value represents a nonlinear function representing the entire neural network structure. , Output value Corresponding to the input label, the K DOA estimates of the input source correspond to angles with a probability of 1 for the input label, and the output DOA estimation results are given.

2. The DOA estimation method based on a dual-channel complex convolutional neural network according to claim 1, characterized in that, The target airspace range is: .

3. The DOA estimation method based on a dual-channel complex convolutional neural network according to claim 1, characterized in that, The standard convolutional layer has 7 layers, represented as follows: Each standard convolutional layer contains 128 convolutional kernels, and each convolutional layer is followed by a batch normalization layer and a non-linear activation function. Regarding the kernel size ,in Layer convolution kernel size , Layer convolution kernel size , stride during the convolution process of a layer , stride during the convolution process of a layer , None of the layers are filled; For complex number input ,in It is the real part. It is the virtual part. and They are all real number vectors. It is the imaginary unit, the complex convolution kernel. , It is a real part matrix. It is an imaginary matrix. and They are all real number matrices. The imaginary unit is used to represent the complex input and complex convolution as follows: ； Represented in matrix form: ； in, Represents the real part of the variable. Represents the imaginary part of a variable; No. The first complex convolutional layer The convolution operation of each filter is as follows: ； ； In the formula: , , Indicates the first The first convolutional layer The output of the convolution operation of the nth filter, i.e., the nth... The first layer Each feature map Indicates the first The output of the layer, where , Indicates the first kernel size of the layer Indicates the first The number of convolutional kernels in a layer Indicates the first The first convolutional layer A complex weight matrix, Indicates deviation, Indicates the first The first convolutional layer The complex convolution weighted sum of filters, sign This represents the convolution operation. Represents a non-linear activation function; Indicates the first A weighted sum of complex convolutions from 1 convolutional layer; Indicates the first The output data of the layer.

4. The DOA estimation method based on a dual-channel complex convolutional neural network according to claim 1, characterized in that, Each node in the input and each node in the output of the fully connected layer are connected by weighted links, as shown in the following expression: In a fully connected layer, complex weights and complex data The product operation is: ； Represented in matrix form ； No. The specific operations of a complex fully connected layer are as follows: ； ； in, Indicates the fully connected layer number 1 Layer weights, Indicates the fully connected layer number 1 The output of the layer, Indicates the first Layer deviation, symbol This represents the convolution operation in a fully connected layer; Represents a non-linear activation function; Indicates the first A weighted sum of complex convolutions from fully connected layers; Indicates the first The output data of the fully connected layer There are 1024 neurons, followed by ReLU and Dropout layers, with weights randomly set to zero with a 30% probability. The output layer consists of a layer with 121 neurons and a sigmoid layer.

Images