DOA estimation method and system based on deep complex value convolution attention residual network

Abstract

The invention discloses a DOA (Direction of Arrival) estimation method and system based on a deep complex value convolution attention residual network, belongs to the technical field of array signal processing, and solves the technical problems of low precision and poor robustness of the existing DOA estimation method under the severe conditions of low signal-to-noise ratio, limited snapshot number and the like. The method comprises the following steps: acquiring data by using a co-prime array and preprocessing to obtain SCM data as original input information of DOA estimation; constructing a deep complex value convolution attention residual network to directly process covariance matrix information of a complex field, and utilizing an initial two-dimensional complex value convolution layer, a cascaded complex value convolution block attention network and a cross-layer residual connection structure to deeply extract complex value features related to a space angle; the DOA estimation module is responsible for finally mapping the extracted high-dimensional complex value feature vector to a representation space directly related to a DOA estimation task, and the output module converts the internal feature representation output by the DOA estimation module into a DOA estimation result which can be explained by a user.

Description

Technical Field

[0001] The present invention relates to the field of array signal processing technology, and in particular to a DOA estimation method and system based on a deep complex-valued convolutional attention residual network. Background Art

[0002] Direction of Arrival (DOA) estimation is a core problem in array signal processing. Its goal is to determine the spatial angle of a signal source relative to a receiving array. It is widely used in numerous fields, including radar detection, wireless communications, sonar positioning, and radio astronomy. Traditional DOA estimation algorithms, such as the Multiple Signal Classification (MUSIC) algorithm, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm, and its various improved versions, such as Weighted MUSIC, Root-MUSIC (R-MUSIC), Weighted ESPRIT, and Total Least Squares ESPRIT (TLS-ESPRIT), are mostly based on regular array structures such as uniform linear arrays (ULAs) and make strong assumptions about the signal's incoherence with Gaussian white noise and signal incoherence. Furthermore, to avoid phase ambiguity, uniform array elements are typically spaced no more than half a wavelength apart. This limits the array aperture, which in turn affects the resolution of DOA estimation and the number of identifiable sources. Expanding the ULA aperture by increasing the number of elements directly leads to a significant increase in hardware cost, system complexity, and power consumption, making it impractical in many practical applications.

[0003] To overcome these limitations, sparse arrays, such as coprime arrays (CA), have emerged. By utilizing non-uniform array placement and coprime subarray design, a large-aperture virtual array can be synthesized with fewer physical elements. While CA offers significant advantages over ULA in increasing array aperture and degrees of freedom, its application to DOA estimation also presents new challenges. The non-uniformity of CA destroys the Vandermonde structure of the array flow pattern. Directly applying algorithms such as MUSIC and ESPRIT based on subspace decomposition can lead to severe model mismatch and a sharp deterioration in performance. To address this, researchers have proposed virtual array processing techniques, a typical example being Spatial Smoothing MUSIC (SS-MUSIC). This method restores the full rank of the virtual array's covariance matrix by spatially smoothing it before applying the MUSIC algorithm. There is also research that incorporates theories such as ESPRIT, Compressed Sensing (CS), and Sparse Bayesian Learning (SBL) into DOA estimation of coprime arrays. However, these model-driven approaches are computationally complex and lack robustness under non-ideal conditions, such as low signal-to-noise ratio (SNR), limited snapshot counts, coherent signal sources or array element position errors, and channel gain / phase mismatches. While off-grid and gridless approaches can alleviate grid mismatch issues, they often sacrifice computational efficiency or are sensitive to noise. Practical applications still require parameter tuning, limiting their applicability.

[0004] Deep learning (DL) provides a new data-driven approach for DOA estimation. Deep Neural Networks (DNNs), with their powerful nonlinear fitting capabilities and ability to automatically learn features from data, employ structures such as fully connected neural networks (FCNNs) and convolutional neural networks (CNNs) to learn the mapping relationship between received array data or its covariance matrix and DOA. CNNs are particularly well-suited to processing the spatial structure of covariance matrices. Furthermore, complex-valued neural networks (CVNNs), by preserving amplitude and phase information, exhibit superior accuracy and robustness compared to real-valued networks in low signal-to-noise ratio (SNR) and low-snapshot scenarios. However, current deep learning research on CA remains insufficient. In particular, the design of efficient network architectures combining complex-valued convolutions, attention mechanisms, and residual connections is urgently needed to address the model mismatch and noise sensitivity issues unique to CA. Summary of the Invention

[0005] In response to the shortcomings and deficiencies in the prior art, the present invention provides a novel deep learning network structure that can fully adapt to and utilize the characteristics of CA, effectively process complex array signal data, and achieve high-precision and high-robustness DOA estimation method and system based on deep complex-valued convolution attention residual network for coprime array signal sources by integrating advanced network components complex-valued convolution, attention mechanism, and residual connection.

[0006] To achieve the above objectives, the present invention is implemented by the following technical solutions: The DOA estimation method based on deep complex-valued convolutional attention residual network (DC-CARN) provided by the present invention comprises the following steps:

[0007] S1. The data preprocessing module obtains complex data, collects data using a coprime array (CA), and preprocesses the data to obtain the complex-valued sample covariance matrix (SCM) data as the original input information for DOA estimation.

[0008] S2, feature extraction module, constructs a deep complex-valued convolutional attention residual network (DC-CARN) to directly process the covariance matrix information in the complex domain. The deep complex-valued convolutional attention residual network uses an initial two-dimensional complex-valued convolutional layer, a complex-valued convolutional block attention network, and a cross-layer residual connection structure to deeply extract complex-valued features related to spatial angles;

[0009] S3, DOA estimation module; including a multi-layer complex-valued fully connected neural network layer (CV-FCNN), which is responsible for ultimately mapping the extracted high-dimensional complex-valued feature vector to a representation space directly related to the DOA estimation task, that is, for mapping the complex-valued features to the angle domain; wherein the complex-valued fully connected neural network layer performs nonlinear transformation and mapping on the one-dimensional complex-valued feature vector, and maps the high-dimensional complex-valued feature vector extracted in step S2 to a representation space directly related to the DOA estimation task;

[0010] S4, output module, is used to convert the angle domain feature representation after completing the DOA estimation task into a user-interpretable DOA estimation probability distribution result.

[0011] Preferably, in step S2, a Complex-valued Convolutional Block Attention Module (CV-CBAM) is embedded in the feature extraction module, which includes channel attention and spatial attention sub-modules specifically designed for complex-valued features. Specifically, it receives the complex-valued SCM data obtained in step S1. Through the channel attention and spatial attention mechanisms, the above sub-module network can adaptively learn and emphasize the feature channels and spatial positions that are most important for the current task, suppress the interference of noise and irrelevant features, and through the initial two-dimensional complex-valued convolutional layer, cascaded complex-valued convolutional block attention modules and cross-layer residual connection structures, deeply extract the complex-valued feature vectors related to the spatial angle.

[0012] Preferably, in step S1, obtaining the complex-valued SCM data specifically includes:

[0013] A co-prime array is established by superimposing and arranging two uniform linear arrays with the number of array elements being co-prime. The number of array elements of the first sub-array is M, and the array element spacing is Nd; the number of array elements of the second sub-array is N, and the array element spacing is Md; M and N are co-prime and M < N, d is the half wavelength of the signal, and the total number of array elements of the co-prime array is P = M + N - 1;

[0014] Receive J far-field narrowband signals to form an array received signal data model:

[0015]

[0016] where, X Ω (t) is the array received signal at time t, N Ω (t) is Gaussian white noise, A Ω is a (M + N - 1)×J dimensional array manifold matrix, a Ω (θ j ) is the array steering vector corresponding to the jth signal;

[0017] Calculate the SCM data according to L snapshot data, specifically:

[0018]

[0019] where, is a P×P dimensional complex matrix, L represents the number of snapshots, (·) Η represents the operation of taking the conjugate transpose.

[0020] Preferably, in step S2, it includes S21. In the deep complex-valued convolutional attention residual network, the initial two-dimensional complex-valued convolutional layer is used to perform preliminary local feature perception and abstraction on the input complex-valued SCM data, specifically:

[0021] The input complex-valued SCM data is first processed by a two-dimensional complex-valued convolutional layer. This convolutional layer has N (q, q)-sized filters for complex-domain operations. (q, q) indicates that the size of the convolution kernel of this two-dimensional complex-valued convolutional layer is q×q. The complex filter matrix W = A + iB is convolved with the complex vector h = x + iy. The vector h is convolved with the filter W. The complex-valued convolution operation is implemented in the following matrix form:

[0022]

[0023] Where A and B are real matrices, x and y are real vectors, R(·) represents the real part, I(·) represents the imaginary part, and * represents a real-valued convolution operation;

[0024] The output of the initial two-dimensional complex-valued convolutional layer is sequentially subjected to two-dimensional complex-valued batch normalization and complex-valued activation function processing; the complex-valued LeakyReLU activation function is applied to the real and imaginary parts of the variables in the previous layer respectively. Therefore, the output of a two-dimensional complex-valued convolutional layer can be expressed as:

[0025] f k (X) = CV-LeakyReLU(CV-BN(W k *X+b k ))

[0026] Among them, W k and b k Represents the filter matrix and bias vector of the k-th 2D complex-valued convolutional layer.

[0027] Preferably, the method further includes S22, wherein the deep complex-valued convolutional attention residual network utilizes a plurality of complex-valued convolutional attention modules connected in series, which are sequentially connected along the signal processing direction to form a deep feature extraction path, and the number of filter channels of the convolution layer in the subsequent complex-valued convolutional attention module is greater than or equal to the number of filter channels of the convolution layer of the preceding module;

[0028] Each complex-valued convolutional attention module includes multiple two-dimensional complex-valued convolutional layers and a complex-valued convolutional block attention network. The two-dimensional complex-valued convolutional layers continue to operate in the complex domain, further performing nonlinear transformations and spatial feature extraction on the feature maps. The number of filters between modules is designed to gradually increase to learn feature representations at different levels and dimensions.

[0029] The channel attention module in the complex-valued convolutional block attention network is used to adjust the channel weight. Its input is the complex-valued feature X obtained by the two-dimensional complex-valued convolution layer, and the complex-valued feature X is mapped to the real number domain to calculate the feature matrix M = |X|; the feature map of each channel is globally max-pooled M max and global average pooling M avg , then splice to get M concat=[M avg ,M max ], the splicing result is used as input to the perceptron MLP, and the complex scaling parameter P = MLP (M concat ); also splits the output into a scaling factor S applied to both the real and imaginary parts r and S i , construct the complex scaling factor S = S r +jS i ; Finally, the feature map is scaled by the complex number of the channel scale to obtain the enhanced feature

[0030] The spatial attention module in the complex-valued convolutional block attention network is used to adjust the spatial position weight. The feature map enhanced by the complex-valued channel attention module is modulo M′=|X′| and the average pooling M′ in the spatial dimension is performed. avg and maximum pooling M′ max , and then splice to get M′ spatial =[M′ avg ,M′ max ], then input into the complex-valued convolutional layer to learn the weight of each position, and pass through the Sigmoid activation function to obtain the spatial attention weight W s , and finally complete the weighting of the feature map to obtain the enhanced feature

[0031] Preferably, the method further includes S23, wherein the deep complex-valued convolutional attention residual network utilizes a cross-layer residual connection structure and adopts a cross-layer shortcut connection to add the input features of the module to the output features of the module directly or after a simple transformation, thereby realizing feature fusion across modules, specifically:

[0032] Each complex-valued convolutional attention module is equipped with a residual connection, which directly adds the module's input feature x to the module's processed output F(x) to form the final output F(x)+x; this helps in gradient propagation and training deep networks.

[0033] The final output end of the feature extraction module is also provided with a flattening layer for structural conversion, which converts the multi-dimensional complex-valued feature map from the feature extraction module into a one-dimensional complex-valued feature vector to adapt to the input requirements of the subsequent fully connected layer.

[0034] Preferably, in step S3, the DOA estimation module includes a plurality of CV-FCNN layers and a complex-valued Dropout layer inserted between every two adjacent CV-FCNN layers;

[0035] The CV-FCNN layer uses a complex weight matrix and a complex bias vector to perform an affine transformation on the input one-dimensional complex-valued feature vector and introduces nonlinearity through a complex-valued activation function to achieve high-level semantic mapping in the feature space. The CV-FCNN of the kth layer can be expressed as:

[0036] n k =W k,k-1 h k-1 +b k

[0037] h k =CV-LeakyReLU(net k )

[0038] Among them, W k,k-1 To represent the complex-valued weight of the k-1th layer, h k-1 is the k-1th layer input, b k is the bias of the kth layer, n k is the output of the kth layer, and LeakyReLU is the complex-valued activation function;

[0039] The complex-valued Dropout layer is used as a regularization method to randomly "drop out" neurons with a specific probability during training, discarding both the real and imaginary parts, reducing the co-adaptation between neurons, enhancing the generalization ability of the model, and preventing overfitting when the training data is limited.

[0040] Preferably, in step S4, the output module specifically includes:

[0041] A feature conversion unit is used to convert the complex-valued feature vector of the complex-valued fully connected network layer into a real-valued representation; the real and imaginary components of the complex-valued vector are concatenated to form a real-valued vector with doubled dimension;

[0042] The output mapping layer is a standard real-valued fully connected layer FCNN, whose number of output neurons is equal to the total number of pre-set discrete angle grid points G; this layer is responsible for linearly mapping the converted high-dimensional real-valued feature vector to G angular dimensions;

[0043] The activation function unit adopts the Sigmoid activation function. The Sigmoid function compresses each output value to the (0, 1) interval so that it can be interpreted as the posterior probability that the signal source exists at the corresponding angle grid point.

[0044] Preferably, the output module outputs a G-dimensional real-valued probability vector, i.e., the estimated angle space spectrum, and maps the feature vector to a pre-divided grid, which is finally mapped to the angle distribution probability space through the Sigmoid activation function to determine the DOA estimate; specifically, it is expressed as:

[0045]

[0046] Where h′={Real(h3),Imag(h3)} represents the concatenation of the real and imaginary parts of the output of the last CV-FCNN layer, and W′ represents the weight matrix of the output layer.

[0047] The DOA estimation system based on the deep complex-valued convolutional attention residual network uses the above-mentioned DOA estimation method, specifically including:

[0048] System input interface, used to receive complex value SCM data from the outside;

[0049] A feature extraction module, whose input end is electrically connected or data-connected to the system input interface and whose output end is connected to the input end of the flattening layer; and is used to extract the complex-valued feature representation related to the DOA from the original SCM layer by layer and in depth;

[0050] The flattening layer converts the multi-dimensional complex-valued feature tensor output by the feature extraction module into a one-dimensional long vector form to adapt to the input requirements of the subsequent fully connected layer;

[0051] The DOA estimation module has its input connected to the output of the flattening layer and its output connected to the output module; it is used to map the high-dimensional complex-valued feature vector extracted by the feature extraction module to a representation space directly related to the DOA estimation task;

[0052] The output module and the output interface are electrically connected or data-connected to the output interface and are used to output the direction of arrival (DOA) estimation probability spectrum.

[0053] The DOA estimation method and system based on deep complex-valued convolutional attention residual network proposed in this invention have the following beneficial effects:

[0054] (1) The DOA estimation method based on the deep complex-valued convolutional attention residual network of the present invention combines the complex-valued network structure with the attention mechanism, completely retains the signal phase information through complex domain operations, and uses complex-valued convolutional attention weighting to enhance key feature extraction and residual connection to optimize gradient propagation, so that the model can still maintain stable performance under low SNR and few snapshot conditions. In addition, the deep complex-valued convolutional attention residual network system adopts an end-to-end learning architecture, breaking through the strong assumptions of traditional methods on signal models, and can automatically learn the complex and highly nonlinear mapping relationship from SCM to DOA from the data, and adaptively mine the virtual aperture characteristics of coprime arrays. Finally, through the coordinated optimization of complex-valued processing, attention weighting and residual connection, the subtle feature differences corresponding to different DOAs can be more finely captured and distinguished, so that the system can achieve higher estimation accuracy while maintaining the powerful expression ability of the deep network, significantly improving the robustness and estimation accuracy under low SNR and few snapshots.

[0055] At the same time, the feature extraction module combines the attention mechanism to focus on key features and the residual connection structure to optimize gradient propagation. The attention mechanism enables the model to adaptively focus on the feature information most relevant to DOA estimation, suppressing redundancy and interference; the residual connection structure allows the construction of deeper network models, promotes the effective transmission and fusion of features, and enables deeper network structures to be stably trained and function, thereby improving the model's capacity and feature expression level.

[0056] (2) The deep complex-valued convolutional attention residual network system of the present invention innovatively uses the complex-valued SCM data generated by CA as input, and implicitly learns the virtual aperture characteristics of the coprime array through the deep complex-valued convolutional attention residual network, thereby obtaining a resolution and degree of freedom that exceeds the limitations of the number of physical array elements; and the use of regularization methods such as complex-valued Dropout helps to prevent overfitting and effectively improve the generalization performance of the deep complex-valued convolutional attention residual network system on unseen data.

[0057] (3) The deep complex-valued convolutional attention residual network system of the present invention integrates multiple advanced deep learning components, such as complex-valued operations, convolutional networks, attention mechanisms, and residual networks, to construct a dedicated optimized architecture for DOA estimation. Furthermore, the modular design also gives the system good scalability and configurability, making it easy to adjust the network size and complexity according to specific application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Schematic diagram of the structure of the coprime array CA in Example 1;

[0059] Figure 2 Schematic diagram of the positions of the elements of a 6-element coprime array with M=3, N=4 in Example 1;

[0060] Figure 3 Schematic diagram of the overall architecture of the deep complex-valued convolutional attention residual network DC-CARN in this embodiment 1;

[0061] Figure 4 for Figure 3 Schematic diagram of the internal structure and data processing flow of the two-dimensional complex-valued convolutional layer;

[0062] Figure 5 for Figure 3 Schematic diagram of the internal structure of the complex-valued convolutional attention module;

[0063] Figure 6 for Figure 5 Schematic diagram of the structure of the complex-valued convolutional block attention network CV-CBAM used in;

[0064] Figure 7 for Figure 6Schematic diagram of the structure of the middle channel attention module;

[0065] Figure 8 For Figure 6 Schematic diagram of the structure of the middle spatial attention module;

[0066] Figure 9 For Figure 3 Or Figure 5 Schematic diagram of the principle of the cross - layer residual connection structure adopted in

[0067] Figure 10 Training and validation loss curve diagram during the training process of the DOA estimation system of the present invention;

[0068] Figure 11 Comparison diagram of the root mean square error of DOA estimation varying with the signal - to - noise ratio performance of the DOA estimation method of the present invention and various existing DOA estimation algorithms under the condition of a fixed number of snapshots;

[0069] Figure 12 Comparison diagram of the root mean square error of DOA estimation varying with the number of snapshots performance of the DOA estimation method of the present invention and various existing DOA estimation algorithms under the condition of a fixed signal - to - noise ratio. Specific implementation manner

[0070] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0071] Embodiment 1

[0072] The DOA estimation method based on a deep complex - valued convolutional attention residual network includes the following steps:

[0073] S1. The data pre - processing module obtains complex data, collects data with a Coprime Array (CA) and pre - processes it to obtain complex - valued sampled covariance matrix (SCM) data, which is used as the original input information for DOA estimation. Specifically, it includes:

[0074] As Figure 1 shown, for the application scenario of direction - of - arrival (DOA) estimation using a Coprime Array, as a sparse array, the Coprime Array is formed by superposing two uniform linear arrays with the number of array elements being relatively prime. Among them, the number of array elements of the first sub - array is M, and the number of array elements of the second sub - array is N. M and N are relatively prime and M < N. The element spacings of the first sub - array and the second sub - array are Nd and Md respectively, where d is the half - wavelength of the signal. By combining the two uniform linear arrays, due to the relatively prime relationship between M and N, only the first elements of the two sub - arrays will coincide, and other elements will not coincide. Therefore, there are a total of M + N - 1 elements.

[0075] like Figure 2 As shown. This embodiment uses a 6-element coprime array P = M + N - 1 = 6, consisting of coprime numbers M = 3 and N = 4. This array is used for signal reception and to generate complex-valued SCM data for subsequent DOA estimation. Since the spacing between the elements of the coprime array is no longer half the signal wavelength, the position of each element in the coprime array is:

[0076] Ω={Mnd}∪{Nmd}

[0077] n=0,1,…,N-1; m=0,1,…,M-1

[0078] Receive J far-field narrowband signals to form the array receiving signal data model:

[0079]

[0080] Among them, X Ω (t) is the array receiving signal at time t, N Ω (t) is Gaussian white noise, A Ω is an array flow matrix of (M+N-1)×J dimensions, a Ω (θ j ) is the array steering vector corresponding to the j-th signal, which is specifically expanded as follows:

[0081]

[0082] Ωi∈Ω,i=1,…,M+N-1

[0083] Among them, Ωi is the actual position of each array element, and the position of the first array element is 0.

[0084] Receive signal X from above array Ω (t) estimates all possible incoming signal directions θ1…θ K , the covariance matrix of the coprime array received signal is obtained, which is specifically expressed as:

[0085]

[0086] Among them, p s =[p s1 ,…,p sJ ] T is the power of each incident signal source; Rs is the covariance matrix of S(t); is the noise power; I M+N-1 is the unit matrix of (M+N-1)×(M+N-1) dimensions; Operations to seek statistical expectations; (·) His the operation for conjugate transpose; diag(·) is a diagonal matrix formed by taking the elements in the vector as the values ​​on the diagonal matrix lines;

[0087] Calculate the SCM based on L snapshot data, specifically:

[0088]

[0089] in, is a P×P dimensional complex matrix, L represents the number of snapshots, (·) Η Indicates the operation of finding the conjugate transpose. When the receiving array has P elements, the SCM data is a P×P dimensional complex matrix.

[0090]

[0091] S2, feature extraction module; receives Figure 2 The complex-valued SCM data shown is a 6×6 complex Hermitian matrix. A deep complex-valued convolutional attention residual network (DC-CARN) is constructed to directly process the covariance matrix information in the complex domain. The deep complex-valued convolutional attention residual network uses an initial two-dimensional complex-valued convolutional layer, a complex-valued convolutional block attention network, and a cross-layer residual connection structure to deeply extract complex-valued features related to spatial angles.

[0092] S21. The initial two-dimensional complex-valued convolutional attention residual network uses the initial two-dimensional complex-valued convolutional layer to perform preliminary local feature perception and abstraction of the input complex-valued SCM. Specifically:

[0093] like Figure 4 As shown, the input complex-valued SCM is first processed by a two-dimensional complex-valued convolutional layer, which operates in the complex domain and uses complex-valued convolution kernels. It is configured with 64 filters of size (3,3), where (3,3) indicates that the convolution kernel size of this two-dimensional complex-valued convolutional layer is 3×3; the stride is (1,1), and the padding is (1,1). The complex filter matrix W = A + iB is convolved with the complex vector h = x + iy, where A and B are real matrices and x and y are real vectors. Convolving vector h with filter W yields W*h = (A*xB*y) + i(B*x + A*y). The complex-valued convolution operation is implemented in the following matrix form:

[0094]

[0095] Where A and B are real matrices, x and y are real vectors, R(·) represents the real part, I(·) represents the imaginary part, and * represents a real-valued convolution operation.

[0096] The output of the initial two-dimensional complex-valued convolutional layer is sequentially subjected to two-dimensional complex-valued batch normalization and complex-valued activation function processing; the complex-valued LeakyReLU activation function is applied to the real and imaginary parts of the variables in the previous layer respectively. Therefore, the output of a two-dimensional complex-valued convolutional layer can be expressed as:

[0097] f k (X) = CV-LeakyReLU(CV-BN(W k *X+b k ))

[0098] Among them, W k and b k Represents the filter matrix and bias vector of the k-th 2D complex-valued convolutional layer.

[0099] S22. The deep complex-valued convolutional attention residual network uses multiple complex-valued convolutional attention modules connected in series, which are connected sequentially along the signal processing direction to form a deep feature extraction path. The number of filter channels in the convolution layer of the subsequent complex-valued convolutional attention module is greater than or equal to the number of filter channels in the convolution layer of the previous module.

[0100] like Figure 5 As shown in the figure, each cascaded complex-valued convolutional attention module includes multiple two-dimensional complex-valued convolutional layers and complex-valued convolutional block attention networks (CV-CBAM); the two-dimensional complex-valued convolutional layers continue to operate in the complex domain, further performing nonlinear transformation and spatial feature extraction on the feature maps. The number of filters and output channels between modules is designed to increase gradually from 64 to 128 to 256 to learn feature representations of different levels and dimensions.

[0101] like Figure 6 As shown in the figure, the complex-valued convolution block attention network in the complex-valued convolution attention module is set between or after two adjacent two-dimensional complex-valued convolution layers, including two sub-modules, the complex-valued channel attention module and the complex-valued spatial attention module, which are connected in series. Both are designed based on the modular information of complex features, and these sub-modules can adaptively learn and emphasize the feature channels and spatial positions that are most important for the current task, suppress irrelevant or noise interference information, and thus improve the discriminability and robustness of the features.

[0102] Among them, such as Figure 7 As shown, the channel attention module in the complex-valued convolutional block attention network is used to adjust the channel weight. The input is the complex-valued feature X obtained by the two-dimensional complex-valued convolution layer, and the complex-valued feature X is mapped to the real number domain. The feature matrix M = |X| is calculated; the feature map of each channel is globally max-pooled M max and global average pooling M avg , then splice to get M concat =[M avg ,M max], the splicing result is used as input to the perceptron MLP, and the complex scaling parameter P = MLP (M concat ); also splits the output into a scaling factor S applied to both the real and imaginary parts r and S i , construct the complex scaling factor S = S r +jS i ; Finally, the feature map is scaled by the complex number of the channel scale to obtain the enhanced feature

[0103] like Figure 8 As shown in the figure, the spatial attention module in the complex-valued convolutional block attention network is used to adjust the spatial position weight, and the feature map enhanced by the complex-valued channel attention module is modulo M′=|X′|, and the average pooling M′ in the spatial dimension is performed. avg and maximum pooling M′ max , and then splice to get M′ spatial =[M′ avg ,M′ max ], then input to the complex-valued convolution layer to learn the weight of each position, and pass the Sigmoid activation function to obtain the spatial attention weight W s , and finally complete the weighting of the feature map to obtain the enhanced feature

[0104] S23, such as Figure 9 As shown in Figure 1, the deep complex-valued convolutional attention residual network uses a cross-layer residual connection structure and a cross-layer shortcut connection to add the input features of the module to the output features of the module directly or after a simple transformation, thereby realizing cross-module feature fusion. Specifically, each complex-valued convolutional attention module is equipped with a residual connection to add the module's input feature x directly to the module's processed output F(x) to form the final output F(x)+x. This helps in gradient propagation and training deep networks. It helps in gradient propagation and training deep networks, specifically expressed as:

[0105]

[0106] From the above formula, we can see that even if the derivative parameter decreases as the network structure deepens, the final derivative value will definitely not be less than 1, and the final result of the gradient chain rule will not tend to 0, so the gradient disappearance phenomenon will not occur when the parameter is updated at this time.

[0107] like Figure 3 As shown, the final output end of the feature extraction module is also provided with a flattening layer for structural conversion, which converts the multi-dimensional complex-valued feature map from the feature extraction module into a one-dimensional complex-valued feature vector to adapt to the input requirements of the subsequent fully connected layer.

[0108] S3, such as Figure 3 As shown in the figure, the flattened feature vector enters the direction of arrival (DOA) estimation module, which performs nonlinear transformation and mapping on the one-dimensional complex-valued feature vector. The module includes multiple complex-valued fully connected network layers (CV-FCNN) and a complex-valued Dropout layer inserted between each two adjacent CV-FCNN layers.

[0109] The present invention uses three CV-FCNN layers, each corresponding to input features and output features respectively. The CV-FCNN layer uses a complex weight matrix and a complex bias vector to perform an affine transformation on the input one-dimensional complex-valued feature vector and introduces nonlinearity through a complex-valued activation function to achieve high-level semantic mapping of the feature space. The CV-FCNN of the kth layer can be expressed as:

[0110] n k =W k,k-1 h k-1 +b k

[0111] h k =CV-LeakyReLU(net k )

[0112] Among them, W k,k-1 represents the complex-valued weight of the k-1th layer. k-1 is the input of the k-1 layer. b k is the bias of the kth layer. k is the output of the kth layer. LeakyReLU is a complex-valued activation function.

[0113] The complex-valued Dropout layer is used as a regularization method to randomly "drop out" neurons with a specific probability during training, discarding both the real and imaginary parts, reducing the co-adaptation between neurons, enhancing the generalization ability of the model, and preventing overfitting when the training data is limited.

[0114] S4, the output module specifically includes a feature conversion unit, an output mapping layer and an activation function unit;

[0115] The feature conversion unit converts the complex-valued feature vector of the complex-valued fully connected network layer into a real-valued representation; the real and imaginary parts of the complex-valued vector are concatenated using real-valued and imaginary-valued concatenation: h′={Real(h3),Imag(h3)} to form a real-valued vector with doubled dimension; the output mapping layer is a standard real-valued fully connected layer FCNN, and the number of its output neurons is equal to the total number of discrete angle grid points G set in advance; this layer is responsible for linearly mapping the converted high-dimensional real-valued feature vector to G angle dimensions; the activation function unit uses the Sigmoid activation function, which compresses each output value to the (0,1) interval so that it can be interpreted as the posterior probability that a signal source exists at the corresponding angle grid point.

[0116] The output module outputs a G-dimensional real-valued probability vector, i.e., the estimated angle space spectrum, and maps the feature vector to the pre-divided grid. It is finally mapped to the angle distribution probability space through the Sigmoid activation function to determine the DOA estimate. The specific expression is:

[0117]

[0118] Where h′={Real(h3),Imag(h3)} represents the concatenation of the real and imaginary parts of the output of the last CV-FCNN layer, and W′ represents the weight matrix of the output layer.

[0119] Example 2

[0120] The present invention is based on a deep complex-valued convolutional attention residual network DOA estimation system, which adopts the DOA estimation method in Example 1 and specifically includes:

[0121] System input interface, used to receive complex value SCM data from the outside;

[0122] A feature extraction module, whose input end is electrically connected or data-connected to the system input interface and whose output end is connected to the input end of the flattening layer; and is used to extract the complex-valued feature representation related to the DOA from the original SCM layer by layer and in depth;

[0123] The flattening layer converts the multi-dimensional complex-valued feature tensor output by the feature extraction module into a one-dimensional long vector form to adapt to the input requirements of the subsequent fully connected layer;

[0124] The DOA estimation module has its input connected to the output of the flattening layer and its output connected to the output module. It is used to map the high-dimensional complex-valued feature vector extracted by the feature extraction module to a representation space directly related to the DOA estimation task.

[0125] The output module and the output interface are electrically connected or data-connected to the output interface and are used to output the direction of arrival (DOA) estimation probability spectrum.

[0126] The DOA estimation system based on the deep complex-valued convolutional attention residual network in this embodiment is trained. There are a total of 121 directions of arrival in the training set. The spatial signal angle range received by the array is selected from [-60°, 60°], and the angle interval is set to 1°. Assuming that there are two signal sources incident on the array, that is, J = 2, the angles of the two signal sources traverse all combinations of 121 angles in the range of [-60°, 60°], and ultimately there are 7260 pairs of different angle combinations. The environment in which each pair of signals is located traverses 7 different SNR levels of {-20dB, -15dB, -10dB, -5dB, 0dB, 5dB, 10dB}, for a total of D = 7 × 7260 = 50,820 training samples. At the specified SNR level, the complex-valued SCM data is constructed from the covariance matrix data corresponding to each angle. The number of sampling snapshots L is set to 500, of which 80% of the samples are used for training and the remaining 20% ​​are used for validation. Each sample is marked with the corresponding arrival angle.

[0127] The Adam optimizer is used to update and optimize the network parameters. It dynamically adjusts the learning rate of the parameters, with an initial learning rate of 0.001 and momentum parameters β1 = 0.85 and β2 = 0.95. Furthermore, based on the decrease in validation set loss, the learning rate is dynamically adjusted with a factor of 0.7 and a patience of 5 epochs. That is, if the validation set loss does not decrease within 5 consecutive epochs, the learning rate is scaled by 0.7, effectively avoiding local optimality. To further mitigate the risk of overfitting, L1 norm regularization is introduced to the FCNN layer weights to ensure the sparsity and stability of the model parameters. The binary cross entropy loss function (BCELoss) is used to measure the error between the model output and the true angle label probability distribution. The goal of network training is to minimize the loss function, which is expressed as follows:

[0128]

[0129] Among them, v represents the learnable parameters of the network model, express and y i The cross entropy of .

[0130] Figure 10The training and validation loss curves of the DOA estimation system of the present invention are shown. It can be seen from the figure that the DOA estimation system based on the deep complex-valued convolutional attention residual network of the present invention has effectively converged on both the training set and the validation set. Although the validation loss is slightly higher than the training loss, the gap between the two is relatively stable, indicating that the model has no overfitting, has strong generalization ability, and the loss ratio remains in a reasonable range. The overall training effect is relatively ideal. After the training is completed, the DOA estimation system based on the deep complex-valued convolutional attention residual network receives new complex-valued SCM data input, and according to the DOA estimation method and Figure 3 The process shown in the figure is used for estimation, and the probability spectrum of DOA estimation is finally output.

[0131] Example 3

[0132] In order to demonstrate the advantages of the deep complex-valued convolutional attention residual network model DC-CARN proposed in this paper in DOA estimation based on coprime arrays, Figure 10 and Figure 11 As shown, the present invention compares the performance of the deep complex-valued convolution attention residual DOA estimation method of Example 1 with the traditional estimation method in the prior art under different signal-to-noise ratio levels and snapshot numbers.

[0133] These traditional estimation methods mainly involve some traditional model-driven methods, including MUSIC, R-MUSIC, Coprime MUSIC, DNN method and CV-CNN method, in which DNN is composed of four layers of FCNN. All traditional methods are implemented in MATLAB 2023b, and simulation experiments are carried out on a computer with a 3.00GHz Intel Core i9 processor and 64GB RAM. The network model is deployed on an NVIDIA GeForce RTX 3090 GPU based on Pytorch. Complex-valued SCM data is used with an initial learning rate of lr = 10-4, a batch size of 32, 200 epochs of training, and the Adam optimizer is used. In order to make a reasonable comparison, the angular resolution set in different methods is the same, and the root mean square error (RMSE) is used to evaluate the DOA estimation performance, which is defined as follows:

[0134]

[0135] Among them, θ j is the true label of the j-th DOA angle, is the estimated value of the j-th DOA angle in the t-th Monte Carlo experiment, M c is the number of Monte Carlo experiments; the CPU time is used to evaluate the time complexity of DOA estimation.

[0136] Figure 11 The curve of the DOA estimation root mean square error as the signal-to-noise ratio changes from low to high -10dB to 20dB under the condition of a fixed number of snapshots L = 200 for the estimation method of the present invention and various existing DOA estimation algorithms. It can be seen from the figure that the DC-CARN network system proposed in the present invention has a significantly lower RMSE value than all the comparison methods in the entire SNR range of the test, especially in the low signal-to-noise ratio area SNR<5dB, where the performance advantage is more obvious. In contrast, the performance of traditional MUSIC and Root-MUSIC methods deteriorates sharply at low SNR, and the RMSE value is very high. Even compared with other deep learning methods such as CV-CNN, the DC-CARN network system of the present invention exhibits a lower RMSE, further proving that the present invention has stronger robustness and higher estimation accuracy under different noise levels.

[0137] Figure 12 The following is a performance curve showing the root mean square error of DOA estimation as the number of snapshots increases from 20 to 1000, under a fixed signal-to-noise ratio (SNR) of 0 dB for the estimation method of the present invention and various existing DOA estimation algorithms. The figure shows that the DC-CARN network system proposed in the present invention maintains a low RMSE value across all tested snapshot numbers, significantly outperforming the comparison methods. In particular, when the number of snapshots is very limited (L<100), the performance advantage of the DC-CARN network system is particularly prominent, demonstrating its powerful ability and robustness in processing small sample data. At the same time, as the number of snapshots increases, although the performance of all methods improves, the DC-CARN network system of the present invention always maintains optimal or near-optimal performance levels.

[0138] like Figure 11 and Figure 12 The performance curves shown fully demonstrate the superior performance and robustness of the DC-CARN network system designed in this paper. This is primarily due to the deep complex-valued network architecture, which utilizes complex-valued convolutional layers and complex-valued fully connected layers. This architecture directly processes covariance matrix information in the complex domain, avoiding the potential loss of information caused by separate processing of the real and imaginary parts, and better aligns with the physical nature of array signal processing.

[0139] Furthermore, a complex-valued convolutional block attention network (CV-CBAM) is embedded in the feature extraction module. Through channel- and spatial-attention mechanisms, the network adaptively focuses on feature channels and spatial regions that contribute most to DOA estimation, suppressing interference from noise and irrelevant features. Furthermore, the residual connection structure effectively alleviates the vanishing gradient problem in deep network training, promotes the efficient transfer and fusion of features, and enables stable training and effective operation of deeper network structures.

[0140] In summary, the DOA estimation method and system based on the deep complex-valued convolutional attention residual network proposed in the present invention, through its unique structural design and component configuration, has demonstrated significant performance improvement compared with the existing technology in simulation verification, especially under challenging conditions such as low signal-to-noise ratio and few snapshots, with higher estimation accuracy and robustness, and has strong practical value.

[0141] On the basis of the above embodiments, the present invention continues to describe in detail the technical features involved therein and the functions and roles played by the technical features in the present invention, so as to help technicians in this field fully understand the technical solutions of the present invention and reproduce them.

[0142] Finally, although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A DOA estimation method based on a deep complex-valued convolutional attention residual network, characterized by: The steps are as follows: S1. The data preprocessing module obtains complex data, collects data using a Coprime Array (CA), preprocesses it to obtain complex-valued sample covariance matrix (SCM) data, which serves as the original input information for DOA estimation; S2. The feature extraction module constructs a Deep Complex-Valued Convolutional Attention Residual Network (DC-CARN) to directly process the covariance matrix information in the complex domain. The deep complex-valued convolutional attention residual network utilizes an initial two-dimensional complex-valued convolutional layer, a complex-valued convolutional block attention network, and a cross-layer residual connection structure to deeply extract complex-valued features related to spatial angles; S3. The DOA estimation module includes multiple layers of complex-valued fully connected neural network layers (Complex-Valued Fully Connected Neural Network, CV-FCNN). This module is responsible for finally mapping the extracted high-dimensional complex-valued feature vectors to a representation space directly related to the DOA estimation task, that is, for mapping the complex-valued features to the angle domain. Among them, the complex-valued fully connected network layer performs non-linear transformation and mapping on the one-dimensional complex-valued feature vectors, mapping the high-dimensional complex-valued feature vectors extracted in step S2 to a representation space directly related to the DOA estimation task; S4. The output module is used to convert the angle-domain feature representation after completing the DOA estimation task into a user-interpretable DOA estimation probability distribution result.

2. The DOA estimation method based on deep complex-valued convolutional attention residual network according to claim 1 is characterized in that In step S 3. The DOA estimation method based on deep complex-valued convolutional attention residual network according to claim 1 is characterized in that ​ ​ ​ Among them, X Ω (t) is the array receiving signal at time t, N Ω (t) is Gaussian white noise, A Ω is an array flow matrix of (M+N-1)×J dimensions, a Ω (θ j ) is the array steering vector corresponding to the j-th signal; ​ in, is a P×P dimensional complex matrix, L represents the number of snapshots, (·) Η Represents the operation of finding the conjugate transpose.

4. The DOA estimation method based on deep complex-valued convolutional attention residual network according to claim 2 is characterized in that In step S2, including S21, the initial two-dimensional complex-valued convolutional layer is used in the deep complex-valued convolutional attention residual network to perform preliminary local feature perception and abstraction on the input complex-valued SCM data, specifically: The input complex-valued SCM data is first processed by a two-dimensional complex-valued convolutional layer. This convolutional layer has N (q, q)-sized filters for complex-domain operations. (q, q) indicates that the size of the convolution kernel of this two-dimensional complex-valued convolutional layer is q×q. The complex filter matrix W = A + iB is convolved with the complex vector h = x + iy. The vector h is convolved with the filter W. The complex-valued convolution operation is implemented in the following matrix form: Where A and B are real matrices, x and y are real vectors, R(·) represents the real part, I(·) represents the imaginary part, and * represents a real-valued convolution operation; The output of the initial two-dimensional complex-valued convolutional layer is sequentially subjected to two-dimensional complex-valued batch normalization and complex-valued activation function processing; the complex-valued LeakyReLU activation function is applied to the real and imaginary parts of the variables in the previous layer respectively. Therefore, the output of a two-dimensional complex-valued convolutional layer can be expressed as: f k (X)=CV-LeakyReLU(CV-BN(W k *X+b k )) Among them, W k and b k Represents the filter matrix and bias vector of the k-th 2D complex-valued convolutional layer.

5. The DOA estimation method based on deep complex-valued convolutional attention residual network according to claim 4 is characterized in that Also included is S22, a deep complex-valued convolutional attention residual network using a plurality of complex-valued convolutional attention modules connected in series, which are sequentially connected along a signal processing direction to form a deep feature extraction path, and the number of filter channels of the convolution layer in the subsequent complex-valued convolutional attention module is greater than or equal to the number of filter channels of the convolution layer of the preceding module; Each complex-valued convolutional attention module includes multiple two-dimensional complex-valued convolutional layers and a complex-valued convolutional block attention network. The two-dimensional complex-valued convolutional layers continue to operate in the complex domain, further performing nonlinear transformations and spatial feature extraction on the feature maps. The number of filters between modules is designed to gradually increase to learn feature representations at different levels and dimensions. The channel attention module in the complex-valued convolution block attention network is used to adjust the channel weight. Its input is the complex-valued feature X obtained by the two-dimensional complex-valued convolution layer, and the complex-valued feature X is mapped to the real number domain to calculate the feature matrix M = |X|; the feature map of each channel is globally max-pooled M. max and global average pooling M avg , then splice to get M concat =[M avg ,M max ], the splicing result is used as input to the perceptron MLP, and the complex scaling parameter P = MLP (M concat ); also splits the output into a scaling factor S applied to both the real and imaginary parts r and S i , construct the complex scaling factor S = S r +jS i ; Finally, the feature map is scaled by the complex number of the channel scale to obtain the enhanced feature Indicates element-level multiplication, that is, multiplying the elements at corresponding positions one by one; The spatial attention module in the complex-valued convolutional block attention network is used to adjust the spatial position weight, and the feature map enhanced by the complex-valued channel attention module is modulo M′=|X′| to perform average pooling M′ in the spatial dimension. avg and maximum pooling M′ max , and then splice to get M′ spatial =[M′ avg ,M′ max ], then input into the complex-valued convolutional layer to learn the weight of each position, and pass through the Sigmoid activation function to obtain the spatial attention weight W s , and finally complete the weighting of the feature map to obtain the enhanced feature 6. The DOA estimation method based on deep complex-valued convolutional attention residual network according to claim 5 is characterized in that It also includes S23, the deep complex-valued convolutional attention residual network uses a cross-layer residual connection structure and a cross-layer shortcut connection to add the input features of the module to the output features of the module directly or after a simple transformation, to achieve cross-module feature fusion. Specifically: Each of the complex-valued convolutional attention modules is configured with a residual connection, which directly adds the module's input feature x to the module's processed output F(x) to form the final output F(x)+x; this facilitates gradient propagation and training of deep networks. The final output end of the feature extraction module is also provided with a flattening layer for structural conversion, which converts the multi-dimensional complex-valued feature map from the feature extraction module into a one-dimensional complex-valued feature vector to adapt to the input requirements of the subsequent fully connected layer.

7. The DOA estimation method based on deep complex-valued convolutional attention residual network according to claim 1 is characterized in that In step S3, the DOA estimation module includes multiple CV-FCNN layers and a complex-valued Dropout layer inserted between every two adjacent CV-FCNN layers; The CV-FCNN layer uses a complex weight matrix and a complex bias vector to perform an affine transformation on the input one-dimensional complex-valued feature vector and introduces nonlinearity through a complex-valued activation function to achieve high-level semantic mapping of the feature space. The CV-FCNN of the kth layer can be expressed as: n k =W k,k-1 h k-1 +b k h k =CV-LeakyReLU(net k ) Among them, W k,k-1 To represent the complex-valued weight of the k-1th layer, h k-1 is the k-1th layer input, b k is the bias of the kth layer, n k is the output of the kth layer, and LeakyReLU is the complex-valued activation function; The complex-valued Dropout layer acts as a regularization method, randomly "dropping" neurons with a specific probability during training, while discarding both the real and imaginary parts, thereby reducing the co-adaptation between neurons, enhancing the generalization ability of the model, and preventing overfitting when the training data is limited.

8. The DOA estimation method based on deep complex-valued convolutional attention residual network according to claim 1 is characterized in that In step S4, the output module specifically includes: A feature conversion unit is used to convert the complex-valued feature vector of the complex-valued fully connected network layer into a real-valued representation; the real and imaginary components of the complex-valued vector are concatenated to form a real-valued vector with doubled dimension; The output mapping layer is a standard real-valued fully connected layer FCNN, whose number of output neurons is equal to the total number of pre-set discrete angle grid points G; this layer is responsible for linearly mapping the converted high-dimensional real-valued feature vector to G angular dimensions; The activation function unit adopts the Sigmoid activation function. The Sigmoid function compresses each output value to the (0, 1) interval so that it can be interpreted as the posterior probability that the signal source exists at the corresponding angle grid point.

9. The DOA estimation method based on deep complex-valued convolutional attention residual network according to claim 8 is characterized in that The output module outputs a G-dimensional real-valued probability vector, i.e., the estimated angle space spectrum, maps the feature vector to a pre-divided grid, and finally maps it to the angle distribution probability space through the Sigmoid activation function to determine the DOA estimate; specifically, it is expressed as: Where h′={Real(h3),Imag(h3)} represents the concatenation of the real and imaginary parts of the output of the last CV-FCNN layer, and W′ represents the weight matrix of the output layer.

10. A DOA estimation system based on a deep complex-valued convolutional attention residual network, characterized by: The DOA estimation method according to any one of claims 1 to 9 is used, specifically comprising: System input interface, used to receive complex value SCM data from the outside; A feature extraction module, whose input end is electrically connected or data-connected to the system input interface and whose output end is connected to the input end of the flattening layer; and is used to extract complex-valued feature representations related to DOA from the original SCM layer by layer and in depth; The flattening layer converts the multi-dimensional complex-valued feature tensor output by the feature extraction module into a one-dimensional long vector form to adapt to the input requirements of the subsequent fully connected layer; A DOA estimation module, whose input end is connected to the output end of the flattening layer and whose output end is connected to the output module; used to map the high-dimensional complex-valued feature vector extracted by the feature extraction module to a representation space directly related to the DOA estimation task; An output module and an output interface, wherein the output module is electrically connected to or data-connected with the output interface and is used to output a DOA estimation probability spectrum.

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