Direction of arrival (DOA) estimation method of sparse array based on residual network

Abstract

The invention discloses a sparse array DOA estimation method based on a residual network, and the method comprises the following steps: reconstructing an ideal Here-Toeplitz covariance matrix of a virtual uniform linear array through deep learning, and achieving the end-to-end training in combination with the differentiability of a Root-MUSIC algorithm. By introducing the multi-delay autocorrelation matrix tensor and residual learning, the method can effectively process challenging scenes such as coherent signals, a small number of snapshots and broadband signals. The effectiveness of the method is verified in the embodiment, high-precision estimation can be achieved under various conditions, the target that the number of estimated information sources is larger than the number of physical array elements is successfully achieved, and a new solution is provided for sparse array DOA estimation.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a DOA estimation method for sparse arrays based on residual networks. Background Technology

[0002] Direction of Arrival (DOA) estimation is the cornerstone of array signal processing and is crucial for applications such as radar, sonar, and wireless communications. Subspace methods such as MUSIC (Multiple Signal Classification) are classic algorithms in this field. For uniform linear arrays (ULAs), the Root-MUSIC algorithm offers computational advantages by replacing spectral peak search with polynomial root finding. However, the effectiveness of these methods relies on several idealized assumptions: the array is a uniform linear array (with a Hermitian-Toplitz structure in its covariance matrix), the source is incoherent, and there is a sufficient number of observation snapshots. In practical applications, these assumptions are often difficult to satisfy, leading to a significant performance degradation of traditional methods.

[0003] The existing DOA estimation methods have the following main problems: 1. Structural mismatch of sparse arrays: The non-uniform geometry of sparse arrays disrupts the Toplitz structure of the covariance matrix, making it impossible to directly apply high-resolution algorithms such as Root-MUSIC. While methods based on sparse reconstruction or matrix filling can recover the Toplitz structure, they typically involve extremely high computational complexity or are sensitive to array defects, making them unsuitable for real-time applications.

[0004] 2. Challenges in Coherent Signal Processing: Coherent signals caused by factors such as multipath propagation can lead to a rank deficiency in the source covariance matrix, rendering traditional subspace methods ineffective. To address this issue, methods such as spatial smoothing have been proposed, but these typically come at the cost of sacrificing the effective aperture of the array or increasing noise sensitivity.

[0005] 3. Dependence on data volume: Traditional methods usually require a large number of observation snapshots to obtain reliable covariance matrix estimates, and their performance is poor in scenarios with a limited number of snapshots.

[0006] 4. Challenges in broadband signal processing: For broadband signals, existing coherent or incoherent subspace methods have limited performance at low signal-to-noise ratios, and the performance of traditional algorithms will further deteriorate when combined with problems such as coherent sources and sparse arrays.

[0007] 5. Limitations of emerging methods: In recent years, although deep learning methods have been introduced into DOA estimation, purely data-driven models lack interpretability and theoretical guarantees, while models that combine traditional algorithms have failed to fully solve the structural constraints of sparse arrays.

[0008] In existing deep networks for direction-of-arrival estimation in low SNR (by Papageorgiou et al. (2021)), a purely data-driven approach was proposed to directly learn the mapping from the covariance matrix to the spatial spectrum through a convolutional neural network. However, such "black box" models lack physical interpretability, and their performance is heavily dependent on the completeness of the training data. When the real-world scenario does not match the training data, their generalization ability is poor. This is one of the core problems that this invention aims to solve by introducing model-driven design.

[0009] In existing Deep Root-MUSIC algorithms for data-driven DOA estimation (by Shmuel et al. (2023)), deep learning is combined with traditional algorithms to reconstruct the covariance matrix of a uniform array using a neural network. However, the network learns only the covariance matrix itself and does not explicitly force the reconstructed matrix to satisfy an ideal Hermit-Toplitz structure, which is insufficient to fundamentally solve the structural mismatch problem of sparse arrays. This invention addresses this deficiency by directly learning the parameters of the Hermit-Toplitz matrix through a network, ensuring an ideal matrix structure, and achieving global optimization for the final estimation accuracy through end-to-end differentiable design. Summary of the Invention

[0010] The main objective of this invention is to overcome the shortcomings and deficiencies of existing DOA estimation techniques and provide a robust and efficient DOA estimation method that remains effective even under challenging conditions such as sparse arrays, coherent signals, a small number of snapshots, and wideband signals.

[0011] The present invention is achieved by at least one of the following technical solutions.

[0012] A DOA estimation method for sparse arrays based on residual networks is proposed. The original signal data is input into a trained residual covariance reconstruction network for DOA angle estimation. The DOA angle estimation using the residual covariance reconstruction network includes the following steps: S1. Data preprocessing: Convert the original signal data into real-valued tensors; S2. Network Processing: The real-valued tensor is input into the residual covariance reconstruction network. The residual covariance reconstruction network learns the complex mapping from the real-valued tensor to the parameters of the ideal covariance matrix through hierarchical feature extraction, and finally outputs a low-dimensional parameter vector containing all the information required for reconstruction. S3, Matrix Reconstruction: The parameter vector output by the network is mapped and reconstructed into a virtual uniform array covariance matrix with an ideal Hermit-Toplitz structure through a deterministic linear transformation, and the virtual uniform array covariance matrix is ​​regularized. S4. DOA estimation: The reconstructed and regularized covariance matrix is ​​used to calculate the final DOA estimate using the Root-MUSIC algorithm.

[0013] Furthermore, the residual covariance reconstruction network includes: The initial convolutional layer is used to extract low-level features, transforming the input tensor from the signal representation space to the feature representation space; Deep residual networks: used to stabilize gradient propagation and extract multi-scale features; Multilayer perceptron: maps high-dimensional feature tensors to low-dimensional parameter vectors, which contain the parameters needed to reconstruct the covariance matrix.

[0014] Furthermore, deep residual networks include dimensionality reduction blocks, feature extraction blocks, and residual connections that enable residual learning through shortcut connections.

[0015] Furthermore, the matrix reconstruction process in step S3 is as follows: The first part of the parameter vector... The elements are taken as the real part of the first row of the matrix, and the remaining elements are... Each element is used as the imaginary part of the off-diagonal elements in the row, and the entire matrix is ​​then completed using Topletz and Hermitian properties.

[0016] Furthermore, in step S3, the covariance matrix of the virtual uniform array is regularized using adaptive diagonal loading.

[0017] Further, the data preprocessing in step S1 includes: calculating the autocorrelation matrix with multiple delays for the original signal data, then separating the real and imaginary parts of the complex-valued autocorrelation matrix tensor and converting it into a real-valued tensor.

[0018] Furthermore, the residual covariance reconstruction network is optimized through end-to-end training. The training process uses the root mean square periodicity error loss function. The loss function solves the permutation ambiguity problem of multi-source estimation by minimizing permutation matching and solves the periodicity problem of angles by modulo operation.

[0019] A system for implementing the aforementioned DOA estimation method based on sparse arrays of residual networks includes: The preprocessing module is used to convert the raw signal data into a multi-channel autocorrelation matrix tensor; The feature learning module is used to extract and fuse high-dimensional feature representations of the autocorrelation matrix tensor; The parameter generation module is used to calculate the parameter vector of the high-dimensional feature representation; The matrix reconstruction module is used to reconstruct the parameter vector into a Hermit-Toplitz covariance matrix; The DOA estimation module is used to estimate the DOA angle of the reconstructed covariance matrix.

[0020] A computer device according to the present invention includes a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, which, when executed by the processor, causes the processor to implement the method described herein.

[0021] The present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor implements the method described herein.

[0022] Compared with the prior art, the present invention has the following technical effects: 1. The RCR-Net framework proposed in this invention can reconstruct an ideal Hermit-Toplitz covariance matrix suitable for the Root-MUSIC algorithm from sparse array data, effectively solving the structural mismatch problem of sparse arrays.

[0023] 2. By introducing a multi-delay autocorrelation matrix tensor as the network input, this method can effectively process coherent signals by utilizing the temporal correlation of the signal, thus solving the performance degradation problem of traditional subspace methods in coherent scenarios.

[0024] 3. This invention combines the Root-MUSIC algorithm with the residual network, enabling end-to-end training of the entire processing flow and direct optimization towards the final DOA estimation accuracy, thereby improving the estimation accuracy.

[0025] 4. This method can expand the effective aperture using a virtual array, thereby achieving effective estimation with fewer physical array elements than the number of signal sources, breaking through the physical limitations of traditional methods. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below.

[0027] Figure 1 This is a schematic diagram of the RCR-Net network architecture proposed in the embodiment.

[0028] Figure 2a This is a diagram of the basic residual block structure used in the network of this invention.

[0029] Figure 2b This is a diagram of the downsampling residual block structure used in the network of this embodiment of the invention.

[0030] Figure 3 This is a performance comparison chart of the method of this invention with various traditional and deep learning methods in incoherent signal scenarios.

[0031] Figure 4 This is a performance comparison chart of the method of this invention with other methods in coherent signal scenarios.

[0032] Figure 5 This is a performance curve showing the impact of the number of snapshots.

[0033] Figure 6 It is a performance curve graph for different numbers of information sources.

[0034] Figure 7 It is a performance curve under broadband signal conditions. Detailed Implementation

[0035] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. It should be noted that the described embodiments are merely some embodiments of the present application, not all embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0036] Example 1 This embodiment considers a... A sparse linear array (SLA) composed of 1000 elements receives... A narrowband far-field signal. In time observation vector for:

[0037] in Indicates the position of the array element. It is an array manifold matrix, and its guiding vector is , It's the wavelength. It is the source signal vector. This represents additive white Gaussian noise. The sparse array can be modeled as a... A subset of a virtual uniform linear array (ULA) of elements is selected by a selection matrix. Make ,in It is the guide vector of the virtual ULA. Indicates the first The position of each array element; Indicates the first Array steering vectors corresponding to each signal source; Indicates the first From the perspective of DOA of each information source; Represents the DOA angle vector; Represents the imaginary unit; Indicates the first From the perspective of DOA of each information source; The guide vector of the sparse array.

[0038] The covariance matrix of the received signal is composed of Given, among which It is the source covariance matrix. It is the noise variance. This represents the N×N dimensional identity matrix. For coherent signals, This can lead to rank deficiency; and for sparse arrays, the directly estimated covariance matrix lacks the Hermitian-Toplitz structure necessary for Root-MUSIC. These problems result in model mismatch and performance degradation of traditional subspace methods. Therefore, this embodiment first establishes a system model, and then achieves accurate estimation of the direction of arrival (DOA) through four steps: data preprocessing, network processing, matrix reconstruction, and DOA estimation. Specifically, the following steps are included: 1. Data Preprocessing: This involves processing the signal vector sequences received by the sparse array at different time points t. , , ..., The observed data are used to calculate the multi-delay autocorrelation matrix to construct a real-valued tensor. Let represent the signal vector received at time t. The theoretical definition of the autocorrelation matrix is:

[0039] in, This indicates that the signal vector has a time delay of... The autocorrelation matrix at time, Represents the statistical expectation operator. This indicates the conjugate transpose. This represents the maximum time delay order. It is achieved by constructing a structure containing multiple time delays ( The autocorrelation matrix tensor of the signal can utilize the non-zero delay spatiotemporal correlation of the signal to provide a richer feature set for the network, thereby effectively processing coherent signals and enhancing model robustness. Since additive white noise mainly affects the diagonal of the covariance matrix, this multi-delay autocorrelation matrix tensor is decoupled from the noise variance, maintaining statistical consistency under different signal-to-noise ratios. In this embodiment, unbiased sample estimation is used:

[0040] in, For the theoretical autocorrelation matrix Sample estimation; This is the total number of observation snapshots; It is the sample mean vector of the observed signal. The complex-valued autocorrelation matrix is ​​then converted into a real-valued tensor to meet the processing requirements of deep networks. The process of converting the complex-valued autocorrelation matrix into a real-valued tensor includes: extracting the real and imaginary parts of the autocorrelation matrices of each order and stacking them.

[0041] For each delay order Extracting the autocorrelation matrix estimation The real and imaginary parts are stacked along the row dimension. The transformed real-valued matrix is:

[0042] in, This represents the transformed real-valued autocorrelation matrix; and These represent the operations of extracting the real and imaginary parts of a complex number, respectively. express The space of real matrices; Indicates the number of physical array elements.

[0043] Then, delay-dimensional tensor quantization: connect all along the new delay dimension. ( To form a three-dimensional tensor As network input:

[0044] The resulting 3D tensor uses delay as the channel dimension and its size is independent of the number of snapshots, enabling the network model to handle observation sequences of varying lengths. To improve model robustness, data augmentation techniques are employed to generate new training samples with different spatial characteristics. Data augmentation involves applying a random angular offset to the true DOA of the training samples and modifying the covariance matrix accordingly.

[0045] 2. Input the preprocessed 3D tensor into the network model, and finally output a model containing all the information needed for reconstruction. dimensional parameter vector .

[0046] The network model in this embodiment uses a Residual Covariance Reconstruction Network (RCR-Net), as shown in the schematic diagram. Figure 1 In this embodiment, DOA estimation is modeled as a regression task, and RCR-Net learns the mapping from the input tensor to the parameters of the ideal Hermit-Toplitz covariance matrix. The RCR-Net network consists of three main parts: Initial convolutional layer: performs low-level feature extraction, transforming the input tensor from the signal representation space to the feature representation space.

[0047] Deep Residual Networks: The main structure of the network uses layered downsampling and residual connections to stabilize gradient propagation and extract robust multi-scale features. Stable gradient propagation extracts robust multi-scale features from the feature representation space output by the initial convolutional layers. Through cascading processing of multiple residual blocks, features are extracted and fused layer by layer, ultimately outputting a high-dimensional feature tensor.

[0048] Multi-Layer Perceptron (MLP): Maps the output of a deep residual network to a... Low-dimensional parameter vector This vector contains the parameters needed to reconstruct the covariance matrix.

[0049] The core of a deep residual network consists of two types of residual blocks: dimensionality reduction blocks and feature extraction blocks.

[0050] The core components of deep residual networks consist of two types of residual blocks: dimensionality reduction blocks and feature extraction blocks. Their structures are as follows: Figure 2a and Figure 2b As shown.

[0051] Basic residual blocks (e.g.) Figure 2a (As shown): used for feature extraction and nonlinear transformation. Its structure includes: Main path: consists of two Convolutional layer (Conv) The convolutional layers are connected in series, with each convolutional layer followed by a batch normalization (BN) layer and a ReLU activation function.

[0052] Shortcut Connection: This connects input features... Directly transmitted to the output, such as Figure 1 The interior of the middle residual block and Figure 2a and Figure 2b As shown by the black arrow in the diagram. This fast connection structure is a feature of deep residual networks. By achieving residual learning and stable gradient propagation, it lays the foundation for end-to-end training of subsequent networks and effectively alleviates the gradient vanishing problem in deep networks.

[0053] Feature fusion: Outputting the main path through addition operations With quick links Add them together to get the final output. .

[0054] Mathematical expression: for input features The result is obtained through two layers of transformation. ,in , These are the convolution weights.

[0055] downsampling residual block (e.g.) Figure 2b As shown): This achieves a reduction in feature map size while extracting features. Its structure includes: Main path: The first convolutional layer uses Unfilled convolution (Conv) Reduce the feature map size, the second one uses Convolution Preserves Dimensions Quick connection: via Convolution (Conv) ) Achieve dimensional matching to ensure feature fusion with the main path output. Feature fusion: It also uses addition operations, but the input and output feature map sizes are different. Mathematical expression: ,in Indicating quick links Convolution Transformation The design of these two residual blocks fully embodies the core idea of ​​residual learning: ensuring lossless transfer of information and gradients through shortcut connections, while utilizing residual mapping. It learns the difference between the input and the target. This structure effectively alleviates the gradient vanishing problem in deep networks, allowing the network to be trained more stably.

[0056] The detailed configuration of the Residual Covariance Reconstruction Network (RCR-Net) network architecture is shown in the table below: Table 1. RCR-Net Network Architecture Configuration

[0057] Note: Conv( , ) indicates having convolution kernel and Convolutional layers with output channels; FC ( ) indicates having A fully connected layer with output units. Each residual block contains two sub-blocks, and each sub-block contains two consecutive convolutional layers. Flatten represents the operation of flattening a multidimensional feature tensor into a one-dimensional vector, used to convert the output of the convolutional layer into a format that the fully connected layer can process.

[0058] Table 2. Data Flow Structure of the RCR-Net Framework

[0059] Note: N represents the number of array elements in the physical array; M represents the number of information sources to be estimated; This represents the number of elements in a virtual uniform linear array. This indicates the maximum delay order. The output dimension of each stage is represented in the format of [number of channels, height, width] or [vector length].

[0060] 3. Matrix Reconstruction. This step reconstructs the parameter vector output by RCR-Net. Reconstruct the Hermitian-Toepilitz covariance matrix to meet the requirements of the Root-MUSIC algorithm. For those with A uniform linear array of equally spaced sensors, with an ideal autocorrelation matrix. It possesses Hermitian and Toplitz properties.

[0061] Within the framework proposed in this invention, the covariance matrix of a sparse linear array (SLA) is reconstructed to have A virtual ULA for each element, which requires Each parameter is independent. The MLP outputs one. dimensional parameter vector By defining a linear transformation , express 3D real vector space, express A 3D complex matrix space can be used to represent parameter vectors. Mapping to a Hermitian-Toplitz matrix The steps are as follows: S31, Parameter Mapping: Mapping parameter vectors The former Composed of elements The real part of the first row, the rest. The elements constitute the imaginary part of the off-diagonal elements in this row.

[0062] S32, Toplitz assignment: The first line determines all the diagonals of the upper triangular portion.

[0063] S33, Hermitian completeness: The lower triangular part is completed by taking the conjugate transpose of the upper triangular part.

[0064] by For example, a 13-dimensional parameter vector Mapping to complex elements The process is as follows: These elements are then arranged to form an Hermit-Toplitz matrix:

[0065] in express The complex conjugate of . This construction operation is linear and differentiable. Represents the imaginary unit; Denotes the complex elements of the first row of the reconstructed Hermit-Toplitz matrix, where diagonal elements It is a non-diagonal element.

[0066] To ensure the reconstruction matrix The positive semidefinite (PSD) property is used for positive semidefinite regularization by adaptive diagonal loading:

[0067] in express An identity matrix of dimension 1 , For numerical stability parameters, This represents the final covariance matrix after regularization; Representation matrix The minimum eigenvalue. This regularization operation ensures that the final matrix is ​​obtained by boosting negative eigenvalues. It maintains the positive semidefiniteness of the structure while preserving its Hermitian-Toplitz structure and improving the numerical stability of subsequent processing.

[0068] 4. DOA estimation: This step uses the Root-MUSIC algorithm to process the reconstructed covariance matrix to achieve end-to-end training optimization, including the following steps: S41. Eigenvalue decomposition and subspace partitioning: Perform eigenvalue decomposition on the reconstructed covariance matrix to obtain the noise subspace projection matrix. :

[0069] in This represents the eigenvector matrix. For There are signal sources, and the noise subspace is composed of corresponding signal sources. The eigenvector with minimum eigenvalues Zhang Cheng, and thereby constructed the noise subspace projection matrix. , The first element of the covariance matrix represents the first element of the covariance matrix. The feature values ​​are arranged in descending order.

[0070] S42. Construction and solution of Root-MUSIC polynomials: Constructing Root-MUSIC polynomials using the Tollitz structure of the covariance matrix:

[0071] in, It is a root-mUSIC polynomial used to determine the DOA angle by the location of its root; It is the z-domain representation of the virtual ULA's guide vector; It is a complex variable, and its form is: ,in It is the spacing between array elements. The DOA angle to be estimated. It is the wavelength.

[0072] Where the coefficient By projection matrix It is obtained by summing the diagonal elements. This is achieved by solving the polynomial. The root can determine the DOA.

[0073] S43, DOA angle estimation, obtained from the solution Among the roots, select the one that is closest to the unit circle and lies inside it. one valid root The final DOA angle estimate is calculated based on the phase of these roots:

[0074] in These are the valid roots after filtering. Let represent the DOA angle estimate of the i-th source; and They represent complex numbers respectively The imaginary and real parts.

[0075] To achieve end-to-end training, the root mean square periodic error (RMSPE) is used as the loss function. This loss function minimizes the permutation matching... To solve the permutation fuzziness problem in multi-source estimation, and through modular arithmetic... This method addresses the angle ordering and angle periodicity problems in DOA estimation. Its mathematical expression is:

[0076] in Indicates all A set of permutation matrices used to optimally match the estimated angles with the true angles before calculating the loss.

[0077] in, and These are the actual and estimated DOA vectors, respectively. For the number of information sources, Let the angular periodicity be (set as) Furthermore, it adjusts the estimated angle sorting to eliminate errors caused by the order of angles, thus accelerating subsequent training efficiency. Through this loss function, the gradient can be backpropagated from the final DOA estimation result to all parameters of RCR-Net. Figure 1 The red arrow pointing from the output layer to the input layer illustrates this gradient backpropagation path, thus achieving end-to-end global optimization for DOA estimation accuracy. This backpropagation mechanism complements the shortcut connection structure shown by the black arrow mentioned earlier, together ensuring the training stability of deep networks.

[0078] Table 3. Functional modules of the forward propagation path of RCR-Net

[0079] Note: Each functional module has been carefully designed to ensure end-to-end differentiability, enabling the entire process to be optimized through backpropagation.

[0080] Example 2 To verify the technical effectiveness of the method described in this invention, this embodiment provides a series of simulation experiments to demonstrate the reliability and superiority of this invention under various challenging scenarios. The embodiment setup includes: Array configuration and data generation. This embodiment uses a 4-element sparse linear array (... Mapped to a 7-element virtual ULA and using maximum time delay. Construct the input tensor, where It's the wavelength. The training dataset contains 90,000 samples, each containing two DOAs. Uniformly distributed within and with a signal-to-noise ratio of Signals within the dB range. Network training: The network is trained using the Adam optimizer with a learning rate of... It is also compared with subspace methods (MUSIC, ESPRIT), sparse reconstruction methods WDA (Wasserstein distance-based approach), SPA (Sparse and Parametric Approach), wideband method BB-MUSIC, DeepRootMUSIC method without Toplitz constraints, and pure data-driven DeepCNN method.

[0081] The performance analysis of each method in the results graph is as follows: 1. RCR-Net (Residual Covariance Reconstruction Network): The network proposed in this invention.

[0082] 2. DeepRootMUSIC: An improved Root-MUSIC algorithm based on deep learning, with slightly lower performance.

[0083] 3. DeepCNN (Deep Convolutional Neural Network): A purely data-driven method that uses end-to-end training.

[0084] 4. ESPRIT (rotation-invariant subspace technique): a traditional subspace method that is greatly affected by sparse array structures.

[0085] 5. Root-MUSIC (Root MUSIC Algorithm): A classic subspace method, its performance drops significantly under sparse arrays.

[0086] 6. WDA (Wasserstein distance method): A sparse reconstruction method based on optimal transport theory, but with high computational complexity.

[0087] 7. SPA (Sparse Parameterization): Combines sparse reconstruction and parameter estimation, but is sensitive to noise.

[0088] 8. CRLB (Crame-Lao Lower Bound): Theoretical performance limit used to evaluate the estimation accuracy of various algorithms.

[0089] Incoherent signal scenarios. As shown in Figure 3, traditional subspace methods (such as Root-MUSIC and ESPRIT) perform poorly when dealing with sparse arrays because their algorithm design relies on the specific manifold structure of uniform linear arrays and the Topplitz property of the covariance matrix. Although sparse reconstruction methods perform reasonably well in high SNR regions, their performance degrades significantly at medium to low SNR. The method of this invention (RCR-Net) exhibits strong robustness across the entire SNR range. Even in the untrained region of medium to low SNR (SNR ≤ 10 dB), it maintains a low estimation error (RMSPE below 0.7 degrees), significantly outperforming other benchmark methods. This is attributed to the present invention's combination of data-driven approaches and model priors (Topplitz structure), effectively improving estimation accuracy in low SNR environments.

[0090] Coherent signal scenarios. For example... Figure 4As shown, when the signal is coherent, the performance of both traditional and sparse reconstruction methods deteriorates significantly, with RMSPE errors fluctuating between 5 and 11 degrees. This is because the rank deficiency of the source covariance matrix violates the core assumptions of these methods. In contrast, the method of this invention exhibits superior robustness. In the medium-to-high signal-to-noise ratio region (SNR≥ 5 dB), its RMSPE error remains below 1 degree, comparable to performance in incoherent scenarios. Its core advantage lies in the fact that the network of this invention does not attempt to repair a rank-deficient matrix, but rather learns a direct mapping from the observed data to an ideal, full-rank virtual array covariance matrix with a Hermitian-Toplitz structure, thereby implicitly completing the decoherent processing of the signal and ensuring the effectiveness of the subsequent Root-MUSIC algorithm.

[0091] The number of snapshots has an impact. For example... Figure 5 As shown, this invention exhibits strong adaptability to small amounts of snapshot data. Even with a signal-to-noise ratio of 10 dB and as few as 10 snapshots (T=10), this method maintains a low RMSPE, and its performance even surpasses that of all benchmark methods at T=200. This advantage is crucial for real-time systems requiring rapid response, as it significantly reduces data acquisition latency. This stability stems from the method's utilization of the spatiotemporal correlation in the multi-delay autocorrelation matrix tensor to reconstruct a physically complete covariance matrix, thereby enabling reliable estimation from a very small number of samples.

[0092] Example 3 This embodiment is used to verify the scalability of the present invention in multi-source scenarios, particularly its ability to achieve effective estimation with fewer physical array elements than the number of sources. The simulation settings are the same as in Embodiment 2, only the number of sources is changed. Figure 6 As shown, this invention overcomes the physical limitations of traditional methods, resolving more signal sources than the number of physical array elements. The degrees of freedom (DoFs) of traditional subspace methods are limited by the number of physical array elements (N-1). For the 4-element physical array in this embodiment, the DoFs are only 3. This invention successfully increases the system's DoFs to 6 by mapping the 4-element sparse array to a 7-element virtual uniform linear array. Experimental results verify this advantage: when the number of signal sources M≤4, the RMSPE is less than 1 degree under high signal-to-noise ratio; when the number of signal sources increases to M=5 or 6, although the performance decreases slightly, effective estimation is still possible, demonstrating the effectiveness of virtual array expansion technology in overcoming the limitations of the number of physical sensors.

[0093] Example 4 This embodiment is used to verify the adaptability and performance of the present invention in a broadband signal scenario. The broadband signal in this embodiment is simulated using 50 orthogonal subcarriers, with a maximum signal frequency of 500Hz and a sampling rate of 1000Hz. Figure 7 As shown, this invention can uniformly process narrowband and wideband signals without modifying the network architecture. Its core lies in its unified conversion of both narrowband and wideband signals into a multi-delay spatiotemporal covariance tensor, enabling the network to learn DOA information from a common data structure. In incoherent wideband scenarios, when the number of snapshots decreases from 200 to 10, the RMSPE of this method increases from approximately 1 degree to 5 degrees, but consistently outperforms all benchmark methods. In the more challenging coherent wideband scenarios, when T≥50, the RMSPE is below 3 degrees; when T≥100, the RMSPE is below 1 degree, significantly outperforming traditional methods such as wideband MUSIC (BB-MUSIC). This result highlights the enormous potential of this invention in real-time wideband DOA estimation applications. The results of various embodiments demonstrate that the method described in this invention maintains stable high-precision estimation performance in various challenging scenarios, including incoherent, coherent, few snapshots, multiple sources, and wideband scenarios.

[0094] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for estimating DOA of sparse arrays based on residual networks, characterized in that, The raw signal data is input into a trained residual covariance reconstruction network for DOA angle estimation; the residual covariance reconstruction network for DOA angle estimation includes the following steps: S1. Data preprocessing: Convert the original signal data into real-valued tensors; S2. Network Processing: The real-valued tensor is input into the residual covariance reconstruction network. The residual covariance reconstruction network learns the complex mapping from the real-valued tensor to the parameters of the ideal covariance matrix through hierarchical feature extraction, and finally outputs a low-dimensional parameter vector containing all the information required for reconstruction. S3, Matrix Reconstruction: The parameter vector output by the network is mapped and reconstructed into a virtual uniform array covariance matrix with an ideal Hermit-Toplitz structure through a deterministic linear transformation, and the virtual uniform array covariance matrix is ​​regularized. S4. DOA estimation: The reconstructed and regularized covariance matrix is ​​used to calculate the final DOA estimate using the Root-MUSIC algorithm.

2. The DOA estimation method for sparse arrays based on residual networks according to claim 1, characterized in that, The residual covariance reconstruction network includes: The initial convolutional layer is used to extract low-level features, transforming the input tensor from the signal representation space to the feature representation space; Deep residual networks: used to stabilize gradient propagation and extract multi-scale features; Multilayer perceptron: maps high-dimensional feature tensors to low-dimensional parameter vectors, which contain the parameters needed to reconstruct the covariance matrix.

3. The DOA estimation method for sparse arrays based on residual networks according to claim 2, characterized in that, Deep residual networks consist of dimensionality reduction blocks, feature extraction blocks, and residual connections that enable residual learning through shortcut connections.

4. The DOA estimation method for sparse arrays based on residual networks according to claim 1, characterized in that, The matrix reconstruction process in step S3 is as follows: The first part of the parameter vector... The elements are taken as the real part of the first row of the matrix, and the remaining elements are... Each element is used as the imaginary part of the off-diagonal elements in the row, and the entire matrix is ​​then completed using Topletz and Hermitian properties.

5. The DOA estimation method for sparse arrays based on residual networks according to claim 1, characterized in that, In step S3, the covariance matrix of the virtual uniform array is regularized by adaptive diagonal loading.

6. The DOA estimation method for sparse arrays based on residual networks according to claim 1, characterized in that, The data preprocessing in step S1 includes: calculating the autocorrelation matrix with multiple delays for the original signal data, then separating the real and imaginary parts of the complex-valued autocorrelation matrix tensor and converting it into a real-valued tensor.

7. The DOA estimation method for sparse arrays based on residual networks according to claim 1, characterized in that, The residual covariance reconstruction network is optimized through end-to-end training. The training process uses the root mean square periodicity error loss function. The loss function solves the permutation ambiguity problem of multi-source estimation by minimizing permutation matching and solves the periodicity problem of angles by modulo operation.

8. A system for implementing the DOA estimation method based on a sparse array of residual networks as described in claim 1, characterized in that, include: The preprocessing module is used to convert the raw signal data into a multi-channel autocorrelation matrix tensor; The feature learning module is used to extract and fuse high-dimensional feature representations of the autocorrelation matrix tensor; The parameter generation module is used to calculate the parameter vector of the high-dimensional feature representation; The matrix reconstruction module is used to reconstruct the parameter vector into a Hermit-Toplitz covariance matrix; The DOA estimation module is used to estimate the DOA angle of the reconstructed covariance matrix.

9. A computer device comprising a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, characterized in that: When the computer program is executed by the processor, it causes the processor to implement the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor implements the method as described in any one of claims 1 to 8.

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