Coherent signal source DOA estimation method, system and device and storage medium

Abstract

The invention relates to a coherent signal source DOA estimation method, system and device and a storage medium, and belongs to the technical field of metasurface signal processing. The method comprises the following steps: establishing an orthogonal modulation metasurface array model in which metasurface units are uniformly arranged, and performing space-time modulation on an incident signal by using the model to form a single-channel receiving signal; sequentially performing de-spreading, down-conversion, integral zero clearing filtering and de-coherence processing based on a forward and backward spatial smoothing technology on the received signal to obtain an observation vector; and inputting the observation vector into the trained deep expansion ADMM network, sequentially executing sparse feature extraction, physical constraint projection and dual residual updating to obtain a sparse spatial spectrum vector, mapping the sparse spatial spectrum vector into a spatial power spectrum vector, and performing spectrum peak search on the spatial power spectrum vector to determine a DOA estimation value. By adopting the method, high-precision and high-efficiency DOA estimation can be realized under the condition of low signal-to-noise ratio, and the method has higher reliability.

Description

Technical Field

[0001] This application relates to the field of metasurface signal processing technology, and in particular to a method, system, device and storage medium for coherent source DOA estimation. Background Technology

[0002] DOA estimation is one of the main research directions in array signal processing, and it has wide applications in wireless sensing, communication, radar and other fields.

[0003] In recent years, reconfigurable smart metasurfaces (RIS) have attracted widespread attention due to their low cost, flexible deployment, and simple design. They can precisely control the amplitude and phase of electromagnetic waves, providing a new approach for DOA estimation. Researchers have combined RIS with array signal processing to achieve direction finding through a single receiving channel, significantly reducing hardware costs and system complexity. However, existing RIS-based DOA estimation methods have shortcomings: large estimation errors in low signal-to-noise ratio scenarios; and the coherent sources generated by multipath effects can lead to rank deficiency in the received data covariance matrix, rendering traditional algorithms ineffective.

[0004] To address the rank deficiency problem in estimating coherent sources, existing research has proposed a compressed sensing reconstruction DOA estimation method based on the Alternating Direction Method of Multipliers (ADMM). However, this method still has shortcomings: the ADMM algorithm has a large number of iterations, resulting in high computational complexity and difficulty in meeting real-time requirements; in addition, multiple hyperparameters need to be manually set during the algorithm iteration process, and there is a lack of unified optimal criteria for the selection of hyperparameters. If the parameters are set improperly, it will directly affect the convergence speed of the algorithm and even lead to a decrease in DOA estimation accuracy. Summary of the Invention

[0005] Therefore, it is necessary to provide a coherent source DOA estimation method, system, device, and storage medium to address the above-mentioned technical problems, which can achieve high-precision and high-efficiency DOA estimation under low signal-to-noise ratio conditions and has stronger reliability.

[0006] A method for estimating the DOA of a coherent source, the method comprising:

[0007] An orthogonal modulation metasurface array model with uniformly arranged metasurface units is established. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal. The received signal is sequentially despread, downconverted, integrally zeroed, filtered, and decoherentized using forward and backward spatial smoothing techniques to obtain the observation vector of the received signal. A deep unfolded ADMM network, comprising a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer, is constructed and trained. During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function including sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss, to perform end-to-end training of the network until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network. The observation vector is input into the optimal depth to unfold the ADMM network, and sparse feature extraction, physical constraint projection and dual residual update are performed in sequence to obtain a sparse spatial spectral vector and map it into a spatial power spectral vector. By searching for spectral peaks in the spatial power spectral vector, the DOA estimate is determined by the position of the spectral peak.

[0008] In one embodiment, an orthogonal modulation metasurface array model with uniformly arranged metasurface units is established, including: The orthogonal modulation metasurface array model is derived from It consists of uniformly arranged metasurface units, with a spacing of [missing information]. , No. Received signal of each metasurface unit Represented as: ; In the formula, This refers to the metasurface unit number. The number of metasurface units, For the number of snapshots, The incident signal number. The number of incident signals, Indicates the wavelength of the incident signal. Indicates the first The elevation angle of the incident signal, Indicates the first Gaussian white noise during air conditioning operation of a metasurface unit. Indicates the first An incident coherent signal, The center carrier frequency of the system. For the first The baseband frequency offset of an incident signal, especially when hour, For an ideal strongly coherent source.

[0009] In one embodiment, after the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are spatially superimposed with equal weights to form a single-channel received signal. , represented as: ; In the formula, The received signal is Gaussian white noise; For the first The continuous temporal modulation signal of each metasurface unit throughout the entire observation time is a single-period modulation signal. The periodic extension; Indicates the sequence number of the modulation period. Single-cycle modulation signal ; For the first The metasurface unit within a modulation period The modulation code corresponds to the orthogonal modulation code matrix. line, number The elements of the column, the orthogonal modulation coding matrix of each metasurface unit is A Hadamard matrix of order O, with a size of O. ; The rectangular pulse function is defined for the duration of a single symbol, and its specific expression is as follows: , For a single complete modulation cycle, The duration of a single symbol. The modulation code number, , In one modulation period The modulation and coding length contained therein.

[0010] In one embodiment, the received signal is sequentially despread, downconverted, integrally zeroed-filtered, and decoherentized using forward and backward spatial smoothing techniques to obtain the observation vector of the received signal, including: Utilizing the mutually orthogonal properties of Hadamard codes to analyze the received signal Despreading is performed to receive the signal. Multiply by the corresponding orthogonal code sequence of each channel, and then multiply by a complex exponential function for down-conversion, shifting it to baseband. The baseband signal after demodulation of each channel Represented as: ; in, For the number of snapshots, The center carrier frequency of the system. For the first The orthogonal modulation coding sequence corresponding to each channel; Introducing an integral reset filter, strictly adhering to a complete modulation cycle. The baseband signal is reconstructed in blocks and its mean is calculated. The first channel in the The recovered signal within each modulation period Represented as: ; in, The integral variable represents the time history within the modulation period; Recover the signal using all channels Construct the original covariance matrix received by the array. , represented as: ; in, This represents the number of valid snapshots after integration. for The conjugate transpose of; Using forward and backward spatial smoothing techniques, the orthogonal modulation metasurface array model is... Each metasurface unit is divided into Each of the following is an overlapping subarray, and each subarray contains For each metasurface element, the covariance matrix of each subarray is calculated and averaged to obtain the forward smoothing matrix. Specifically, it is expressed as: ; in, Represents the original covariance matrix The extracted first The diagonal block matrix corresponding to each submatrix; Represents the field of complex numbers; Using the transposition matrix right Perform conjugate flipping to obtain the backward smoothing matrix. Specifically, it is expressed as: ; In the formula, This indicates the conjugate operation; Combining the forward smoothing matrix and the backward smoothing matrix, we obtain the final coherent smoothing covariance matrix. , represented as: ; Solve the coherent smoothing covariance matrix The signal is vectorized and normalized to form the observation vector of the received signal. .

[0011] In one embodiment, the sparse feature extraction sublayer, the physically constrained projection sublayer, and the dual residual update sublayer in the deep unfolded ADMM network are respectively represented as follows: ; in, , and They represent the network's first and second generations respectively. The sparsed spatial spectral vector output by the layer, the network's first... Layers are used for auxiliary variables in physical constraint projections, and the network's first layer. Layers are used for Lagrange multiplier directions in dual residual updates; The soft thresholding operator is defined as follows: This is used to achieve feature sparsity and denoising. This represents the feature vector of the input soft threshold operator. The threshold parameter represents the soft thresholding operator; For array manifold matrix, for transpose, The observation vector is in complex form. For the identity matrix, the network's first... Layer penalty parameters Regularization parameters Relaxation factor and globally shared array manifold matrix All are learnable parameters in the network; network initialization state , and The zero vector, at the th... The network sequentially executes the mapping of three functional sub-layers, and the maximum number of layers is set through the network. After cascaded forward propagation, the network outputs the sparse space spectral vector of the last layer. At the same time, it outputs the optimized array manifold matrix.

[0012] In one embodiment, the network input data during training is obtained by concatenating the observation vector in complex form with an array manifold matrix, including: First define A dictionary matrix consisting of virtual guide vectors corresponding to each grid angle under a predetermined grid, where the grid angle range is from... arrive Grid spacing is , represented as: ; Among them, the From one angle Corresponding virtual guide vector It consists of the Kronecker product of the smooth submatrix guiding vectors, i.e. In the formula, Represents the Kronecker product. For inclusion The smooth subarray guiding vector of the nth metasurface unit, where the th Each element is defined as: , Indicates the wavelength of the incident signal. The spacing between adjacent metasurface units. This indicates the conjugate operation; Will Reconstructed into an array manifold matrix consisting of real and imaginary parts. At the same time, the observation vector Reconstruct the observation vector into a complex form consisting of real and imaginary parts. , respectively represented as: ; ; Among them, superscript Indicates transpose; Ultimately and A common input depth unfolded ADMM network was used for end-to-end training.

[0013] In one embodiment, a hybrid loss function, comprising sparsity-assisted loss, support set reconstruction loss, and physical consistency loss, is solved using the sparse spatial spectral vector output by the network, including: The sparse space spectral vector output by the network is represented as ; The sparsity auxiliary loss is used to constrain the sparsity of the output, employing the L1 norm loss, denoted as: ; Support set reconstruction loss is used to measure the difference between the sparse spatial spectral vector of the predicted output and the true label. The error is expressed as mean square error. ;in, The square of the L2 norm; Physical consistency loss is used to measure the degree of agreement between the reconstructed signal and the actual observed signal, and it is applied to the sparse spatial spectral vector. With array manifold matrix The signal is reconstructed by multiplication, and then multiplied by the complex form of the observation vector input to the network. Calculate the mean square error, expressed as ; The final mixture loss function is expressed as: ;in, For sparse weight parameters, This is the physical consistency weight parameter.

[0014] A coherent source DOA estimation system, the system comprising: The first module is used to establish an orthogonal modulation metasurface array model with uniformly arranged metasurface units. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal. The second module is used to sequentially perform despreading, downconversion, integral zeroing filtering, and decoherence processing based on forward and backward spatial smoothing techniques on the received signal to obtain the observation vector of the received signal. The third module is used to construct and train a deep unfolded ADMM network, which includes a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer. During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function, which includes sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss, to train the network end-to-end until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network. The fourth module is used to input the observation vector into the optimal depth unfolded ADMM network, and sequentially perform sparse feature extraction, physical constraint projection and dual residual update to obtain a sparse spatial spectral vector and map it into a spatial power spectral vector. By searching for spectral peaks in the spatial power spectral vector, the DOA estimate is determined by the position of the spectral peak.

[0015] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps: An orthogonal modulation metasurface array model with uniformly arranged metasurface units is established. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal. The received signal is sequentially despread, downconverted, integrally zeroed, filtered, and decoherentized using forward and backward spatial smoothing techniques to obtain the observation vector of the received signal. A deep unfolded ADMM network, comprising a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer, is constructed and trained. During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function including sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss, to perform end-to-end training of the network until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network. The observation vector is input into the optimal depth to unfold the ADMM network, and sparse feature extraction, physical constraint projection and dual residual update are performed in sequence to obtain a sparse spatial spectral vector and map it into a spatial power spectral vector. By searching for spectral peaks in the spatial power spectral vector, the DOA estimate is determined by the position of the spectral peak.

[0016] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor: An orthogonal modulation metasurface array model with uniformly arranged metasurface units is established. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal. The received signal is sequentially despread, downconverted, integrally zeroed, filtered, and decoherentized using forward and backward spatial smoothing techniques to obtain the observation vector of the received signal. A deep unfolded ADMM network, comprising a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer, is constructed and trained. During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function including sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss, to perform end-to-end training of the network until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network. The observation vector is input into the optimal depth to unfold the ADMM network, and sparse feature extraction, physical constraint projection and dual residual update are performed in sequence to obtain a sparse spatial spectral vector and map it into a spatial power spectral vector. By searching for spectral peaks in the spatial power spectral vector, the DOA estimate is determined by the position of the spectral peak.

[0017] The aforementioned method, system, device, and storage medium for estimating the DOA of a coherent source have the following advantages compared to existing technologies: First, by temporally modulating the incident signal using an orthogonal modulation metasurface array model, and then superimposing the reflected signals from all metasurface units to form a single-channel received signal, hardware costs and system complexity can be significantly reduced. Second, compared to traditional spatiotemporally coded metasurfaces, this application utilizes orthogonal codes to achieve higher estimation accuracy with smaller apertures, while also improving estimation accuracy at low signal-to-noise ratios using spatiotemporal coding. Third, addressing the rank deficiency problem in coherent source estimation, [the following is a separate point, likely related to a specific technology or method]. Based on forward and backward spatial smoothing (FBSS) for decoherence processing, the classic ADMM iterative solution process is transformed into a trainable neural network hierarchical structure. By leveraging the end-to-end learning capability of the deep unfolded ADMM network, a hybrid loss function including sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss is used during training to adaptively optimize the array manifold matrix and algorithm hyperparameters. This not only effectively removes the coherence of coherent sources but also significantly shortens the iteration convergence time. Ultimately, high-precision and high-efficiency DOA estimation is achieved under low signal-to-noise ratio conditions, with stronger reliability. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the DOA estimation method for coherent sources; Figure 2 This is a schematic diagram of the metasurface unit arrangement in an orthogonal modulation metasurface array model; Figure 3 This is a schematic diagram of the orthogonal spatiotemporal coded modulation sequence of a metasurface; Figure 4 This is a schematic diagram of the training loss and validation loss values ​​of a DU-ADMM (Deep Unfolded ADMM) network with 40 layers and different training epochs. Figure 5 This is a schematic diagram of the direction-of-arrival spatial spectrum obtained after passing through a trained DU-ADMM network when the signal-to-noise ratio is -24dB and the incident angle is -10° and 30°. Figure 6 This is a schematic diagram of the direction-of-arrival spatial spectrum obtained by estimating untrained angles of 10.2° and -25° using the DU-ADMM network; Figure 7 This is a schematic diagram of the direction-of-arrival spatial spectrum calculated from the original ADMM parameters with 400 iterations and the optimized parameters after training the DU-ADMM network with 40 iterations, respectively, when the signal-to-noise ratio is -24dB and the incident angle is -30° and 10°. Figure 8This is a schematic diagram of the direction-of-arrival spatial spectrum calculated from the original ADMM parameters with 400 iterations and the optimized parameters after training the DU-ADMM network with 40 iterations, when the signal-to-noise ratio is -26dB, the incident angle is -30° and 10°, respectively. Figure 9 This is a diagram comparing the convergence speed of the DU-ADMM network and the traditional ADMM method during iteration. Figure 10 A schematic diagram of an ablation experiment using an integrator zeroer at a signal-to-noise ratio of -24dB. Figure 11 A schematic diagram of an ablation experiment without using an integrator zeroer at a signal-to-noise ratio of -24dB. Figure 12 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0020] In one embodiment, such as Figure 1 As shown, a method for estimating the DOA of a coherent source is provided, including the following steps: Step 1: Establish an orthogonal modulation metasurface array model with uniformly arranged metasurface units. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal.

[0021] The orthogonal modulation metasurface array model is derived from It consists of uniformly arranged metasurface units, with a spacing of [missing information]. , No. Received signal of each metasurface unit Represented as: ; In the formula, This refers to the metasurface unit number. The number of metasurface units, For the number of snapshots, The incident signal number. The number of incident signals, Indicates the wavelength of the incident signal. Indicates the first The elevation angle of the incident signal, Indicates the first Gaussian white noise during air conditioning operation of a metasurface unit. Indicates the first An incident coherent signal, The center carrier frequency of the system. For the first The baseband frequency offset of an incident signal, especially when hour, For an ideal strongly coherent source.

[0022] Specifically, Figure 2 The orthogonal modulation metasurface array model shown has 16 metasurface units. With unit 1 as the reference unit, the distances between adjacent units (such as unit 2 and unit 1, unit 3 and unit 2, etc.) are sequentially calculated, and are all half the wavelength of the incident signal, thus forming a uniform linear arrangement. Figure 2 In this context, d represents the geometric distance between the center points of adjacent metasurface coding units in the column; h represents the vertical distance from the receiving antenna located directly above the center of the metasurface to the metasurface plane; g represents the geometric distance from the metasurface coding unit to the center of the receiving antenna; and D represents the spatial path difference generated by the incident plane wave between adjacent metasurface coding units.

[0023] After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are spatially superimposed with equal weights to form a single-channel received signal. , represented as: ; In the formula, The received signal is Gaussian white noise; For the first The continuous temporal modulation signal of each metasurface unit throughout the entire observation time is a single-period modulation signal. The periodic extension; Indicates the sequence number of the modulation period. That is, within the total duration of the signal, it contains a total of A complete modulation cycle; single-cycle modulation signal ; For the first The metasurface unit within a modulation period The modulation code corresponds to the orthogonal modulation code matrix. line, number The elements of the column, the orthogonal modulation coding matrix of each metasurface unit is A Hadamard matrix of order O(n), with a size of O(n). ; The rectangular pulse function is defined for the duration of a single symbol, and its specific expression is as follows: , For a single complete modulation cycle, The duration of a single symbol. The modulation code number, , In one modulation period The modulation and coding length contained therein.

[0024] Specifically, A Hadamard matrix of order 1 is of order 2. An orthogonal matrix consisting of +1 and -1. A second-order Hadamard matrix can be represented as: ; The Hadamard matrix of order 1 can be obtained by The Hadamard matrix of order 1 is obtained recursively: .

[0025] Figure 3 It is a 16×16 orthogonal modulation coding matrix (i.e., Hadamard matrix) for each metasurface unit. Each row represents the modulation sequence of one unit, and there are a total of 16 coding sequences. Figure 3 Yellow indicates a modulation coefficient of 1, meaning the metasurface modulation phase is 0°; blue indicates a modulation coefficient of -1, meaning the metasurface modulation phase is 180°. Each column represents the modulation code of each unit in the same time period, with a total of 16 units modulated. After modulation by the orthogonal modulation coding matrix, the reflected signals of each unit are linearly superimposed with equal weights in space, converging to form a single-channel received signal.

[0026] Step 2 involves sequentially despreading, downconverting, integrating and zeroing filtering, and decoherent processing based on forward and backward spatial smoothing techniques to obtain the observation vector of the received signal.

[0027] At the receiving end, in order to receive signals from a single channel The original received signals of each metasurface unit are separated from the signal. The orthogonality of the Hadamard codes is then used to analyze the received signals. Despreading is performed to receive the signal. Multiply by the corresponding orthogonal code sequence of each channel, and then multiply by a complex exponential function for down-conversion, shifting it to baseband. The baseband signal after demodulation of each channel Represented as: ; in, For the number of snapshots, The center carrier frequency of the system. For the first The quadrature modulation coding sequence corresponding to each channel.

[0028] Because the despreading process generates orthogonal residual terms and high-frequency harmonics in other channels, this application introduces an integral zeroing filter, strictly adhering to a complete modulation cycle. The baseband signal is reconstructed in blocks and its mean is calculated. The first channel in the The recovered signal within each modulation period Represented as: ; in, The integral variable represents the time history within the modulation period.

[0029] Then, recover the signal using all channels. Construct the original covariance matrix received by the array. , represented as: ; in, This represents the number of valid snapshots after integration. for The conjugate transpose of; Using forward and backward spatial smoothing techniques, the orthogonal modulation metasurface array model is... Each metasurface unit is divided into Each of the following is an overlapping subarray, and each subarray contains For each metasurface element, the covariance matrix of each subarray is calculated and averaged to obtain the forward smoothing matrix. Specifically, it is expressed as: ; in, Represents the original covariance matrix The extracted first The diagonal block matrix corresponding to each submatrix; Represents the complex field.

[0030] Using the transposition matrix right Perform conjugate flipping to obtain the backward smoothing matrix. Specifically, it is expressed as: ; In the formula, This indicates the conjugate operation.

[0031] Combining the forward smoothing matrix and the backward smoothing matrix, we obtain the final coherent smoothing covariance matrix. , represented as: ; Finally, the coherent smoothing covariance matrix will be solved. The signal is vectorized and normalized to form the observation vector of the received signal. .

[0032] Specifically, when the number of metasurface elements is 16, the orthogonal characteristic sequence of the Hadamard code is used to despread the single-channel received signal. After the despread signal is rapidly down-converted to the baseband, it is integrated and cleared to zero strictly according to a complete orthogonal coding cycle, thereby reconstructing the equivalent baseband signal of 16 independent array elements without distortion. The array covariance matrix is ​​obtained based on the reconstructed baseband signals of each array element. The 16-element array is divided into 7 overlapping subarrays, each containing 10 array elements. The forward and backward smoothed covariance matrices are calculated separately and averaged to obtain the completely decoherent smoothed covariance matrix, which is then vectorized to obtain the equivalent observation vector.

[0033] Step 3: Construct and train a deep unfolded ADMM network including a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer. During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function including sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss to train the network end-to-end until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network.

[0034] The three sublayers in the deep unfolded ADMM network are represented as follows: The sparse feature extraction sublayer (X-update) is used to extract sparse features of the target spatial spectrum using a soft-threshold activation function. ; The physically constrained projection sublayer (Z-update) is used to perform a quadratic minimization update by incorporating the physical properties of the array manifold matrix, achieved by solving a system of linear equations: ; Dual residual update sublayer: ; in, , and They represent the network's first and second generations respectively. The sparsed spatial spectral vector output by the layer, the network's first... Layers are used for auxiliary variables in physical constraint projections, and the network's first layer. Layers are used for Lagrange multiplier directions in dual residual updates; The soft thresholding operator is defined as follows: This is used to achieve feature sparsity and denoising. This represents the feature vector of the input soft threshold operator. The threshold parameter represents the soft thresholding operator; For array manifold matrix, for transpose, The observation vector is in complex form. For the identity matrix, the network's first... Layer penalty parameters Regularization parameters Relaxation factor and globally shared array manifold matrix These are all learnable parameters in the network. Network initialization state. , and The zero vector, at the th... The network executes the mapping of three functional sub-layers sequentially. The maximum number of layers in the network is set. After cascaded forward propagation, the network outputs the sparse space spectral vector of the last layer. At the same time, it outputs the optimized array manifold matrix.

[0035] During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix, specifically including the following steps: First define A dictionary matrix consisting of virtual guide vectors corresponding to each grid angle under a predetermined grid, where the grid angle range is from... arrive Grid spacing is , is represented as: ; Among them, the From one angle Corresponding virtual guide vector It consists of the Kronecker product of the smooth submatrix guiding vectors, i.e. In the formula, Represents the Kronecker product. For inclusion The smooth subarray guiding vector of the nth metasurface unit, where the th Each element is defined as: , Indicates the wavelength of the incident signal. The spacing between adjacent metasurface units. This indicates the conjugate operation.

[0036] To reduce computational complexity, Reconstructed into an array manifold matrix consisting of real and imaginary parts. At the same time, the observation vector Reconstruct the observation vector into a complex form consisting of real and imaginary parts. , respectively represented as: ; ; Among them, superscript This indicates transpose.

[0037] Ultimately and A common input depth unfolded ADMM network was used for end-to-end training.

[0038] Furthermore, during training, to guide network optimization, this application incorporates multi-label one-hot encoding from real signal angles. (i.e., the real spatial spectrum) A hybrid loss function integrating physical mechanisms and data-driven approaches was constructed. This function utilizes the sparse spatial spectrum vector output by the network to solve for a hybrid loss function including sparsity-assisted loss, support set reconstruction loss, and physical consistency loss, comprising: The sparse space spectral vector output by the network is represented as .

[0039] The sparsity auxiliary loss is used to constrain the sparsity of the output, employing the L1 norm loss, denoted as: .

[0040] Support set reconstruction loss is used to measure the difference between the sparse spatial spectral vector of the predicted output and the true label. The error is expressed as mean squared error (MSE), denoted as... ;in, It is the square of the L2 norm.

[0041] Physical consistency loss is used to measure the degree of agreement between the reconstructed signal and the actual observed signal, and it is applied to the sparse spatial spectral vector. With array manifold matrix The signal is reconstructed by multiplication, and then multiplied by the complex form of the observation vector input to the network. Calculate the mean square error, expressed as .

[0042] The final mixture loss function is expressed as: ;in, For sparse weight parameters, This is the physical consistency weight parameter.

[0043] During training, the DU-ADMM network undergoes end-to-end supervised learning using the training dataset. The Adam optimization algorithm is employed to update network weights: a learning rate decay strategy is used, automatically reducing the learning rate when the validation set loss no longer decreases after several epochs. A gradient pruning anti-explosion mechanism is implemented to prevent gradient explosion during backpropagation of penalty parameters based on exponential operations, by truncating the maximum gradient norm of the overall network parameters. An early stopping mechanism is introduced to monitor the validation set loss; if the validation set loss does not substantially decrease within several consecutive epochs, training is terminated early, and the optimal model parameters with the minimum validation set loss are retained.

[0044] Step 4: Input the observation vector into the optimal depth to expand the ADMM network, and sequentially perform sparse feature extraction, physical constraint projection and dual residual update to obtain a sparse spatial spectral vector and map it to a spatial power spectral vector. By searching for spectral peaks in the spatial power spectral vector, the DOA estimate is determined by the position of the spectral peak.

[0045] Because the optimal depth unfolded ADMM network learns the mapping relationship, its output... It exhibits a distinct sparse strong peak at the true signal angle, while showing a tiny value close to zero at the noise direction. Therefore, the output sparse spatial spectral vector... Perform energy mapping and calculate the spatial power spectrum vector. : ; In the formula, This represents the square operation of taking the modulus of each element in the vector.

[0046] Then, the peak search algorithm is used to analyze the spatial power spectrum vector. The processing includes: Set a preset amplitude threshold to convert the spatial power spectrum vector Spectral lines smaller than this threshold are filtered out.

[0047] Spectral vector after spectral line filtering Perform a local extremum search to extract the top values ​​with the largest amplitudes. Set of position indices corresponding to each spectral peak ,in K This indicates the number of incident signals.

[0048] Extracted Each peak index is mapped to a corresponding spatial grid domain. Based on the constructed grid angle range (i.e., -60° to 60°, with a step size of 1°), the final direction-of-arrival (DOA) estimate is obtained. : ; in, Indicates index index The corresponding physical angle value within the preset spatial grid domain.

[0049] In summary, the coherent source DOA estimation method provided in this application employs an orthogonal modulation metasurface array model to precisely temporally modulate the incident signal. By superimposing the reflected signals of all metasurface units and converging them to form a single-channel received signal, it can significantly reduce system hardware costs and overall complexity. Compared to traditional spatiotemporally coded metasurfaces, this method uses an orthogonal code design, which can achieve higher parameter estimation accuracy under smaller array aperture conditions. At the same time, the spatiotemporal coding mechanism effectively improves the estimation stability and accuracy in low signal-to-noise ratio scenarios. To address the challenge of rank deficiency in estimating coherent sources, this method employs forward and backward spatial smoothing techniques for efficient decoherence. It transforms the traditional ADMM iterative solution process into a trainable neural network hierarchical structure, leveraging the end-to-end learning capabilities of the deep unfolded ADMM network. During training, a hybrid loss function consisting of sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss is used to adaptively optimize the array manifold matrix and algorithm hyperparameters. This not only reliably removes the coherence characteristics of coherent sources but also significantly accelerates the iterative convergence speed. Ultimately, it achieves high-precision and high-efficiency DOA estimation even in complex low SNR environments, demonstrating stronger robustness and reliability.

[0050] Furthermore, the beneficial performance of the proposed method was verified through experiments. During the experiment, training of the DU-ADMM network involved random sampling within the angle interval [-60°, 60°] to generate training samples containing 6200 angle combinations, with a signal-to-noise ratio (SNR) range of -25dB to 20dB. Appropriate maximum network layers and training epochs were set. On the one hand, the optimal number of training epochs needs to be selected based on the training and validation loss values; too many epochs can lead to overfitting. On the other hand, more network layers result in longer training time, while fewer layers lead to larger estimation errors. An early stopping mechanism with a patience value of 20 was introduced during training to prevent overfitting. Figure 4 This involves calculating the training and validation loss values ​​of a DU-ADMM network with 40 layers and different numbers of training epochs. Figure 4 It can be seen that when the number of layers is 40, the optimal number of training rounds is 100 rounds.

[0051] To verify the effectiveness of this application in DOA estimation, based on the optimal number of training rounds, Figure 5 This is a schematic diagram of the direction-of-arrival spatial spectrum obtained after passing through a trained DU-ADMM network when the signal-to-noise ratio is -24dB and the incident angle is -10° and 30°. Figure 6This is a schematic diagram of the direction-of-arrival (DOA) spatial spectrum obtained by estimating untrained angles of 10.2° and -25° using the DU-ADMM network. A sharp DOA spatial spectrum is still obtained. It can be seen that this application can effectively estimate the azimuth angle of multipath coherent signals, effectively overcoming the failure problem of traditional single-channel time-varying mechanisms when processing coherent signals, and has strong generalization ability.

[0052] To verify the advantages of this application over the traditional ADMM algorithm, the network parameters optimized based on the optimal number of training rounds were substituted into the test. Figure 7 The DOA spatial spectra are calculated from the original ADMM parameters with 400 iterations and the optimized parameters after training the DU-ADMM network with 40 iterations, when the signal-to-noise ratio is -24dB, the incident angle is -30° and 10°, respectively. It can be seen that the DOA estimation obtained by the DU-ADMM network parameters is more accurate. Figure 8 The direction-of-arrival (DOA) spatial spectra are calculated using the original ADMM parameters (400 iterations) and the optimized parameters trained by the DU-ADMM network (40 iterations) at an DNOW ratio of -26dB, an incident angle of -30°, and a 10° angle. This demonstrates that the DU-ADMM network can still achieve high-precision angle measurement even when the traditional ADMM algorithm fails. Furthermore, the method in this application, due to its deep unfolding architecture, only requires 50 fixed forward network calculations for online direction finding, eliminating the need for hundreds of iterations of inversion required by the traditional ADMM algorithm. Figure 9 This is a comparison of the convergence speed of the DU-ADMM network and the traditional ADMM method during iteration. Figure 9 As can be seen, this application has a faster convergence speed. Therefore, compared with the traditional ADMM method, this application can improve accuracy and convergence speed with fewer iterations and lower signal-to-noise ratio, achieving better results.

[0053] To further verify the effectiveness of the integral zeroing filter in this application under low signal-to-noise ratio conditions. Figure 10 and Figure 11 Ablation experiments were conducted to compare the use of an integrator zeroing filter at a signal-to-noise ratio of -24dB. Tests showed that without this integrator averaging process, the baseband signal was submerged in significant noise due to severe residual cross-interference in the orthogonal modulation coding sequence within incomplete cycles. This resulted in severe spurious peaks in the spatial spectrum output by the subsequent DU-ADMM network, leading to complete failure of direction finding. Conversely, when using the complete processing link of this application, the integrator zeroing filter module, which executes strictly according to the complete cycle, perfectly utilizes the orthogonal cancellation characteristics of the Hadamard code, effectively filtering out interference and achieving smooth noise reduction. This comparison fully demonstrates that there is a synergistic optimization effect between the unique integrator zeroing filter and the deep unfolded network, which is the core prerequisite for ensuring that the single-channel architecture still possesses high-precision and high-reliability direction finding capabilities at extremely low signal-to-noise ratios.

[0054] In one embodiment, a coherent source DOA estimation system is provided, comprising: The first module is used to establish an orthogonal modulation metasurface array model with uniformly arranged metasurface units. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal. The second module is used to sequentially perform despreading, downconversion, integral zeroing filtering, and decoherence processing based on forward and backward spatial smoothing techniques on the received signal to obtain the observation vector of the received signal. The third module is used to construct and train a deep unfolded ADMM network, which includes a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer. During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function, which includes sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss, to train the network end-to-end until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network. The fourth module is used to input the observation vector into the optimal depth unfolded ADMM network, and sequentially perform sparse feature extraction, physical constraint projection and dual residual update to obtain a sparse spatial spectral vector and map it into a spatial power spectral vector. By searching for spectral peaks in the spatial power spectral vector, the DOA estimate is determined by the position of the spectral peak.

[0055] Specific limitations regarding the DOA estimation system for coherent sources can be found in the limitations of the coherent source DOA estimation method described above, and will not be repeated here. Each module in the aforementioned coherent source DOA estimation system can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0056] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 12As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a coherent source DOA estimation method. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0057] Those skilled in the art will understand that Figure 12 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0058] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to perform the following steps: An orthogonal modulation metasurface array model with uniformly arranged metasurface units is established. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal. The received signal is sequentially despread, downconverted, integrally zeroed, filtered, and decoherentized using forward and backward spatial smoothing techniques to obtain the observation vector of the received signal. A deep unfolded ADMM network, comprising a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer, is constructed and trained. During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function including sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss, to perform end-to-end training of the network until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network. The observation vector is input into the optimal depth to unfold the ADMM network, and sparse feature extraction, physical constraint projection and dual residual update are performed in sequence to obtain a sparse spatial spectral vector and map it into a spatial power spectral vector. By searching for spectral peaks in the spatial power spectral vector, the DOA estimate is determined by the position of the spectral peak.

[0059] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor: An orthogonal modulation metasurface array model with uniformly arranged metasurface units is established. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal. The received signal is sequentially despread, downconverted, integrally zeroed, filtered, and decoherentized using forward and backward spatial smoothing techniques to obtain the observation vector of the received signal. A deep unfolded ADMM network, comprising a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer, is constructed and trained. During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function including sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss, to perform end-to-end training of the network until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network. The observation vector is input into the optimal depth to unfold the ADMM network, and sparse feature extraction, physical constraint projection and dual residual update are performed in sequence to obtain a sparse spatial spectral vector and map it into a spatial power spectral vector. By searching for spectral peaks in the spatial power spectral vector, the DOA estimate is determined by the position of the spectral peak.

[0060] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0061] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0062] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application.

Claims

1. A method for estimating the DOA of a coherent source, characterized in that, The method includes: An orthogonal modulation metasurface array model with uniformly arranged metasurface units is established. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal. The received signal is sequentially despread, downconverted, integrally zeroed, filtered, and decoherentized using forward and backward spatial smoothing techniques to obtain the observation vector of the received signal. A deep unfolded ADMM network, comprising a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer, is constructed and trained. During training, the network input data is obtained by concatenating the complex form of the observation vector with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function including sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss, to perform end-to-end training of the network until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network. The observation vector is input into the optimal depth to unfold the ADMM network, and sparse feature extraction, physical constraint projection and dual residual update are performed in sequence to obtain a sparse spatial spectral vector and map it into a spatial power spectral vector. By performing spectral peak search on the spatial power spectral vector, the DOA estimate is determined by the position corresponding to the spectral peak.

2. The method for estimating the DOA of a coherent source according to claim 1, characterized in that, A model of an orthogonally modulated metasurface array with uniformly arranged metasurface units is established, including: The orthogonal modulation metasurface array model is derived from It consists of uniformly arranged metasurface units, with a spacing of [missing information]. , No. Received signal of each metasurface unit Represented as: ； In the formula, This refers to the metasurface unit number. The number of metasurface units, For the number of snapshots, The incident signal number. The number of incident signals, Indicates the wavelength of the incident signal. Indicates the first The elevation angle of the incident signal, Indicates the first Gaussian white noise during air conditioning operation of a metasurface unit. Indicates the first An incident coherent signal, The center carrier frequency of the system. For the first The baseband frequency offset of an incident signal, especially when hour, For an ideal strongly coherent source.

3. The method for estimating the DOA of a coherent source according to claim 2, characterized in that, After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are spatially superimposed with equal weights to form a single-channel received signal. , represented as: ； In the formula, The received signal is Gaussian white noise; For the first The continuous temporal modulation signal of each metasurface unit throughout the entire observation time is a single-period modulation signal. The periodic extension; Indicates the sequence number of the modulation period. Single-cycle modulation signal ; For the first The metasurface unit within a modulation period The modulation code corresponds to the orthogonal modulation code matrix. line, number The elements of the column, the orthogonal modulation coding matrix of each metasurface unit is A Hadamard matrix of order O, with a size of O. ; The rectangular pulse function is defined for the duration of a single symbol, and its specific expression is as follows: , For a single complete modulation cycle, The duration of a single symbol. The modulation code number, , In one modulation period The modulation and coding length contained therein.

4. The method for estimating the DOA of a coherent source according to claim 3, characterized in that, The received signal is sequentially despread, downconverted, integrally zeroed, filtered, and decoherentized using forward and backward spatial smoothing techniques to obtain the observation vector of the received signal, including: Utilizing the mutually orthogonal properties of Hadamard codes to analyze the received signal Despreading is performed to receive the signal. Multiply by the corresponding orthogonal code sequence of each channel, and then multiply by a complex exponential function for down-conversion, shifting it to baseband. The baseband signal after demodulation of each channel Represented as: ； in, For the number of snapshots, The center carrier frequency of the system. For the first The orthogonal modulation coding sequence corresponding to each channel; Introducing an integral reset filter, strictly adhering to a complete modulation cycle. The baseband signal is reconstructed in blocks and its mean is calculated. The first channel in the The recovered signal within each modulation period Represented as: ； in, The integral variable represents the time history within the modulation period; Recover the signal using all channels Construct the original covariance matrix received by the array. , represented as: ； in, This represents the number of valid snapshots after integration. Indicates conjugate transpose; Using forward and backward spatial smoothing techniques, the orthogonal modulation metasurface array model is... Each metasurface unit is divided into Each of the following is an overlapping subarray, and each subarray contains For each metasurface element, the covariance matrix of each subarray is calculated and averaged to obtain the forward smoothing matrix. Specifically, it is expressed as: ； in, Represents the original covariance matrix The extracted first The diagonal block matrix corresponding to each submatrix; Represents the field of complex numbers; Using the transposition matrix right Perform conjugate flipping to obtain the backward smoothing matrix. Specifically, it is expressed as: ； In the formula, This indicates the conjugate operation; Combining the forward smoothing matrix and the backward smoothing matrix, we obtain the final coherent smoothing covariance matrix. , represented as: ； Solve the coherent smoothing covariance matrix The signal is vectorized and normalized to form the observation vector of the received signal. .

5. The method for estimating the DOA of a coherent source according to claim 4, characterized in that, The sparse feature extraction sublayer, physically constrained projection sublayer, and dual residual update sublayer in the deep unfolded ADMM network are respectively represented as: ； in, , and They represent the network's first and second generations respectively. The sparsed spatial spectral vector output by the layer, the network's first... Layers are used for auxiliary variables in physical constraint projections, and the network's first layer. Layers are used for Lagrange multiplier directions in dual residual updates; The soft thresholding operator is defined as follows: This is used to achieve feature sparsity and denoising; This represents the feature vector of the input soft threshold operator. The threshold parameter represents the soft thresholding operator; For array manifold matrix, for transpose, The observation vector is in complex form. For the identity matrix, the network's first... Layer penalty parameters Regularization parameters Relaxation factor and globally shared array manifold matrix All are learnable parameters in the network; network initialization state , and The zero vector, at the th... The network sequentially executes the mapping of three functional sub-layers, and the maximum number of layers is set through the network. After cascaded forward propagation, the network outputs the sparse space spectral vector of the last layer. At the same time, it outputs the optimized array manifold matrix.

6. The method for estimating the DOA of a coherent source according to claim 5, characterized in that, During training, the network input data is obtained by concatenating the observation vector in complex form with the array manifold matrix, including: First define A dictionary matrix consisting of virtual guide vectors corresponding to each grid angle under a predetermined grid, where the grid angle range is from... arrive Grid spacing is , represented as: ； Among them, the From one angle Corresponding virtual guide vector It consists of the Kronecker product of the smooth submatrix guiding vectors, i.e. In the formula, Represents the Kronecker product. For inclusion The smooth subarray guiding vector of the nth metasurface unit, where the th Each element is defined as: , Indicates the wavelength of the incident signal. The spacing between adjacent metasurface units. This indicates the conjugate operation; Will Reconstructed into an array manifold matrix consisting of real and imaginary parts. At the same time, the observation vector Reconstruct the observation vector into a complex form consisting of real and imaginary parts. , respectively represented as: ； ； Among them, superscript Indicates transpose; Ultimately and A common input depth unfolded ADMM network was used for end-to-end training.

7. The method for estimating the DOA of a coherent source according to claim 6, characterized in that, Using the sparse spatial spectral vector output by the network, a hybrid loss function is solved, which includes sparsity-assisted loss, support set reconstruction loss, and physical consistency loss. The sparse space spectral vector output by the network is represented as ; The sparsity auxiliary loss is used to constrain the sparsity of the output, employing the L1 norm loss, denoted as: ; Support set reconstruction loss is used to measure the difference between the sparse spatial spectral vector of the predicted output and the true label. The error is expressed as mean square error. ;in, The square of the L2 norm; Physical consistency loss is used to measure the degree of agreement between the reconstructed signal and the actual observed signal, and it is applied to the sparse spatial spectral vector. With array manifold matrix The signal is reconstructed by multiplication, and then multiplied by the complex form of the observation vector input to the network. Calculate the mean square error, expressed as ; The final mixture loss function is expressed as: ;in, For sparse weight parameters, This is the physical consistency weight parameter.

8. A coherent source DOA estimation system, characterized in that, The system includes: The first module is used to establish an orthogonal modulation metasurface array model with uniformly arranged metasurface units. After the incident signal is temporally modulated by the orthogonal modulation coding matrix of each metasurface unit in the model, the reflected signals of all metasurface units are linearly superimposed in space with equal weights and converged to form a single-channel received signal. The second module is used to sequentially perform despreading, downconversion, integral zeroing filtering, and decoherence processing based on forward and backward spatial smoothing techniques on the received signal to obtain the observation vector of the received signal. The third module is used to construct and train a deep unfolded ADMM network, which includes a sparse feature extraction sublayer, a physical constraint projection sublayer, and a dual residual update sublayer. During training, the network input data is obtained by concatenating the complex form observation vector with the array manifold matrix. The sparse spatial spectral vector output by the network is used to solve a hybrid loss function, which includes sparsity auxiliary loss, support set reconstruction loss, and physical consistency loss, to perform end-to-end training of the network until convergence to obtain the optimal deep unfolded ADMM network. The array manifold matrix is ​​a learnable parameter of the network. The fourth module is used to input the observation vector into the optimal depth unfolded ADMM network, and sequentially perform sparse feature extraction, physical constraint projection and dual residual update to obtain a sparse spatial spectral vector and map it into a spatial power spectral vector. By performing spectral peak search on the spatial power spectral vector, the DOA estimate is determined by the position corresponding to the spectral peak.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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