A deep learning-based off-grid direction of arrival estimation method

Abstract

The application discloses an off-grid direction of arrival estimation method based on deep learning, and belongs to the cross field of array signal processing and artificial intelligence technology. The method constructs a sample covariance matrix by using array receiving signals, extracts real parts, imaginary parts and phases to form three-channel input features; global array features are obtained through convolution feature extraction, feature enhancement and global feature extraction, and classification features and off-grid offset features are generated; angle grids are set in a preset angle range, and corresponding trainable angle parameters are configured for each angle grid, and the same angle parameter is used to generate corresponding classification responses and off-grid offset responses; the target angle grid is determined according to the classification response, the off-grid offset response with the same number is determined, and after being subjected to bounded transformation, the angle value of the target angle grid is added, and a continuous direction of arrival estimation value is output. The application can establish the corresponding relationship between angle grid classification and off-grid offset estimation, and reduce angle grid quantization error.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of array signal processing and artificial intelligence technology, and relates to an off-grid direction of arrival estimation method based on deep learning. Background Technology

[0002] Direction of arrival (DOA) estimation is a crucial technique in array signal processing. It's used to determine the incident direction of one or more signal sources relative to the array based on the received signal. It has wide applications in sonar detection, radar detection, wireless communication, target localization, and environmental sensing. The received array signal contains amplitude, phase, and correlation information between different array elements. By processing this information, the DOA of the signal source can be estimated.

[0003] Traditional direction-of-arrival (DOA) estimation methods include those based on spatial spectrum search, subspace decomposition or rotation invariance, and sparse reconstruction. These methods typically rely on array manifold models, sample covariance matrices, eigenvalue decomposition, spectral peak search, or iterative optimization processes. When the array model is accurate, the signal-to-noise ratio (SNR) is high, and the number of snapshots is sufficient, traditional methods can achieve good estimation results. However, under conditions of low SNR, limited snapshots, multiple signal sources with similar angles, or errors in the array model, problems such as decreased estimation accuracy, difficulty in resolving spectral peaks, increased computational cost, or reduced estimation stability may occur.

[0004] With the development of deep learning technology, neural networks have been used to learn the nonlinear mapping relationship between array observation features and direction of arrival (DOA). Related methods can input the array received signal, sample covariance matrix, or features constructed from the sample covariance matrix into the neural network, which then extracts the array observation features and outputs the DOA estimation result. Compared with traditional methods that rely on explicit peak search, subspace decomposition, or iterative optimization, deep learning methods can establish the mapping relationship between array observation features and DOA through training data.

[0005] Deep learning-based direction-of-arrival (DOA) estimation methods typically set up multiple angle grids arranged in angular order within a preset angle search range, and determine the angle grid where the signal source is located based on the network's response to each angle grid's output. When the true DOA coincides with or approximately coincides with the angle value of a certain angle grid, the angle value of the angle grid with the larger response is directly output to obtain the corresponding on-network DOA estimation result. However, the output angle of this type of method is limited by the angle grid spacing. When the true DOA is located between adjacent angle grids, directly outputting the angle grid's angle value cannot represent the offset of the true DOA relative to that angle grid, thus generating off-network error and angle quantization error. Reducing the angle grid spacing can reduce quantization error, but it increases the number of angle grids and the network output size.

[0006] To obtain continuous direction-of-arrival (DOA) estimation results, an off-grid offset estimation process can be added to the angular grid classification. This process estimates the offset of the true DOA relative to the angular grid angle values, and adds the angular grid angle values ​​to the corresponding off-grid offsets to obtain continuous DOA estimates between the angular grids. Therefore, the classification response is used to determine the target angular grid, while the off-grid offset response is used to continuously correct the determined angular grid.

[0007] However, when the classification response and off-grid migration response are generated through independent feature representation or output mapping processes, although they can have the same number of output positions, there may be a lack of common angular connections established by the network's internal mechanisms between these output positions. In this case, the target angle grid determined based on the classification response may not correspond accurately with the off-grid migration response used to correct that angle grid. Especially when the signal-to-noise ratio is low, the number of observation snapshots is limited, and the angles of multiple signal sources are close or the true directions of arrival are close to the boundaries of adjacent angle grids, errors in angle grid selection or inaccurate correspondence in the off-grid migration response can both affect the continuous direction of arrival estimation results.

[0008] Therefore, a deep learning-based off-grid direction-of-arrival (DOA) estimation method is needed. Based on the determination of the target angular position using angular grid classification, a correspondence between the angular grid and the classification response and off-grid offset response is established, so that the classification response and off-grid offset response related to the same angular grid have common angular conditions, and continuous DOA estimation results are output according to the determined target angular grid and its corresponding off-grid offset. Summary of the Invention

[0009] The purpose of this invention is to provide an off-grid direction-of-arrival estimation method based on deep learning, so as to reduce the angle quantization error caused by fixed-angle grid classification, and to make the classification response of the angle grid and the off-grid offset response have a clear angular position correspondence in the output generation process.

[0010] To achieve the above objectives, this invention provides an off-grid direction-of-arrival estimation method based on deep learning, comprising the following steps:

[0011] S1. Obtain the array received signal matrix According to the array received signal matrix Constructing the sample covariance matrix And based on the sample covariance matrix The real part, imaginary part, and phase construct the array covariance input features .

[0012] S2. Construct an off-network convolutional neural network, including a convolutional feature extraction module, a feature enhancement module, a global array feature extraction module, a classification feature generation branch, an off-network offset regression branch, and an angle joint decoding module.

[0013] S3, Input the array covariance into the feature The convolutional feature extraction module is input to the array covariance input feature. Convolutional feature extraction is performed to obtain two-dimensional array spatial features that retain the spatial distribution information of array elements. .

[0014] S4. The spatial features of the two-dimensional array The feature enhancement module is input, and the feature enhancement result is compared with the two-dimensional array spatial features. Residual combining is performed to obtain enhanced two-dimensional spatial features. Then, it is input into the global array feature extraction module for global feature extraction to obtain global array features. .

[0015] S5, the global array features The classification features are obtained by inputting the classification feature generation branch and the off-network offset regression branch respectively. Off-network offset characteristics ;

[0016] S6. Classify the features and the off-network offset feature The angle joint decoding module is input, and multiple angle grids are obtained within a preset angle search range. These angle grids are then numbered according to angle order, and the grids numbered as follows: The angle value of the angle grid is denoted as And for each angle grid, a trainable angle parameter is set that corresponds one-to-one with it. For numbering An angle grid, using trainable angle parameters corresponding to that angle grid. For the classification features respectively and the off-network offset feature Perform angle conditional mapping to generate the first... The classification response corresponding to each angle grid Off-network offset response .

[0017] S7. Classification response based on the grid at each angle. At least one target angle grid is identified, and the corresponding off-grid offset response is determined based on the grid number. Response to the off-grid offset Perform a bounded transformation to obtain the corresponding off-network offset. and the angle value of the target angle grid With the off-network offset Add them together to obtain the estimated direction of arrival of the continuous wave.

[0018] Furthermore, step S1 specifically includes:

[0019] S11. Obtain the array received signal matrix and receive signal matrix based on the array Calculate the sample covariance matrix : ,in, This represents the array receiving signal matrix. This indicates the total number of snapshots. This indicates the conjugate transpose operation.

[0020] S12. Extract the real part, imaginary part, and phase of the sample covariance matrix respectively: , , ,in, The eigenvalue matrix representing the real part of the sample covariance matrix. The eigenvalue matrix represents the imaginary part of the sample covariance matrix. The phase characteristic matrix represents the sample covariance matrix. This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part. This indicates the operation of taking the complex phase angle.

[0021] S13, the real part feature matrix, imaginary part feature matrix, and phase feature matrix are concatenated along the channel dimension to obtain the array covariance input features input to the deep learning network. : ,in, This indicates a channel splicing operation.

[0022] Furthermore, step S3 specifically includes:

[0023] The array covariance input features are input into the convolution feature extraction module. Local spatial features are extracted from the array covariance input features through convolution operation. The spatial arrangement relationship between different array element combinations in the array covariance input features is preserved according to the two-dimensional position corresponding to the array element index, so as to obtain the two-dimensional array spatial features.

[0024] Furthermore, step S4 specifically includes:

[0025] S41, the spatial features of the two-dimensional array The feature enhancement module is input to perform feature enhancement, and the feature enhancement result is obtained. The feature enhancement result is then compared with the two-dimensional array spatial features. Residual combining is performed to obtain enhanced two-dimensional spatial features. : ,in, This represents the feature enhancement process. This represents the learnable enhancement parameters used to adjust the feature enhancement results. This indicates element-wise multiplication.

[0026] S42, the enhanced two-dimensional spatial features The global array feature extraction module is input, and the enhanced two-dimensional spatial features are processed by convolution transformation. Spatial dimension aggregation is performed to obtain the global feature map. : ,in, This represents the convolution transformation process in the global feature extraction module; for the global feature map The data is flattened and then processed through a learnable global feature mapping process to obtain global array features. : ,in, This represents the operation of flattening the feature map into feature vectors. This represents the global feature mapping process. This represents the global array features used by both the classification feature generation branch and the off-network offset regression branch.

[0027] Furthermore, the process of step S5 is as follows:

[0028] The global array features The classification features are input separately to generate the classification branch and the off-network offset regression branch, and the classification features are obtained. Off-network offset characteristics : , ,in, This represents the classification mapping matrix in the classification feature generation branch. This represents the off-network offset mapping matrix in the off-network offset regression branch.

[0029] Furthermore, the process of step S6 is as follows:

[0030] S61. Determine the starting angle of the preset angle search range. Termination angle and candidate angle grid spacing and according to the angle grid interval The preset angle search range is divided into equally spaced intervals to obtain... An angle grid arranged in angular order; among which, numbered as The angle values ​​of the angle grid are represented as follows: ,in, Indicates the number is The angle values ​​of the angle grid. Indicates the angle grid number, and , Indicates the total number of angle grids.

[0031] S62, is the numbered The angle grid settings and their corresponding trainable angle parameter vectors The trainable angle parameter vector These are the trainable parameters in the off-network convolutional neural network, and the angle grids are associated with the trainable parameter vectors according to their grid numbers, such that the grid numbers are... Angular grid With trainable parameter vector Correspondingly.

[0032] S63. During the forward propagation process of the off-network convolutional neural network, for the numbered... An angle grid, utilizing the same trainable angle parameter corresponding to the angle grid. For the classification features respectively and the off-network offset feature Perform angle conditional mapping to generate the numbered... Classification response corresponding to the angle grid Off-network offset response , so that the classification response and the off-network offset response Together they form the angle grid. The corresponding response pair is represented as follows: , ,in, Indicates the number is The classification response corresponding to the angle grid. Indicates the number is The off-grid offset response corresponding to the angle grid. This represents the process of generating a classified response. This indicates the process of generating the off-network offset response.

[0033] Furthermore, the process of step S7 is as follows:

[0034] S71. Classification response according to each angle grid. The angle grid is sorted in descending order based on its size, and then the number of directions of arrival to be estimated is determined according to a preset number. Select the classifier with the larger classification response from the angle grid. The first angle grid is used as the target angle grid to determine the second angle grid. The target angle grid is numbered as follows: ,in, .

[0035] S72, according to the... Numbering of each target angle grid Read the number as Off-grid offset response corresponding to the angle grid and respond to the off-network offset. Perform a bounded transformation to obtain the first... Off-grid offset corresponding to each target angle grid : ,in, This indicates the preset maximum allowable off-grid offset. This represents the element-wise hyperbolic tangent bounded mapping operation.

[0036] S73, the first Angle values ​​of each target angle grid With the off-network offset Add them together to get the first one. Estimated directions of arrival for each continuous wave: ,in, Indicates the first One continuous direction of arrival estimate.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. This invention constructs a sample covariance matrix based on the received array signal, and extracts its real part, imaginary part, and phase to form a three-channel array covariance input feature, providing an input basis for the network to extract spatial information related to array elements.

[0039] 2. This invention obtains global array features containing local information of array elements and overall array information through convolutional feature extraction, feature enhancement and global array feature extraction, providing a feature basis for the generation of classification features and off-network offset features.

[0040] 3. This invention configures trainable angle parameters corresponding to the number of each angle grid, and uses the same trainable angle parameter corresponding to the same angle grid to generate the classification response and off-grid offset response corresponding to that angle grid, so that the classification result and the off-grid offset result establish a clear angle correspondence.

[0041] 4. This invention determines the target angle grid based on the classification response, determines the off-grid offset response with the same number, obtains the off-grid offset through bounded transformation, and adds it to the angle value of the target angle grid to output the continuous wave direction of arrival estimate, thereby reducing the quantization error caused by the fixed angle grid. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating the overall process of an off-grid direction-of-arrival estimation method based on deep learning, as described in this invention.

[0043] Figure 2 This is a schematic diagram of the array receiving structure of the present invention.

[0044] Figure 3 This is a schematic diagram of the off-network convolutional neural network structure used in this invention.

[0045] Figure 4 This is a comparison chart of off-grid dual-source RMSE under different signal-to-noise ratio conditions.

[0046] Figure 5 This is a comparison chart of the success rate of offline dual-source joint operation under different signal-to-noise ratio conditions.

[0047] Figure 6 This is a comparison chart of mesh pairing accuracy under negative off-grid conditions.

[0048] Figure 7 A comparison chart of RMSE under different off-grid offset conditions. Detailed Implementation

[0049] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0050] Example 1: This example uses... Figure 2 Taking the example of a uniform linear array receiving array observation data from two signal sources, this paper illustrates the complete implementation process of the method of the present invention from network training to test inference. First, according to... Figure 2 The array structure shown generates array signal training data, validation data, and independent test data, and uses the training data to... Figure 3 The off-network convolutional neural network shown is used for parameter learning. After the network training is complete, independent test samples are input into the trained network, and then... Figure 1 The method flow shown sequentially completes the construction of array covariance input features, spatial feature extraction, generation of classification features and off-network offset features, joint decoding of angle grids, and continuous direction of arrival output. The following first explains the training data and network parameter learning process, and then uses a test sample as an example, combined with... Figures 1 to 3The specific reasoning process of the method is explained. The number of array elements, signal sources, snapshots, angle search range, angle grid interval, and network dimension in this embodiment are used to illustrate a specific implementation and do not constitute a limitation on the scope of protection of this invention.

[0051] The embodiment uses a 16-element uniform linear array with an element spacing of half a wavelength, and sets up two signal sources. The angle search range is set to... to Angular grid spacing set to The angles are divided at equal intervals in ascending order, resulting in 121 angle grids. The training signal-to-noise ratio is set to... , , , and For each signal-to-noise ratio condition, 8000 training samples and 1000 validation samples are generated, resulting in a total training set of 40,000 samples and a validation set of 5000 samples. Each sample contains array observation data from two signal sources, with the minimum angular spacing between the two sources set to... The maximum off-grid offset of the true direction of arrival relative to the candidate angle grid is set to .

[0052] For each training sample, the corresponding angle grid is determined based on the true directions of arrival (DOA) of the two signal sources, and classification labels and off-grid offset labels are generated. The classification labels are soft labels centered on the angle grid corresponding to the true DOA; the off-grid offset labels represent the difference between the true DOA and the angle value of the corresponding angle grid, and the off-grid offset regression loss is calculated only at the angle grid position corresponding to the true signal using an offset mask.

[0053] The network training employs a joint optimization objective comprised of classification loss, off-network offset regression loss, and adjacent angle grid offset smoothing constraint. During training, the loss between the network output and the target label is calculated based on the labels of the training samples. Backpropagation is then used to update the trainable parameters in the convolutional feature extraction module, feature enhancement module, global array feature extraction module, classification feature generation branch, off-network offset regression branch, and angle joint decoding module, including the trainable angle parameters corresponding to each angle grid. The trained network parameters are selected based on the validation set error.

[0054] After the network parameters are trained, independent test samples are input into the trained off-network convolutional neural network. The following uses a test sample containing two signal sources as an example to illustrate the specific processing of this test sample from the formation of the array received signal to the continuous direction of arrival output.

[0055] S1: Acquire array received signal

[0056] This embodiment uses a uniform linear array to receive signals from two narrowband signal sources as an example. The array consists of... The array consists of several elements, with the spacing between adjacent elements set to half a wavelength. Two signal sources are located in directions of arrival. and Incident light is projected onto the array, which then continuously collects the data. The first snapshot. For a uniform linear array, the first... The array steering vector for each signal source is represented as: ,in, Indicates the first The true direction of arrival of each signal source; It represents the ratio of the spacing between adjacent array elements to the signal wavelength; Represents the imaginary unit; This indicates the transpose operation.

[0057] The array manifold matrix is ​​composed of the array steering vectors corresponding to each signal source. : ,in, Indicates the number of signal sources, in this embodiment .

[0058] In the In a quick snapshot, the array receives the vector Represented as: ,in, Indicates the first A quick snapshot captures the signal vector composed of signals from each signal source; Indicates the first The noise vector is composed of complex Gaussian white noise received by each array element in a snapshot. In this embodiment, the noise is zero-mean complex Gaussian white noise.

[0059] In the During a snapshot, the array received signal vector is represented as follows: ,in, This represents the array manifold matrix determined by the directions of arrival of each signal source; Indicates that each signal source is at the th A signal vector captured in a quick snapshot; This indicates the true direction of arrival of each signal source.

[0060] Array continuous acquisition After each snapshot, the array receive vectors corresponding to each snapshot are arranged in the snapshot order to form an array receive signal matrix. : .

[0061] S2. Construction of Sample Covariance Matrix and Array Covariance Input Features

[0062] According to the array received signal matrix Calculate the sample covariance matrix: ,in, This represents the array receiving signal matrix. This indicates the total number of snapshots. This represents the conjugate transpose operation;

[0063] because Given a complex matrix, extract its three real-valued feature matrices: , , ,in, The eigenvalue matrix representing the real part of the sample covariance matrix. The eigenvalue matrix represents the imaginary part of the sample covariance matrix. The phase characteristic matrix represents the sample covariance matrix. This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part. This indicates the operation of taking the complex phase angle. The dimensions of the three characteristic matrices mentioned above are: .

[0064] Subsequently, the three feature matrices are concatenated along the channel dimension to construct the array covariance input feature. : ,in, This indicates a channel splicing operation. .

[0065] S3, Convolutional Feature Extraction

[0066] The three-channel array covariance obtained in S2 is used as an input feature. Input convolutional feature extraction module. In this embodiment, The size is The first dimension represents the input channel, and the latter two dimensions correspond to the row and column positions of the sample covariance matrix, respectively. The convolutional feature extraction module processes the input features in the following order.

[0067] First, through the first convolutional layer... Perform a convolution transformation to change the number of input channels from... Transform into The convolution stride is With the spatial dimensions remaining constant, we obtain: The first convolutional layer extracts local combined features between the real part, imaginary part, and phase of the three input channels, so that the covariance information in different channels is fused at the same spatial location.

[0068] Then, through the second convolutional layer... Perform convolution and downsampling to change the spatial size from Transform into The number of channels remains at ,get: The downsampling is used to compress the spatial size of the feature map while preserving the spatial distribution information of the array elements.

[0069] Next, the number of channels is increased from [previous value] through a third convolutional layer. Transform into and change the space size from downsampling ,get: .

[0070] Subsequently, the fourth convolutional layer maintains 256 feature channels, and the spatial size is changed from... downsampling The spatial features of the two-dimensional array are obtained: In the above processing, the convolutional layer calculates the local receptive field for adjacent spatial locations, and encodes the relevant information of different element combinations in the sample covariance matrix into the feature map step by step.

[0071] S4. Feature Enhancement and Global Array Feature Extraction

[0072] The two-dimensional array spatial features obtained in S3 Input feature enhancement module.

[0073] First, through a Convolution reduces the number of feature channels from Transform into The space size remains as The intermediate features are obtained: .

[0074] Then, Feature enhancement is performed using the NAF feature enhancement unit. This embodiment employs... A series of consecutive NAF feature enhancement units, with each unit's parameters learned independently. The output of each NAF unit is represented as: ,in, Indicates the first Each NAF feature enhancement unit, Indicates the first The enhanced features output by each unit. The feature size before and after each processing step is: Each NAF unit first normalizes and transforms the input features, then extracts enhancement information through local feature processing, gated feature transformation, and channel attention modulation, and finally preserves the input features through residual connections. After passing through three NAF units, the input features are then processed by another... Convolution restores the number of channels from 64 to 256, yielding the feature enhancement result. This enhanced result is then combined with the original two-dimensional array spatial features. Residual combining is performed to obtain enhanced two-dimensional spatial features. : ,in, This represents the feature enhancement process. This represents the learnable enhancement parameters used to adjust the feature enhancement results. This indicates element-wise multiplication.

[0075] Subsequently, the enhanced two-dimensional spatial features Input global array feature extraction module. This module uses convolutional transformation where the kernel size matches the current spatial size to change the spatial size of the feature map. Aggregate into And change the number of channels from Transform into The global feature map is obtained. : ,in, This represents the convolution transformation process in the global feature extraction module; for the global feature map Flatten the surface: ,in, This means flattening the two-dimensional feature map into a one-dimensional feature vector, and then obtaining the global array features through a global feature mapping process: : ,in, This represents the global feature mapping process. This represents the global array features used by both the classification feature generation branch and the off-network offset regression branch.

[0076] S5. Generation of classification features and off-network offset features

[0077] The global array features obtained in S4 Input the classification feature generation branch and the off-network offset regression branch respectively. The classification feature generation branch performs a linear mapping on the global array features to obtain the classification features: ,in, This represents the classification mapping matrix in the classification feature generation branch; the off-network offset regression branch performs a linear mapping on the same global array features to obtain the off-network offset features: , where represents the off-network offset mapping matrix in the off-network offset regression branch. In this embodiment, It is a 512-dimensional global array feature. and All are 121-dimensional features, corresponding to 121 candidate angular grids respectively.

[0078] VI. Parameter Configuration for Angular Grid and Joint Response Generation

[0079] In this embodiment, the angle search range is set to... to Angular grid spacing set to The angles were divided at equal intervals in ascending order, resulting in 121 angle grids. The grids are numbered as follows: The angle values ​​of the angle grid are represented as follows: ,in, Indicates the number is The angle values ​​of the angle grid. Indicates the angle grid number, and , This indicates the total number of angle grid cells. In this embodiment, , , ,therefore: ,For example, Corresponding to the 61st candidate angle grid, This corresponds to the 64th candidate angle grid. For each candidate angle grid, a trainable angle parameter is configured that corresponds one-to-one with its number. Among them, the number is Candidate angle grid With trainable angle parameter vector Correspondingly, the trainable angle parameter vector These are the trainable parameters of an off-network convolutional neural network. During network training, the parameters are adjusted based on the backpropagation results of the classification loss and the off-network offset regression loss. The grid is updated so that different angle grids can form parameter representations corresponding to their angular positions. For the grid numbered... The candidate angle grid is generated using the same trainable angle parameter vector corresponding to the candidate angle grid. For classification features respectively Off-network offset characteristics Perform angle-conditional mapping to generate the classification response corresponding to the candidate angle grid. Off-network offset response : , ,in, Indicates the number is The classification response corresponding to the angle grid. Indicates the number is The off-grid offset response corresponding to the angle grid. This represents the process of generating a classified response. This indicates the process of generating the off-network offset response.

[0080] For all candidate angle grids, the network generates: Therefore, in this embodiment, each angle grid has a set of corresponding classification responses and off-grid offset responses. For example, for the 61st candidate angle grid, its corresponding... generate and For the 64th candidate angle grid, use its corresponding... generate and Subsequently, when the classification response determines that the 61st and 64th grids are the target grids, they are respectively used... and Perform offline correction.

[0081] S7. Target Angle Grid Selection and Continuous Direction of Arrival Output

[0082] Based on the classification responses of each candidate angle grid obtained in S6 Determine the target candidate angle grid.

[0083] In this embodiment, it is necessary to estimate the directions of arrival (DOA) of the two signal sources. Therefore, the 121 candidate angle grids are sorted according to the classification response magnitude, and the two candidate angle grids with larger classification responses are selected as the target candidate angle grids. Let the first... The grid numbers for the candidate angles of the targets are: According to the first Numbering of each target angle grid Read the number as Off-grid offset response corresponding to the angle grid and respond to the off-network offset. Perform a bounded transformation to obtain the first... Off-grid offset corresponding to each target angle grid : ,in, This indicates the preset maximum allowable off-grid offset. This represents the element-wise hyperbolic tangent bounded mapping operation. Because, ,therefore: In this embodiment, the maximum allowable off-grid offset is set as follows: Therefore, the off-grid offset corresponding to each target candidate angle grid is limited to... Within the range.

[0084] The first Angle values ​​of each target angle grid With the off-network offset Add them together to get the first one. Estimated directions of arrival for each continuous wave: ,in, Indicates the first One continuous direction of arrival estimate.

[0085] The two objectives in this embodiment are calculated according to the following formulas: , For example, when the classification response selects the 61st and 64th candidate angle grids: , At this time, the network uses... and Calculate the two off-grid offsets: , The final result is: , When the true angles of the two targets are respectively and At that time, under ideal conditions, the corresponding off-grid offsets are approximately and The network learns the offset response of the output to the target grid through training, so that the final output can be located between integer angle grids.

[0086] Example 2: Figure 4 The image shows a comparison of the off-network dual-source RMSE of the method of the present invention with CNN-NAFNet, MUSIC and ESPRIT under different signal-to-noise ratio conditions. This is used to verify the performance of the method of the present invention in continuous direction-of-arrival estimation when the true direction of arrival does not strictly fall on the candidate angle grid.

[0087] The array structure, angle grid, and network configuration in this embodiment are the same as in Embodiment 1. The true directions of arrival of the two signal sources are set as follows: and Both true directions of arrival deviate from the grid center of the adjacent candidate angle grid, and the number of snapshots is set to... The signal-to-noise ratio is set to... to Step size is Performed under each signal-to-noise ratio condition Monte Carlo experiment.

[0088] Depend on Figure 4 It can be seen that as the signal-to-noise ratio increases, the direction-of-arrival estimation error of each method generally decreases. Under the fixed off-grid dual-source test conditions of this embodiment, the method of the present invention... , and The root mean square errors under the signal-to-noise ratio are respectively , and ;exist to Within the test range, the root mean square error is... Reduce to The results show that, under the off-grid dual-source conditions in this embodiment, the method of the present invention can continuously correct the grid angle according to the off-grid offset corresponding to the target angle grid, thereby reducing the quantization error when the true direction of arrival deviates from the grid center.

[0089] Example 3: Figure 5 This is a comparison chart of the success rate of the offline dual-source joint method of the present invention with CNN-NAFNet, MUSIC and ESPRIT under different signal-to-noise ratio conditions, which is used to further verify the ability of the present invention to simultaneously estimate two directions of arrival under fixed offline dual-source conditions.

[0090] The array structure, true directions of arrival (DOA), candidate angle grid, number of snapshots, signal-to-noise ratio (SNR) range, comparison method, and number of Monte Carlo trials in this embodiment are the same as in Embodiment 2. For each Monte Carlo trial under each SNR condition, the two DOA estimation results output by each method are optimally matched one-to-one with the two true DOA; when the estimation errors of the two matched DOA do not exceed [the specified value], the optimal matching is performed. At that time, the experiment was deemed a success.

[0091] Depend on Figure 5 It can be seen that, under the fixed offline dual-source condition of this embodiment, the overall success rate of the combined methods increases with the increase of the signal-to-noise ratio. The method of this invention... , and The success probabilities of joint estimation under signal-to-noise ratio are respectively , and ,exist The test points of 20 and above reached The results show that, under the test conditions of this embodiment with a signal-to-noise ratio of not less than approximately -12 dB, the method of the present invention can determine the target angle grid based on the classification response and read the corresponding off-grid offset response to obtain continuous direction of arrival estimation results.

[0092] Example 4: Figure 6 This is a comparison chart of mesh pair accuracy under negative off-grid conditions, used to verify the reliability of the correlation between the classification results of candidate angle meshes and the corresponding off-grid offset responses.

[0093] This embodiment uses the same array structure and network training configuration as Embodiment 1, and sets two reference angles as follows: and Performed under each off-network offset condition Second Monte Carlo test. The same negative off-grid offset was applied to two reference angles, the negative off-grid offset being set sequentially as follows: , , , , , , , and At this point, the two true directions of arrival are located on the negative side of the center angle of the corresponding candidate angle grid.

[0094] This embodiment compares the method of this invention with the independent offset output head method. Both methods use the same array input, test conditions, and network backbone. The method of this invention configures corresponding trainable angle parameters for each candidate angle grid and uses the same angle parameters to generate the classification response and off-network offset response for that angle grid; the independent offset output head method uses an offset output structure independent of the classification response.

[0095] For each trial, if the classification responses of the two targets respectively select the two candidate angle grids corresponding to their true directions of arrival, the trial is considered to have correctly selected the grid pairs. The grid pairing accuracy under each off-grid offset condition is calculated as the ratio of the number of trials with correctly selected grid pairs to the total number of trials.

[0096] Depend on Figure 6 It can be seen that as the absolute value of the negative off-grid offset increases, the mesh pairing accuracy of both the proposed method and the independent offset output head method decreases. However, the proposed method outperforms the independent offset output head method under all test conditions. , and The grid pair accuracy at time is respectively , and The independent offset output head method, under the same conditions, is respectively... , and .

[0097] The above results demonstrate that even when the negative off-grid offset approaches the candidate angle grid boundary, the method of this invention can still improve the reliability of paired selection of target candidate angle grids. Its function is that after the classification response determines the target angle grid, the off-grid offset response of that target grid can be read according to the same angle correspondence, providing corresponding offset information for the subsequent generation of continuous direction-of-arrival estimates.

[0098] Example 5: Figure 7This chart compares the root mean square error of the direction of arrival (ROA) of the method of this invention with CNN-NAFNet, MUSIC, and ESPRIT under different off-grid offset conditions. It is used to verify the continuous ORA estimation performance of the method of this invention under different degrees of angular grid mismatch.

[0099] This embodiment uses the same array structure and network training configuration as Embodiment 1, and sets two reference directions of arrival as follows: and Two true directions of arrival (DOAs) are obtained by applying the same positive off-grid offset to two reference DOAs. The off-grid offsets are respectively set as follows: , , , and .

[0100] Depend on Figure 7 It can be seen that when the off-network offset is from Increase to At that time, the RMSE of CNN-NAFNet generally showed an upward trend. This is because its main output is a discrete angle grid, and the deviation of the true direction of arrival from the grid center will produce a significant quantization error. The method of this invention, by outputting the off-grid offset corresponding to the target candidate angle grid, can maintain a low root mean square error even with an increasing offset. When the off-grid offset is... , , and At that time, the root mean square error of the method of the present invention is approximately , , and The error results are lower than those of CNN-NAFNet under the corresponding conditions.

[0101] Offline offset is When the true direction of arrival (DOA) is close to the boundary of adjacent angle grids, the method of this invention can still output continuous DOA estimates by reading the off-grid offset response corresponding to the target candidate angle grid and adding the off-grid offset to the target grid angle. The above results demonstrate that the main advantage of the method of this invention lies in its ability to reduce the quantization error caused by fixed angle grids when the off-grid offset is large.

Claims

1. A deep learning-based off-grid direction-of-arrival estimation method, characterized in that, Includes the following steps: S1. Obtain the array received signal matrix According to the array received signal matrix Constructing the sample covariance matrix And based on the sample covariance matrix The real part, imaginary part, and phase construct the array covariance input features ; S2. Construct an off-network convolutional neural network, including a convolutional feature extraction module, a feature enhancement module, a global array feature extraction module, a classification feature generation branch, an off-network offset regression branch, and an angle joint decoding module; S3, Input the array covariance into the feature The convolutional feature extraction module is input to the array covariance input feature. Convolutional feature extraction is performed to obtain two-dimensional array spatial features that retain the spatial distribution information of array elements. ; S4. The spatial features of the two-dimensional array The feature enhancement module is input, and the feature enhancement result is compared with the two-dimensional array spatial features. By performing residual combination, the enhanced two-dimensional spatial features are obtained. Then, it is input into the global array feature extraction module for global feature extraction to obtain global array features. ; S5, The global array features The classification features are obtained by inputting the classification feature generation branch and the off-network offset regression branch respectively. Off-network offset characteristics ; S6. Classify the features and the off-network offset feature The angle joint decoding module is input, and multiple angle grids are obtained within a preset angle search range. These angle grids are then numbered according to angle order, and the grids numbered as follows: The angle value of the angle grid is denoted as And for each angle grid, a trainable angle parameter is set that corresponds one-to-one with it. For numbering An angle grid, using trainable angle parameters corresponding to that angle grid. For the classification features respectively and the off-network offset feature Perform angle-conditional mapping to generate the number. Classification response corresponding to the angle grid Off-network offset response ; S7. Classification response based on the grid at each angle. At least one target angle grid is identified, and the corresponding off-grid offset response is determined based on the grid number. Response to the off-grid offset Perform a bounded transformation to obtain the corresponding off-network offset. and the angle value of the target angle grid With the off-network offset Add them together to obtain the estimated direction of arrival of the continuous wave.

2. The off-network direction-of-arrival estimation method based on deep learning as described in claim 1, characterized in that, Step S1 specifically includes: S11. Obtain the array received signal matrix and receive signal matrix based on the array Calculate the sample covariance matrix : ,in, This represents the array receiving signal matrix. This indicates the total number of snapshots. This represents the conjugate transpose operation; S12. Extract the real part, imaginary part, and phase of the sample covariance matrix respectively: , , ,in, The eigenvalue matrix representing the real part of the sample covariance matrix. The eigenma matrix representing the imaginary part of the sample covariance matrix. The phase characteristic matrix represents the sample covariance matrix. This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part. This indicates the operation of taking the complex phase angle; S13, the real part feature matrix, imaginary part feature matrix, and phase feature matrix are concatenated along the channel dimension to obtain the array covariance input features input to the deep learning network. : ,in, This indicates a channel splicing operation.

3. The off-network direction-of-arrival estimation method based on deep learning as described in claim 1, characterized in that, The processing procedure in step S3 is as follows: Input the array covariance feature The convolutional feature extraction module is input to the array covariance input feature through convolution operations. Local spatial features are extracted, and the array covariance input features are retained according to the two-dimensional positions corresponding to the array element indices. The spatial arrangement relationship between different array element combinations yields the spatial features of the two-dimensional array. .

4. The off-network direction-of-arrival estimation method based on deep learning as described in claim 1, characterized in that, Step S4 specifically includes: S41, the spatial features of the two-dimensional array The feature enhancement module is input to perform feature enhancement, and the feature enhancement result is obtained. The feature enhancement result is then compared with the two-dimensional array spatial features. By performing residual combination, the enhanced two-dimensional spatial features are obtained. : ,in, This represents the feature enhancement process. This represents the learnable enhancement parameters used to adjust the feature enhancement results. This represents element-wise multiplication; S42, the enhanced two-dimensional spatial features The global array feature extraction module is input, and the enhanced two-dimensional spatial features are processed by convolution transformation. Spatial dimension aggregation is performed to obtain the global feature map. : ,in, This represents the convolution transformation process in the global feature extraction module; for the global feature map The data is flattened and then processed through a learnable global feature mapping process to obtain global array features. : ,in, This represents the operation of flattening the feature map into feature vectors. This represents the global feature mapping process. This represents the global array features used by both the classification feature generation branch and the off-network offset regression branch.

5. The off-network direction-of-arrival estimation method based on deep learning as described in claim 1, characterized in that, The processing procedure for step S5 is as follows: The global array features The classification features are input separately to generate the classification branch and the off-network offset regression branch, and the classification features are obtained. Off-network offset characteristics : , ,in, This represents the classification mapping matrix in the classification feature generation branch. This represents the off-network offset mapping matrix in the off-network offset regression branch.

6. The off-network direction-of-arrival estimation method based on deep learning as described in claim 1, characterized in that, Step S6 specifically includes: S61. Determine the starting angle of the preset angle search range. Termination angle and candidate angle grid spacing and according to the angle grid interval The preset angle search range is divided into equally spaced intervals to obtain... An angle grid arranged in angular order; among which, the number is... The angle values ​​of the angle grid are represented as follows: ,in, Indicates the number is The angle values ​​of the angle grid. Indicates the angle grid number, and , Indicates the total number of angle grids; S62, is the numbered The angle grid settings and their corresponding trainable angle parameter vectors The trainable angle parameter vector These are the trainable parameters in the off-network convolutional neural network, and the angle grids are associated with the trainable parameter vectors according to their grid numbers, such that the grid numbers are... Angular grid With trainable parameter vector Correspondingly; S63. During the forward propagation process of the off-network convolutional neural network, for the numbered... An angle grid, utilizing the same trainable angle parameter corresponding to the angle grid. For the classification features respectively and the off-network offset feature Perform angle conditional mapping to generate the numbered... Classification response corresponding to the angle grid Off-network offset response , so that the classification response and the off-network offset response Together they form the angle grid. The corresponding response pair is represented as follows: , ,in, Indicates the number is The classification response corresponding to the angle grid. Indicates the number is The off-grid offset response corresponding to the angle grid. This represents the process of generating a classified response. This indicates the process of generating the off-network offset response.

7. The off-network direction-of-arrival estimation method based on deep learning as described in claim 1, characterized in that, Step S7 specifically includes: S71. Classification response according to the grid at each angle. The angle grid is sorted in descending order based on its size, and then the number of directions of arrival to be estimated is determined according to a preset number. Select the classifier with the larger classification response from the angle grid. The first angle grid is used as the target angle grid to determine the second angle grid. The target angle grid is numbered as follows: ,in, ; S72, according to the... Numbering of each target angle grid Read the number as Off-grid offset response corresponding to the angle grid and respond to the off-network offset. Perform a bounded transformation to obtain the first... Off-grid offset corresponding to each target angle grid : ,in, This indicates the preset maximum allowable off-grid offset. This represents the element-wise hyperbolic tangent bounded mapping operation; S73, the first Angle values ​​of each target angle grid With the off-network offset Add them together to get the first one. Estimated directions of arrival for each continuous wave: ,in, Indicates the first One continuous direction of arrival estimate.

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