Low-sample-dependence complex electromagnetic environment high-precision DOA estimation method

Abstract

The invention relates to the technical field of signal processing, in particular to a low-sample-dependence complex electromagnetic environment high-precision DOA (direction of arrival) estimation method which comprises the steps of 1, signal data preprocessing, 2, pre-training model construction, 3, model migration and fine adjustment and 4, classification task DOA estimation. The method comprises the following steps: constructing a pre-training model taking a bidirectional long short-term memory network BiLSTM and a residual attention network RAN as cores to extract rich features of signal data; and then, effective migration of pre-training knowledge in a snapshot number limited scene is realized through fine adjustment of the model, so that model parameters are efficiently optimized. Experimental results show that under the condition of limited snapshots, the DOA estimation precision is remarkably improved, and meanwhile excellent robustness is shown. Therefore, the pre-training model can retain effective information of signal data, and a new solution is provided for real-time prediction of the array in a limited number scene.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a high-precision DOA estimation method for complex electromagnetic environments with low sample dependence. Background Technology

[0002] In the field of array signal processing, direction of arrival (DOA) estimation is a core technology for target localization, interference suppression, and beamforming, and is widely used in key areas such as radar, communication, and sonar. Its core objective is to accurately estimate the spatial location of a signal source by receiving signals from an array. However, in practical engineering, complex electromagnetic environments, hardware resource limitations, and dynamic scene requirements often lead to challenges in signal acquisition with a small number of snapshots (i.e., limited observation samples), which severely restricts the accuracy and stability of DOA estimation.

[0003] Early beamforming-based methods were limited by the Rayleigh diffraction limit and could not achieve super-resolution. While subspace-based methods broke the Rayleigh limit, in small snapshot scenarios, the finite number of snapshots led to a rank deficiency in the sample covariance matrix, and the eigenvalue distributions of the signal and noise subspaces overlapped, rendering eigenvalue decomposition-based subspace partitioning methods ineffective. Furthermore, the models were sensitive to prior errors such as array coupling, resulting in decreased robustness. Sparse representation methods relied on grid partitioning, introducing quantization errors. Iterative optimization in small snapshot scenarios was prone to getting trapped in local optima and had high computational complexity. Data-driven deep learning methods improved adaptability to complex scenarios through end-to-end modeling, but mainstream supervised learning networks required large-scale labeled data training, while obtaining massive labeled samples in small snapshot scenarios was extremely costly and prone to model overfitting. Unsupervised methods reduced data dependence but required pre-set prior models, had insufficient generalization ability under non-ideal noise, and did not fundamentally solve the problem of insufficient feature space representation in small sample scenarios. However, in implementing the inventive technical solutions in the embodiments of this application, the inventors of this application discovered that the above technologies had at least the following technical problems:

[0004] (1) Limited observation samples are difficult to support the assumptions of traditional statistical models and the training of deep learning parameters, resulting in the coexistence of risks of "underfitting" and "overfitting"; the efficiency of parameter space exploration is low.

[0005] (2) Traditional optimization methods are difficult to cover the complete parameter space under small data, while deep learning optimization is prone to getting trapped in local extrema due to sample noise; the integration of physical priors and data-driven approaches is lacking.

[0006] (3) Existing methods either rely on precise priors or are completely detached from the physical model, and cannot effectively utilize array geometric prior constraints to improve robustness in small snapshots. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing technologies by proposing a high-precision DOA estimation method for complex electromagnetic environments with low sample dependence. This method effectively solves the problems of insufficient array signal feature extraction, model dependence on a large amount of labeled data, and insufficient robustness in existing technologies under small snapshot scenarios, and achieves efficient and accurate signal source localization in complex electromagnetic environments.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A high-precision DOA estimation method for complex electromagnetic environments with low sample dependence includes the following steps:

[0010] Step 1: Signal data preprocessing. Extract the real and imaginary parts of each element signal from the noisy signal received by the uniform linear array (ULA) to construct an input matrix X of dimension 2L×N. IQ This bypasses the traditional covariance matrix calculation process, where L is the number of snapshots and N is the number of array elements;

[0011] Step 2: Pre-trained model construction, designing parallel dilated convolution branches to extract multi-scale features, combining residual attention modules (including efficient channel attention ECA) to enhance key features, and capturing bidirectional temporal correlations of signals through a bidirectional long short-term memory network BiLSTM;

[0012] Step 3: Model transfer and fine-tuning. After pre-training the model on a large-scale dataset, the parameters are divided into a "basic feature group" and a "task adaptation group". The former is frozen to retain general knowledge of the source domain, while the latter is fine-tuned to adapt to the target domain's small snapshot task.

[0013] Step 4: Classification task DOA estimation. The probability of existence of the angle interval is output through a fully connected layer and a sigmoid activation function. The angle of the signal source is determined based on the maximum a posteriori probability criterion.

[0014] Preferably, step 1 includes the following method:

[0015] Assume a uniform linear array (ULA) consisting of N omnidirectional antennas with an element spacing of d = λ / 2, and K far-field narrowband signals with wavelength λ. (k=1,2,...,K) from different directions If a signal = [θ1, θ2, ..., θK] is incident on the ULA, then the signal received by the ULA at time t is:

[0016] x(t)=A(θ)s(t)+n(t),t=1,...,L (1)

[0017] The parameters are defined as follows:

[0018] x(t): The received signal vector of ULA at time t, with a dimension of N×1 (N is the number of array elements), containing the received signals of N array elements at time t;

[0019] A(θ): Array manifold matrix with dimensions N×K (N is the number of array elements, K is the number of signal sources), which is composed of the steering vectors corresponding to each signal source;

[0020] θ: The set of directions of arrival (DOA) of K signal sources, θ = [θ1, θ2, ..., θK], where θ k Indicates the direction of arrival (in degrees) of the k-th signal source;

[0021] s(t): The output vector of K far-field narrowband signal sources at time t, with a dimension of K×1, containing the complex amplitude of each signal source at time t;

[0022] n(t): The additive white Gaussian noise vector at time t, with dimension N×1, assumed to have a mean of 0 and a variance of σ. 2 , which follows a complex Gaussian distribution;

[0023] t: Time sampling index, ranging from 1 to L;

[0024] L: Snapshot count (number of observation samples), which is the total number of times the signal is sampled.

[0025] The source and array manifold matrices are represented as follows:

[0026] s(t)=[s1(t),s2(t),···,s K (t)] T (2)

[0027] The parameters are defined as follows:

[0028] s(t): Consistent with the definition in formula (1), it is the output vector of K signal sources at time t;

[0029] s k (t): The complex amplitude of the k-th signal source at time t (k=1,2,...,K), representing the intensity and phase information of the signal source at time t;

[0030] T: Vector transpose operation, converts a row vector into a column vector.

[0031] A(θ)=[a(θ1),···,a(θ K )]∈C N×K (3)

[0032] The parameters are defined as follows:

[0033] A(θ): Consistent with the definition in formula (1), it is an array manifold matrix;

[0034] a(θk): The steering vector corresponding to the k-th signal source, with a dimension of N×1, describes the phase relationship of the signals received by each array element when the signal source is incident on the ULA;

[0035] C: Complex field, indicating that the matrix elements are complex numbers;

[0036] N: The number of elements in a uniform linear array (ULA), consistent with the definition of N in formula (1);

[0037] K: Number of signal sources, consistent with the definition of K in formula (1).

[0038] in, It is the relative direction of arrival of ULA. The guiding vector can be expressed as:

[0039]

[0040] The parameters are defined as follows:

[0041] a(θk): Consistent with the definition in formula (3), it is the steering vector of the k-th signal source;

[0042] d: The element spacing of the ULA, given that d = λ / 2 (λ is the signal wavelength);

[0043] λ: The wavelength of the incident signal, consistent with the definition of "far-field narrowband signal with wavelength λ" in the given conditions;

[0044] j: Imaginary unit, satisfying j 2 =-1;

[0045] sin(θ K ): The direction of arrival (θ) of the k-th signal source K The sine value, since ULA is a linear array, the direction of arrival is given by sin(θ). K This determines the array phase difference;

[0046] N: Number of array elements, consistent with the definition of N in formulas (1) and (3);

[0047] T: Vector transpose operation, consistent with the definition of T in formula (2).

[0048] For the original received signal:

[0049]

[0050] Each row represents the sampled signal on a single array element. Next, the real and imaginary parts of the received signal for each array element are extracted:

[0051]

[0052] The parameters are defined as follows:

[0053] X IQ The preprocessed input matrix serves as the input to the subsequent neural network.

[0054] (·): Operator for extracting the real part of a complex signal. (x(t)) represents the real part of the received signal vector x(t) at time t;

[0055] (·): Operator that retrieves the imaginary part of a complex signal. (x(t)) represents the imaginary part of the received signal vector x(t) at time t.

[0056] Preferably, step 2 includes the following method:

[0057] First, multi-scale convolution is used to extract local spatial features of the signal data. Then, a residual network with embedded Efficient Channel Attention (ECA) is used to enhance the model's attention to important features and reduce the computational load. The processed features are then input into BiLSTM to further extract the temporal correlation features of the signal. Finally, feature mapping is performed through a fully connected layer, and the Sigmoid activation function is used to output the multi-label classification results.

[0058] Preferably, step 2 includes the following method:

[0059] First, multi-scale convolution is used to extract local spatial features of the signal data. Then, a residual network with embedded Efficient Channel Attention (ECA) is used to enhance the model's attention to important features and reduce the computational load. The processed features are then input into BiLSTM to further extract the temporal correlation features of the signal. Finally, feature mapping is performed through a fully connected layer, and the Sigmoid activation function is used to output the multi-label classification results.

[0060] Preferably, dilated convolution is used to expand the receptive field while reducing the number of parameters. Specifically, three 3×1 dilated convolution kernels with different dilation rates are used in parallel to extract multi-scale spatial features, as shown below:

[0061]

[0062] The parameters are defined as follows:

[0063] Xi: Output feature map of the i-th dilated convolution branch (i=1,2,3 correspond to three branches with different dilation rates);

[0064] DilatedConv(·): Dilated convolution operation, which expands the receptive field by setting the dilation rate;

[0065] d: The hole rate of the i-th branch, used to expand the receptive field. The d values ​​of the three branches are set to 1, 2, and 3 respectively to ensure multi-scale feature extraction.

[0066] i: Branch index, with values ​​of 1, 2, and 3, corresponding to three parallel dilated convolution branches.

[0067] Each branch output is sequentially processed by batch normalization and the Mish activation function to stabilize training and enhance the non-linear expressive power of the features. Let the three outputs be X′1, X′2, and X′3, then:

[0068] X′i=Mish(BN(Xi)),i=1,2,3 (8)

[0069] The parameters are defined as follows:

[0070] X′i: The output feature map of the i-th branch after batch normalization (BN) and Mish activation;

[0071] Mish(·): Mish activation function, used to enhance the non-linear expressive power of features;

[0072] BN(·): Batch normalization operation, used to stabilize network training, reduce the risk of gradient vanishing, and normalize the feature dimensions of Xi;

[0073] Xi: the original output of the i-th dilated convolution branch;

[0074] i: Branch index;

[0075] After performing channel-wise dimensionality reduction on the features of each branch using 1×1 convolution, the dimensionality-reduced features of the three branches are concatenated along the channel dimensions to form a feature tensor that fuses multi-scale information:

[0076] Xcat=Concat{ X′1, X′2, X′3} (9)

[0077] The parameters are defined as follows:

[0078] Xcat: The fused feature tensor after concatenating multiple branch features;

[0079] Concat{·}: Feature concatenation operation, which is explicitly defined here as concatenation along the channel dimension, that is, concatenating the features of the three branches along the channel dimension;

[0080] Apply max pooling to the fused features:

[0081] Xpool=MaxPool(Xcat) (10)

[0082] The parameters are defined as follows:

[0083] Xpool: Output feature map after max pooling;

[0084] MaxPool(·): Max pooling operation.

[0085] Spatial dimension compression is performed to highlight local salient features and reduce computational cost.

[0086] Preferably, in the deep network design, to alleviate the gradient vanishing or gradient exploding problems that may occur during the training of deep networks, a residual attention module based on the ResNet structure is introduced. This module consists of four progressive residual attention blocks. Each residual attention block contains convolution, batch normalization (BN), activation function and channel attention mechanism, and enhances gradient propagation and feature reuse through skip connections. In particular, the residual attention block adopts the efficient channel attention (ECA) mechanism, captures the relationship between channels through global average pooling (GAP) and one-dimensional convolution (Conv1D), and uses the Sigmoid function to generate attention weights for channel weighting. Through a progressive channel expansion strategy, the number of channels of the four residual attention blocks are 64→128→256→512 respectively.

[0087] After processing by the residual attention module, the network undergoes dimensionality reduction through global average pooling (AvgPool), which preserves global semantics while reducing the risk of overfitting. Subsequently, a bidirectional long short-term memory network (BiLSTM) further models the sequence features, using forward and backward LSTM subnetworks to capture bidirectional contextual information. Compared with unidirectional LSTM, BiLSTM can extract time series correlations more comprehensively and enhance signal representation capabilities.

[0088] After feature sequence encoding, the network maps the high-dimensional features output by BiLSTM to the target label space through a fully connected (FC) layer. To meet the requirements of multi-source DOA estimation, the final layer uses a sigmoid activation function to constrain the output to the interval [0, 1]. To accurately predict the existence of signals at various angles, a binary cross-entropy (BCE) loss is used.

[0089] (11)

[0090] The parameters are defined as follows:

[0091] L BCE Binary cross-entropy (BCE) loss function is used to measure the difference between the model's predicted values ​​and the true labels.

[0092] : The true label of the i-th angle interval, with a value of 1 or 0;

[0093] : The probability that a signal source exists in the i-th angle interval predicted by the model, with a value range of [0,1];

[0094] The logarithm of the probability that the i-th angle belongs to the positive class (label 1) as predicted by the model;

[0095] : The logarithm of the probability that the i-th angle belongs to the negative class (label 0) predicted by the model.

[0096] Preferably, step 3 includes the following method:

[0097] Transfer learning process: An 8-element uniform linear array (ULA) was used, with element spacing of half a wavelength and an angular coverage range of -60° to 60°. Two signal sources were used. Signal data from the source domain (100 snapshots) and the target domain (10 snapshots) were generated with different signal-to-noise ratios (SNRs), ranging from -10 dB to 20 dB in 5 dB increments, for a total of seven SNR levels. Each SNR level contained 200,000 samples. The source domain dataset was randomly divided into training, validation, and test subsets in an 8:1:1 ratio. These subsets were used to pre-train the model, enabling it to learn the characteristics of the array signals across a large number of snapshots. For fine-tuning, a small portion (5%) of the target domain data was used, with the remaining 95% used for testing.

[0098] A group fine-tuning strategy is adopted, specifically dividing the network parameters into a "basic feature group" (RAN core layer, BiLSTM low layer) and a "task adaptation group" (BiLSTM high layer, fully connected layer). The layers in the basic feature group have already learned general signal features during source domain training, so their parameters are frozen to avoid feature degradation. The layers in the task adaptation group are directly associated with the DOA classification task and are fine-tuned with a higher learning rate to quickly adapt to the target domain. In addition, a dual-learning-rate Adam optimizer is used: the learning rate of the basic feature group is set to 0.0001 to ensure parameter stability, and the learning rate of the task adaptation group is set to 0.001 to accelerate model response. By monitoring gradients and validation set performance in stages and dynamically adjusting the learning rate, this strategy achieves a balance between source domain knowledge inheritance and target domain adaptation through hierarchical optimization, effectively improving the accuracy and robustness of DOA estimation under small sample conditions.

[0099] Preferably, step 4 includes the following method:

[0100] DOA estimation: Discretize the DOA range, and construct an overcomplete spatial grid set by equally spaced division of the spatial region where the incident signal may exist. Assume that the range of the incident signal's direction of arrival is the range of this spatial region. , ] Perform angular intervals as By dividing the space into equally spaced grids, an overcomplete set of spatial grids is obtained:

[0101]

[0102] The parameters are defined as follows:

[0103] G: A complete set of spatial grids containing all possible candidate values ​​for direction of arrival;

[0104] θmin: Lower limit of the angle range estimated by DOA, set to -60° in this paper;

[0105] θmax: The upper limit of the angle range estimated by DOA, which is set to 60° in this paper;

[0106] Δθ: Angle discrete interval (grid step size).

[0107] This set can be viewed as the set of all possible direction-of-arrival angles of the incident signal, containing the following number of elements: For multiple signal sources, the task boils down to predicting the set of most likely angles. ={ }, given by maximizing the posterior probability:

[0108]

[0109] The parameters are defined as follows:

[0110] : The DOA estimate of the k-th signal source, i.e., the optimal candidate angle selected from the grid set G;

[0111] : Find the angle θ in the grid set G that maximizes the posterior probability P(θ|X);

[0112] P(θ|X): Posterior probability, representing the probability that the angle θ is the true direction of arrival given the input matrix X (directly represented by the output of the Sigmoid model).

[0113] Compared with the prior art, the present invention has the following beneficial effects:

[0114] 1. This invention can overcome the limitations of small sample size: by transferring the general signal-angle mapping relationship learned in large-scale source domain data to the target domain through transfer learning, combined with parameter grouping fine-tuning strategy, the dependence on small snapshot data in the target domain is reduced, effectively alleviating the risks of "underfitting" and "overfitting", and improving the generalization ability of the model under small sample size.

[0115] 2. This invention can enhance feature representation capabilities: Through the synergistic effect of multi-scale dilated convolution and residual attention module, it can achieve adaptive extraction of spatial features at different scales in the signal and enhancement of key features. Combined with BiLSTM to capture bidirectional temporal correlation, it can significantly improve the representation accuracy of signal features in complex electromagnetic environments, thereby improving the accuracy and stability of DOA estimation.

[0116] 3. This invention can reduce computational complexity and training cost: dilated convolution expands the receptive field through dilation rate without significantly increasing the number of parameters, and efficient channel attention (ECA) adopts a lightweight one-dimensional convolution design to reduce computational overhead; at the same time, the transfer learning framework avoids repeated training of underlying general features by freezing the parameters of basic feature groups, thereby reducing the overall training cost of the network, especially in medium-to-high signal-to-noise ratio scenarios with significant performance advantages. Attached Figure Description

[0117] Figure 1 This is a flowchart of the present invention;

[0118] Figure 2 This is a schematic diagram of the pre-trained model in this invention;

[0119] Figure 3 This is a schematic diagram of the residual attention block in this invention;

[0120] Figure 4 This is a schematic diagram of a bidirectional long short-term memory network in an embodiment of the present invention;

[0121] Figure 5 This is a simulation diagram of the DOA direction finding accuracy of different algorithms under different generalized signal-to-noise ratios in an embodiment of the present invention, with independent signals, 8 array elements, half-wavelength array element spacing, and 10 snapshots.

[0122] Figure 6 The following is a simulation diagram of RMSE for different algorithms under different generalized signal-to-noise ratios in an embodiment of the present invention, with independent signals, 8 array elements, half-wavelength spacing between array elements, and 10 snapshots. Detailed Implementation

[0123] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the scope of protection of the present invention. The embodiments described in this invention are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0124] Example:

[0125] A high-precision DOA estimation method for complex electromagnetic environments with low sample dependence includes the following steps:

[0126] Step 1: Signal data preprocessing. Extract the real and imaginary parts of each element signal from the noisy signal received by the uniform linear array (ULA) and construct an input matrix X of dimension 2L×N. IQ This bypasses the traditional covariance matrix calculation process, where L is the number of snapshots and N is the number of array elements;

[0127] Step 2: Pre-trained model construction, designing parallel dilated convolution branches to extract multi-scale features, combining residual attention modules (including efficient channel attention ECA) to enhance key features, and capturing bidirectional temporal correlations of signals through a bidirectional long short-term memory network BiLSTM;

[0128] Step 3: Model transfer and fine-tuning. After pre-training the model on a large-scale dataset, the parameters are divided into a "basic feature group" and a "task adaptation group". The former is frozen to retain general knowledge of the source domain, while the latter is fine-tuned to adapt to the target domain's small snapshot task.

[0129] Step 4: Classification task DOA estimation. The probability of existence of the angle interval is output through a fully connected layer and a sigmoid activation function. The angle of the signal source is determined based on the maximum a posteriori probability criterion.

[0130] Specifically, step 1 includes the following methods:

[0131] Assume a uniform linear array (ULA) consisting of N omnidirectional antennas with an element spacing of d = λ / 2, and K far-field narrowband signals with wavelength λ. (k=1,2,...,K) from different directions If a signal = [θ1, θ2, ..., θK] is incident on the ULA, then the signal received by the ULA at time t is:

[0132] x(t)=A(θ)s(t)+n(t),t=1,...,L (1)

[0133] The parameters are defined as follows:

[0134] x(t): The received signal vector of ULA at time t, with a dimension of N×1 (N is the number of array elements), containing the received signals of N array elements at time t;

[0135] A(θ): Array manifold matrix with dimensions N×K (N is the number of array elements, K is the number of signal sources), which is composed of the steering vectors corresponding to each signal source;

[0136] θ: The set of directions of arrival (DOA) of K signal sources, θ = [θ1, θ2, ..., θK], where θ k Indicates the direction of arrival (in degrees) of the k-th signal source;

[0137] s(t): The output vector of K far-field narrowband signal sources at time t, with a dimension of K×1, containing the complex amplitude of each signal source at time t;

[0138] n(t): The additive white Gaussian noise vector at time t, with dimension N×1, assumed to have a mean of 0 and a variance of σ. 2 , which follows a complex Gaussian distribution;

[0139] t: Time sampling index, ranging from 1 to L;

[0140] L: Snapshot count (number of observation samples), which is the total number of times the signal is sampled.

[0141] The source and array manifold matrices are represented as follows:

[0142] s(t)=[s1(t),s2(t),···,s K (t)] T (2)

[0143] The parameters are defined as follows:

[0144] s(t): Consistent with the definition in formula (1), it is the output vector of K signal sources at time t;

[0145] s k (t): The complex amplitude of the k-th signal source at time t (k=1,2,...,K), representing the intensity and phase information of the signal source at time t;

[0146] T: Vector transpose operation, converts a row vector into a column vector.

[0147] A(θ)=[a(θ1),···,a(θ K )]∈C N×K (3)

[0148] The parameters are defined as follows:

[0149] A(θ): Consistent with the definition in formula (1), it is an array manifold matrix;

[0150] a(θk): The steering vector corresponding to the k-th signal source, with a dimension of N×1, describes the phase relationship of the signals received by each array element when the signal source is incident on the ULA;

[0151] C: Complex field, indicating that the matrix elements are complex numbers;

[0152] N: The number of elements in a uniform linear array (ULA), consistent with the definition of N in formula (1);

[0153] K: Number of signal sources, consistent with the definition of K in formula (1).

[0154] in, It is the relative direction of arrival of ULA. The guiding vector can be expressed as:

[0155]

[0156] The parameters are defined as follows:

[0157] a(θk): Consistent with the definition in formula (3), it is the steering vector of the k-th signal source;

[0158] d: The element spacing of the ULA, given that d = λ / 2 (λ is the signal wavelength);

[0159] λ: The wavelength of the incident signal, consistent with the definition of "far-field narrowband signal with wavelength λ" in the given conditions;

[0160] j: Imaginary unit, satisfying j 2 =-1;

[0161] sin(θ K ): The direction of arrival (θ) of the k-th signal source KThe sine value, since ULA is a linear array, the direction of arrival is given by sin(θ). K This determines the array phase difference;

[0162] N: Number of array elements, consistent with the definition of N in formulas (1) and (3);

[0163] T: Vector transpose operation, consistent with the definition of T in formula (2).

[0164] For the original received signal:

[0165]

[0166] Each row represents the sampled signal on a single array element. Next, the real and imaginary parts of the received signal for each array element are extracted:

[0167]

[0168] The parameters are defined as follows:

[0169] X IQ The preprocessed input matrix serves as the input to the subsequent neural network.

[0170] (·): Operator for extracting the real part of a complex signal. (x(t)) represents the real part of the received signal vector x(t) at time t;

[0171] (·): Operator that retrieves the imaginary part of a complex signal. (x(t)) represents the imaginary part of the received signal vector x(t) at time t.

[0172] Specifically, step 2 includes the following methods:

[0173] First, multi-scale convolution is used to extract local spatial features of the signal data. Then, a residual network with embedded Efficient Channel Attention (ECA) is used to enhance the model's attention to important features and reduce the computational load. The processed features are then input into BiLSTM to further extract the temporal correlation features of the signal. Finally, feature mapping is performed through a fully connected layer, and the Sigmoid activation function is used to output the multi-label classification results.

[0174] In this embodiment, the powerful learning capability of deep learning on raw data is utilized to directly extract the real and imaginary parts of each array element signal from the raw signal, and construct the input matrix X. IQ (Dimension 2L×N) avoids the statistical instability problem of traditional covariance matrix calculation under small snapshot number.

[0175] Specifically, step 2 includes the following methods:

[0176] Constructing a pre-trained model (RAN-BILSTM, RAB): The proposed RAB network model integrates RAN (Residual Attention Network) and BiLSTM (Bidirectional Long Short-Term Memory Network) to capture the complex nonlinear relationship between the original signal and its corresponding DOA. The model first utilizes multi-scale convolutions to extract local spatial features of the signal data. Then, it enhances the model's focus on important features by embedding an efficient channel attention (ECA) residual network, reducing the model's computational load. The processed features are then input into the BiLSTM to further extract the temporal correlation features of the signal. Finally, feature mapping is performed through fully connected layers, and the multi-label classification result is output using the sigmoid activation function.

[0177] Specifically, dilated convolution is employed to expand the receptive field while reducing the number of parameters. Specifically, three 3×1 dilated convolution kernels with different dilation rates are used in parallel to extract multi-scale spatial features, as shown below:

[0178]

[0179] The parameters are defined as follows:

[0180] Xi: Output feature map of the i-th dilated convolution branch (i=1,2,3 correspond to three branches with different dilation rates);

[0181] DilatedConv(⋅): Dilated convolution operation, which expands the receptive field by setting the dilation rate;

[0182] d: The hole rate of the i-th branch, used to expand the receptive field. The d values ​​of the three branches are set to 1, 2, and 3 respectively to ensure multi-scale feature extraction.

[0183] i: Branch index, with values ​​of 1, 2, and 3, corresponding to three parallel dilated convolution branches.

[0184] Each branch output is sequentially processed by batch normalization and the Mish activation function to stabilize training and enhance the non-linear expressive power of the features. Let the three outputs be X′1, X′2, and X′3, then:

[0185] X′i=Mish(BN(Xi)),i=1,2,3 (8)

[0186] The parameters are defined as follows:

[0187] X′i: The output feature map of the i-th branch after batch normalization (BN) and Mish activation;

[0188] Mish(·): Mish activation function, used to enhance the non-linear expressive power of features;

[0189] BN(·): Batch normalization operation, used to stabilize network training, reduce the risk of gradient vanishing, and normalize the feature dimensions of Xi;

[0190] Xi: the original output of the i-th dilated convolution branch;

[0191] i: Branch index;

[0192] After performing channel-wise dimensionality reduction on the features of each branch using 1×1 convolution, the dimensionality-reduced features of the three branches are concatenated along the channel dimensions to form a feature tensor that fuses multi-scale information:

[0193] Xcat=Concat{ X′1, X′2, X′3} (9)

[0194] The parameters are defined as follows:

[0195] Xcat: The fused feature tensor after concatenating multiple branch features;

[0196] Concat{·}: Feature concatenation operation, which is explicitly defined here as concatenation along the channel dimension, that is, concatenating the features of the three branches along the channel dimension;

[0197] Apply max pooling to the fused features:

[0198] Xpool=MaxPool(Xcat) (10)

[0199] The parameters are defined as follows:

[0200] Xpool: Output feature map after max pooling;

[0201] MaxPool(·): Max pooling operation.

[0202] Spatial dimension compression is performed to highlight local salient features and reduce computational cost.

[0203] In deep network design, to alleviate the gradient vanishing or exploding problems that may occur during deep network training, a residual attention module based on the ResNet structure is introduced. This module consists of four progressive residual attention blocks, each containing convolution, batch normalization (BN), activation functions, and a channel attention mechanism. Skip connections are used to enhance gradient propagation and feature reuse. Specifically, the residual attention blocks employ an efficient channel attention (ECA) mechanism, capturing inter-channel relationships through global average pooling (GAP) and one-dimensional convolution (Conv1D), and using the Sigmoid function to generate attention weights for channel weighting. Through a progressive channel expansion strategy, the number of channels in the four residual attention blocks changes sequentially from 64 to 128 to 256 to 512.

[0204] After processing by the residual attention module, the network undergoes dimensionality reduction through global average pooling (AvgPool), which preserves global semantics while reducing the risk of overfitting. Subsequently, a bidirectional long short-term memory network (BiLSTM) further models the sequence features, using forward and backward LSTM subnetworks to capture bidirectional contextual information. Compared with unidirectional LSTM, BiLSTM can extract time series correlations more comprehensively and enhance signal representation capabilities.

[0205] After feature sequence encoding, the network maps the high-dimensional features output by BiLSTM to the target label space through a fully connected (FC) layer. To meet the requirements of multi-source DOA estimation, the final layer uses a sigmoid activation function to constrain the output to the interval [0, 1]. To accurately predict the existence of signals at various angles, a binary cross-entropy (BCE) loss is used.

[0206] (11)

[0207] The parameters are defined as follows:

[0208] L BCE Binary cross-entropy (BCE) loss function is used to measure the difference between the model's predicted values ​​and the true labels.

[0209] : The true label of the i-th angle interval, with a value of 1 or 0;

[0210] : The probability that a signal source exists in the i-th angle interval predicted by the model, with a value range of [0,1];

[0211] The logarithm of the probability that the i-th angle belongs to the positive class (label 1) as predicted by the model;

[0212] : The logarithm of the probability that the i-th angle belongs to the negative class (label is 0) predicted by the model.

[0213] In this embodiment, the above technical solution has the following technical effects or advantages:

[0214] (1) Multi-scale feature extraction of the input matrix is ​​performed by parallel dilated convolution branches (dilation rates 1, 2, 3). After batch normalization, activation, dimensionality reduction cascade and max pooling, spatial features of different scales in the signal can be captured, enriching feature expression and reducing computational complexity.

[0215] (2) Introducing a progressive residual attention block based on ResNet, using the efficient channel attention (ECA) mechanism to generate channel weights to strengthen key features, the number of channels is progressively expanded from 64 to 128 to 256 to 512 and gradient propagation is enhanced through skip connections, which alleviates the gradient vanishing problem in deep networks and improves model stability and feature reuse efficiency.

[0216] (3) The output of the residual attention module is input into the bidirectional long short-term memory network (BiLSTM) after global average pooling. The forward and backward sub-networks capture the bidirectional temporal correlation of the signal, which extracts the time series context information more comprehensively than the unidirectional LSTM and enhances the dynamic representation capability of the signal.

[0217] Specifically, step 3 includes the following methods:

[0218] Transfer learning process: Due to limitations in hardware and the difficulty of signal acquisition, obtaining sufficient snapshot data is quite challenging. The fine-tuning strategy learns more general feature representations by pre-training the model on a large-scale dataset, enabling it to maintain good performance even when data is scarce.

[0219] An 8-element uniform linear array (ULA) with element spacing of half a wavelength and an angular coverage range of -60° to 60° was used, with two signal sources. Signal data from the source domain (100 snapshots) and the target domain (10 snapshots) were generated at different signal-to-noise ratios (SNRs), ranging from -10 dB to 20 dB in 5 dB increments, for a total of seven SNR levels. Each SNR level contained 200,000 samples. The source domain dataset was randomly divided into training, validation, and test subsets in an 8:1:1 ratio. These subsets were used to pre-train the model, enabling it to learn the characteristics of the array signals across a large number of snapshots. For fine-tuning, a small portion (5%) of the target domain data was used, with the remaining 95% used for testing.

[0220] A group fine-tuning strategy is adopted, specifically dividing the network parameters into a "basic feature group" (RAN core layer, BiLSTM low layer) and a "task adaptation group" (BiLSTM high layer, fully connected layer). The layers in the basic feature group have already learned general signal features during source domain training, so their parameters are frozen to avoid feature degradation. The layers in the task adaptation group are directly associated with the DOA classification task and are fine-tuned with a higher learning rate to quickly adapt to the target domain. Furthermore, a dual-learning-rate Adam optimizer is used: the learning rate for the basic feature group is set to 0.0001 to ensure parameter stability, and the learning rate for the task adaptation group is set to 0.001 to accelerate model response. By monitoring gradients and validation set performance in stages and dynamically adjusting the learning rate, this strategy achieves a balance between source domain knowledge inheritance and target domain adaptation through hierarchical optimization, effectively improving the accuracy and robustness of DOA estimation under small sample conditions.

[0221] In this embodiment, the model is pre-trained on a large-scale dataset to learn more general feature representations, reducing reliance on small snapshot data and improving model generalization.

[0222] Specifically, step 4 includes the following methods:

[0223] DOA estimation: Discretize the DOA range, and construct an overcomplete spatial grid set by equally spaced division of the spatial region where the incident signal may exist. Assume that the range of the incident signal's direction of arrival is the range of this spatial region. , ] Perform angular intervals as By dividing the space into equally spaced grids, an overcomplete set of spatial grids is obtained:

[0224]

[0225] The parameters are defined as follows:

[0226] G: A complete set of spatial grids containing all possible candidate values ​​for direction of arrival;

[0227] θmin: Lower limit of the angle range estimated by DOA, set to -60° in this paper;

[0228] θmax: The upper limit of the angle range estimated by DOA, which is set to 60° in this paper;

[0229] Δθ: Angle discrete interval (grid step size).

[0230] This set can be viewed as the set of all possible direction-of-arrival angles of the incident signal, containing the following number of elements: For multiple signal sources, the task boils down to predicting the set of most likely angles. ={ }, given by maximizing the posterior probability:

[0231]

[0232] The parameters are defined as follows:

[0233] : The DOA estimate of the k-th signal source, i.e., the optimal candidate angle selected from the grid set G;

[0234] : Find the angle θ in the grid set G that maximizes the posterior probability P(θ|X);

[0235] P(θ|X): Posterior probability, representing the probability that the angle θ is the true direction of arrival given the input matrix X (directly represented by the output of the Sigmoid model).

[0236] Among them, such as Figure 1 The diagram shows the four core steps of the DOA estimation method of this invention: signal data preprocessing → pre-trained model construction → model transfer and fine-tuning → classification task DOA estimation. The arrows indicate the data flow direction, and the output of each step becomes the input of the next step.

[0237] like Figure 2 The diagram shows the network structure of the RAN-BiLSTM pre-trained model. The input is an XIQ matrix, which is processed through "parallel dilated convolution → BN → Mish activation → 1×1 dimensionality reduction → cascade → max pooling → residual attention module → global average pooling → BiLSTM → fully connected layer → Sigmoid activation". The output has an angular probability. The core modules are residual attention and BiLSTM, which are used to enhance feature extraction and temporal modeling.

[0238] like Figure 3 The diagram shows the internal structure of a single residual attention block, which includes "convolution + BN + activation → 1×1 convolution dimensionality reduction → ECA channel attention → global pooling → skip connections". The ECA mechanism strengthens key feature channels, and the skip connections alleviate gradient vanishing.

[0239] like Figure 4 As shown: This is a bidirectional long short-term memory network structure, which includes a forward LSTM (capturing future temporal information) and a backward LSTM (capturing historical temporal information). The output is a bidirectional feature concatenation result, which is used to comprehensively extract the temporal correlation of the signal.

[0240] like Figure 5As shown: the horizontal and vertical axes represent the signal-to-noise ratio (SNR, in dB) and the DOA estimation accuracy (in %), respectively; the curves represent the performance comparison between the method of this invention (RAB-TL) and traditional methods (MUSIC, ESPRIT), and other deep learning methods (DNN, ResNet, SE-ResNet, Transformer).

[0241] like Figure 6 As shown: the horizontal and vertical axes represent the signal-to-noise ratio (SNR, in dB) and the root mean square error (RMSE, in °), respectively; the smaller the RMSE, the higher the estimation accuracy; the curve comparison shows that the RMSE of the method of this invention (RAB-TL) is always lower than that of traditional methods (MUSIC, ESPRIT) and other deep learning methods (DNN, ResNet, etc.), and it decreases rapidly with the increase of SNR, verifying the high accuracy advantage under the condition of small snapshots (L=10).

[0242] In summary, this invention constructs a pre-trained model based on BiLSTM and RAN to extract rich features from signal data. Subsequently, model fine-tuning enables effective transfer of pre-trained knowledge in scenarios with a limited number of snapshots, thereby efficiently optimizing model parameters. Experimental results show that, under conditions of a limited number of snapshots, the proposed method not only significantly improves the accuracy of DOA estimation but also exhibits excellent robustness.

[0243] The descriptions and practices disclosed in this invention are readily apparent and understandable to those skilled in the art, and various modifications and refinements can be made without departing from the principles of this invention. Therefore, any modifications or improvements made without departing from the spirit of this invention should also be considered within the scope of protection of this invention.

Claims

1. A high-precision DOA estimation method for complex electromagnetic environments with low sample dependence, characterized in that, Includes the following steps: Step 1: Signal data preprocessing. Extract the real and imaginary parts of each element signal from the noisy signal received by the uniform linear array ULA, and construct an input matrix X with dimension 2L×N. IQ This bypasses the traditional covariance matrix calculation process, where L is the number of snapshots and N is the number of array elements; Step 2: Pre-trained model construction, designing parallel dilated convolution branches to extract multi-scale features, combining residual attention modules to enhance key features, and capturing bidirectional temporal correlations of signals through a bidirectional long short-term memory network (BiLSTM). Step 3: Model transfer and fine-tuning. After pre-training the model on a large-scale dataset, the parameters are divided into a basic feature group and a task adaptation group. The former is frozen to retain general knowledge of the source domain, while the latter is fine-tuned to adapt to the target domain's small snapshot task. Step 4: Classification task DOA estimation. The probability of existence of the angle interval is output through a fully connected layer and a sigmoid activation function. The angle of the signal source is determined based on the maximum a posteriori probability criterion.

2. The high-precision DOA estimation method for complex electromagnetic environments with low sample dependence according to claim 1, characterized in that, Step 1 includes the following methods: Assume a uniform linear array ULA consisting of N omnidirectional antennas, with an element spacing of d = λ / 2, and K far-field narrowband signals with wavelength λ. (k=1,2,...,K) from different directions If a signal = [θ1, θ2, ..., θK] is incident on the ULA, then the signal received by the ULA at time t is: x(t)=A(θ)s(t)+n(t),t=1,...,L (1) The parameters are defined as follows: x(t): The received signal vector of ULA at time t, with a dimension of N×1, where N is the number of array elements, containing the received signals of N array elements at time t; A(θ): Array manifold matrix with dimensions N×K, where N is the number of array elements and K is the number of signal sources, and it is composed of the steering vectors corresponding to each signal source; θ: The set of directions of arrival (DOA) of K signal sources, θ = [θ1, θ2, ..., θK], where θ k Indicates the direction of arrival of the k-th signal source; s(t): The output vector of K far-field narrowband signal sources at time t, with a dimension of K×1, containing the complex amplitude of each signal source at time t; n(t): The additive white Gaussian noise vector at time t, with dimension N×1, assumed to have a mean of 0 and a variance of σ. 2 , which follows a complex Gaussian distribution; t: Time sampling index, ranging from 1 to L; L: Snap count, which is the total number of times the signal is sampled; The source and array manifold matrices are represented as follows: s(t)=[s1(t),s2(t),···,s K (t)] T (2) The parameters are defined as follows: s(t): The output vector of K signal sources at time t; s k (t): The complex amplitude of the k-th signal source at time t, k=1,2,...,K, representing the intensity and phase information of the signal source at time t; T: Vector transpose operation, converts a row vector into a column vector; A(θ)=[a(θ1),···,a(θ K )]∈C N×K (3) The parameters are defined as follows: A(θ): is the array manifold matrix; a(θ K ): The steering vector corresponding to the k-th signal source, with a dimension of N×1, describes the phase relationship of the signals received by each array element when the signal source is incident on the ULA; C: Complex field, indicating that the matrix elements are complex numbers; N: The number of elements in a uniform linear array ULA; K: Number of signal sources; It is the relative direction of arrival of ULA. The guiding vector is represented as: ； The parameters are defined as follows: a(θ K ): is the steering vector of the k-th signal source; d: The element spacing of the ULA, given that d = λ / 2, where λ is the signal wavelength; λ: The wavelength of the incident signal, consistent with the definition of a far-field narrowband signal with wavelength λ in the known conditions; j: Imaginary unit, satisfying j 2 =-1; sin(θ K ): The direction of arrival (θ) of the k-th signal source K The sine value, since ULA is a linear array, the direction of arrival is given by sin(θ). K This determines the array phase difference; N: Number of array elements; T: Vector transpose operation; For the original received signal: ； Each row represents the sampled signal on a single array element. Next, the real and imaginary parts of the received signal for each array element are extracted: ； The parameters are defined as follows: X IQ The preprocessed input matrix serves as the input to the subsequent neural network. (·): Operator for extracting the real part of a complex signal. (x(t)) represents the real part of the received signal vector x(t) at time t; (·): Operator that retrieves the imaginary part of a complex signal. (x(t)) represents the imaginary part of the received signal vector x(t) at time t.

3. The high-precision DOA estimation method for complex electromagnetic environments with low sample dependence according to claim 1, characterized in that, Step 2 includes the following methods: First, multi-scale convolution is used to extract local spatial features of the signal data. Then, a residual network with embedded efficient channel attention (ECA) is used to enhance the model's attention to important features and reduce the computational load. The processed features are then input into BiLSTM to further extract the temporal correlation features of the signal. Finally, feature mapping is performed through a fully connected layer, and the Sigmoid activation function is used to output the multi-label classification results.

4. The high-precision DOA estimation method for complex electromagnetic environments with low sample dependence according to claim 3, characterized in that, Dilated convolution is employed to expand the receptive field while reducing the number of parameters. Three 3×1 dilated convolution kernels with different dilation rates are used in parallel to extract multi-scale spatial features, as shown below: ； The parameters are defined as follows: Xi: The output feature map of the i-th dilated convolution branch, i=1,2,3 corresponding to three branches with different dilation rates; DilatedConv(·): Dilated convolution operation, which expands the receptive field by setting the dilation rate; d: The porosity of the i-th branch, used to expand the receptive field. The d values ​​for the three branches are set to 1, 2, and 3 respectively to ensure multi-scale feature extraction. i: Branch index, with values ​​of 1, 2, and 3, corresponding to three parallel dilated convolution branches; Each branch output is sequentially processed by batch normalization and the Mish activation function to stabilize training and enhance the non-linear expressive power of the features. Let the three outputs be X′1, X′2, and X′3, then: X′i=Mish(BN(Xi)),i=1,2,3 (8) The parameters are defined as follows: X′i: The output feature map of the i-th branch after batch normalization (BN) and Mish activation; Mish(·): Mish activation function, used to enhance the non-linear expressive power of features; BN(·): Batch normalization operation, used to stabilize network training, reduce the risk of gradient vanishing, and normalize the feature dimensions of Xi; Xi: the original output of the i-th dilated convolution branch; i: Branch index; After performing channel-wise dimensionality reduction on the features of each branch using 1×1 convolution, the dimensionality-reduced features of the three branches are concatenated along the channel dimensions to form a feature tensor that fuses multi-scale information: Xcat=Concat{ X′1, X′2, X′3} (9) The parameters are defined as follows: Xcat: The fused feature tensor after concatenating multiple branch features; Concat{·}: Feature concatenation operation, which is explicitly defined here as concatenation along the channel dimension, that is, concatenating the features of the three branches along the channel dimension; Apply max pooling to the fused features: Xpool=MaxPool(Xcat) (10) The parameters are defined as follows: Xpool: Output feature map after max pooling; MaxPool(·): Max pooling operation; Spatial dimension compression is performed to highlight local salient features and reduce computational cost.

5. The high-precision DOA estimation method for complex electromagnetic environments with low sample dependence according to claim 3, characterized in that, In deep network design, a residual attention module based on the ResNet structure is introduced. This module consists of four progressive residual attention blocks. Each residual attention block contains convolution, batch normalization (BN), activation function and channel attention mechanism, and gradient propagation and feature reuse are enhanced through skip connections. The residual attention block adopts an efficient channel attention ECA mechanism, which captures the relationship between channels through global average pooling (GAP) and one-dimensional convolution (Conv1D), and uses the Sigmoid function to generate attention weights for channel weighting. Through a progressive channel expansion strategy, the number of channels in the four residual attention blocks are 64→128→256→512 respectively. After processing by the residual attention module, the network is reduced in dimensionality by global average pooling (AvgPool), which preserves global semantics while reducing the risk of overfitting. Subsequently, the bidirectional long short-term memory network (BiLSTM) further models the sequence features and uses forward and backward LSTM subnetworks to capture bidirectional contextual information. After feature sequence encoding, the network maps the high-dimensional features output by BiLSTM to the target label space through a fully connected FC layer. To meet the requirements of multi-source DOA estimation, the final layer uses the Sigmoid activation function to constrain the output to the interval [0,1]. To accurately predict the existence of signals at various angles, binary cross-entropy (BCE) loss is used. (11) The parameters are defined as follows: L BCE Binary cross-entropy (BCE) loss function is used to measure the difference between the model's predicted values ​​and the true labels. : The true label of the i-th angle interval, with a value of 1 or 0; : The probability that a signal source exists in the i-th angle interval predicted by the model, with a value range of [0,1]; The logarithm of the probability that the i-th angle belongs to the positive class as predicted by the model; : The logarithm of the probability that the i-th angle belongs to the negative class as predicted by the model.

6. The high-precision DOA estimation method for complex electromagnetic environments with low sample dependence according to claim 1, characterized in that, Step 3 includes the following methods: Transfer learning process: An 8-element uniform linear array (ULA) was used, with an element spacing of half a wavelength and an angular coverage range of -60° to 60°. The number of signal sources was set to 2. The signal data of the source and target domains were generated with different signal-to-noise ratios (SNRs), ranging from -10 dB to 20 dB in increments of 5 dB, for a total of 7 SNR levels. There were 200,000 samples at each SNR level. The source domain dataset was randomly divided into training, validation, and test subsets in an 8:1:1 ratio. A group fine-tuning strategy is adopted, specifically dividing the network parameters into a basic feature group and a task adaptation group. The layers in the basic feature group have already learned general signal features during training in the source domain, so their parameters are frozen to avoid feature degradation. The layers in the task adaptation group are directly associated with the DOA classification task and are fine-tuned with a higher learning rate to quickly adapt to the target domain. In addition, a dual-learning-rate Adam optimizer is used: the learning rate of the basic feature group is set to 0.0001 to ensure parameter stability, and the learning rate of the task adaptation group is set to 0.001 to accelerate the model response.

7. The high-precision DOA estimation method for complex electromagnetic environments with low sample dependence according to claim 1, characterized in that, Step 4 includes the following methods: DOA estimation: Discretize the DOA range, and construct an overcomplete spatial grid set by equally spaced division of the spatial region where the incident signal may exist. Assume that the range of the incident signal's direction of arrival is the range of this spatial region. , ] Perform angular intervals as By dividing the space into equally spaced grids, an overcomplete set of spatial grids is obtained: ； The parameters are defined as follows: G: A complete set of spatial grids containing all possible candidate values ​​for direction of arrival; θmin: Lower limit of the angle range estimated by DOA; θmax: The upper limit of the angle range estimated by DOA; Δθ: angular discrete interval; This set can be viewed as the set of all possible direction-of-arrival angles of the incident signal, containing the following number of elements: For multiple signal sources, the task boils down to predicting the set of most likely angles. ={ }, given by maximizing the posterior probability: ； The parameters are defined as follows: : The DOA estimate of the k-th signal source, i.e., the optimal candidate angle selected from the grid set G; : Find the angle θ in the grid set G that maximizes the posterior probability P(θ|X); P(θ|X): Posterior probability, representing the probability that the angle θ is the true direction of arrival given the input matrix X.

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