DOA estimation method based on self-supervised contrast learning under non-ideal array

Abstract

The invention belongs to the technical field of communication signal processing, and more specifically relates to a DOA estimation method based on self-supervised contrast learning under a non-ideal array. The invention provides a two-stage cascade DOA (direction of arrival) estimation framework. The framework is composed of two modules which are respectively a control reconstruction network (CRN) and a direction of arrival (DOA) estimation network (DEN), and the two modules are respectively a control reconstruction network (CRN) and a direction of arrival (DOA) estimation network (DEN). The CRN adopts self-supervised contrast learning to recover a covariance matrix, so that the network has robustness when facing array defects. And the DEN takes the reconstructed covariance matrix output by the CRN as input to complete a DOA estimation task. In order to improve the generalization ability of the network, non-ideal enhancement modes such as amplitude disturbance, phase disturbance and random array element shielding are introduced into a training sample, and a two-stage training strategy is adopted to optimize CRN and DEN network parameters respectively.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of communication signal processing, and more particularly relates to a DOA estimation method based on self-supervised contrast learning under a non-ideal array. BACKGROUND

[0002] With the continuous development of communication signal processing technology, Direction of Arrival (DOA) estimation has become a core task of array signal processing and is widely used in radar, sonar, wireless positioning and other fields. Uniform Linear Array (ULA) has the characteristics of simple structure and strong analyticality, and is very suitable for DOA estimation tasks. In the framework of ULA-based array direction finding, traditional model-driven DOA estimation methods include subspace-based MUSIC algorithm, ESPRIT algorithm and Root-MUSIC algorithm, and compressive sensing-based l 2,1 -SVD algorithm. Although the subspace algorithm performs well under ideal conditions, the DOA estimation performance is not ideal in complex environments such as limited snapshots and low signal-to-noise ratio. Although the compressive sensing-based method solves the problem that the subspace algorithm is easily affected by noise, the computational complexity of this algorithm is too large, and it faces great challenges in practical applications.

[0003] In recent years, deep learning has achieved great success in image processing, speech recognition, and other fields, and has also been introduced into the DOA estimation task. For example, in the paper titled "Nested U-Shape Network for Robust Direction-of-Arrival Estimation" (IEEE Transactions on Vehicular Technology, Vol. 74 No. 7, pp. 11081-11094, July 2025), researchers proposed using a nested U-shaped convolutional neural network to extract multi-scale features from both local and global aspects. This method showed excellent robustness in multi-target DOA estimation tasks. In addition, in the paper titled "DOA Estimation with Deep Learning: A Limited Training Data Framework" (IEEE Transactions on Communications, 2025), a framework based on the meta-learning concept was proposed, enabling the model to learn how to quickly adapt to different tasks, thereby achieving good estimation performance with limited training data. In the conference paper titled "Deep Learning Based Direction of Arrival Estimation of Multiple Targets" (2022 IEEE 5th International Conference on Electronic Information and Communication Technology, pp. 138-143), it was proposed to use the in-phase and quadrature components of the original signal as the input of a deep neural network (such as ResNet) to significantly improve the performance of multi-source DOA estimation.

[0004] However, in practical applications, array systems may suffer from various defects due to imperfect sensor design and manufacturing, and mutual interference between sensors, such as element failure and amplitude / phase uncertainty. To address this, in the paper titled "Direction-of-Arrival Estimation Based on Deep Neural Networks With Robustness to Array Imperfections" (IEEE Transactions on Antennas and Propagation, Vol. 66, No. 12, pp. 7315-7327, December 2018), researchers proposed a network framework employing a multi-task autoencoder combined with a parallel multi-classifier structure to maintain good generalization performance even with array defects. Furthermore, in the paper titled "Learning-based robust direction-of-arrival estimation with array imperfections" (Signal Processing, Vol. 234, p. 110000, 2025), researchers used the covariance vector as input to a convolutional attention neural network, achieving high-precision DOA estimation under non-ideal array conditions. Although these methods have made some progress in solving the problem of DOA estimation under array defects, they often rely heavily on a large number of precisely labeled training samples, which limits their application in real-world scenarios where data acquisition is difficult.

[0005] In applications lacking labeled data, self-supervised learning (SSL) has garnered significant attention due to its ability to learn data structures through pre-tasks, thereby reducing reliance on manual labels. In recent years, contrastive learning, as a representative method of self-supervised learning, constructs positive and negative sample pairs to guide the model in learning discriminative features, thus achieving effective feature extraction without the need for precise labels. Summary of the Invention

[0006] To address this, this invention proposes a two-stage cascaded DOA estimation framework to improve the robustness and generalization ability of the model under array defects and interference. The first stage trains a CRN module based on self-supervised contrastive learning to reconstruct the covariance matrix; the second stage extracts the reconstructed covariance matrix from the CRN and uses it as input to the DEN module to complete the DOA estimation task. This cascaded framework fully leverages the advantages of self-supervised contrastive learning, effectively reducing reliance on a large number of labeled samples while improving DOA estimation performance under complex conditions such as array defects.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A self-supervised contrastive learning-based DOA estimation method for non-ideal arrays includes the following steps:

[0009] Step S1: Constructing a signal model and preprocessing data: Based on the signal model of the receiving array, the original received signal is preprocessed. Specifically, the received signal is converted into a covariance matrix, and non-ideal array conditions are simulated through a preset data augmentation strategy to generate signal sample pairs for network training.

[0010] Step S2: Construct and execute cascaded DOA estimation: Based on the signal model and preprocessed data, construct a two-stage cascaded DOA estimation framework, which includes a cascaded contrast recovery network module and a DOA estimation network module. In the first stage, using data-augmented signal sample pairs, train the contrast recovery network module using self-supervised contrastive learning to recover a robust covariance matrix from the disturbed signal. In the second stage, use the reconstructed covariance matrix output by the contrast recovery network module as the input to the DOA estimation network module, and train the module using supervised learning to complete the final DOA angle estimation task.

[0011] In a further optimization of this technical solution, the signal model constructed in step S1 is as follows:

[0012] Suppose that K narrowband far-field signals are incident on a ULA with M elements, and the element spacing is d. The DOA angles corresponding to the K signals are denoted as θ. k Where k = 1, 2, ..., K, the array received signal x(t) at time t can be expressed as:

[0013] x(t)=A(θ)s(t)+n(t) (13)

[0014] Where t = 1, 2, ..., T is the number of snapshots. Let a(θ) represent the array manifold matrix. i ) represents the steering vector of the i-th signal, expressed as:

[0015]

[0016] Where λ represents the signal wavelength, s(t)=[s1(t),s2(t),...,s K (t)] T And n(t) = [n1(t), n2(t), ... n M (t)] T Let them represent the signal vector and the Gaussian white noise vector, respectively.

[0017] The covariance matrix R of the received signal is expressed as:

[0018] R = E[x(t)x(t)] H ]=A(θ)R S A(θ) H +σ 2 I (15)

[0019] Where R S I and L represent the signal covariance matrix and identity matrix, respectively. In practical applications, the covariance matrix is ​​approximated by L snapshots.

[0020]

[0021] At the same time, in order to improve training stability, Normalization using the Frobenius norm:

[0022]

[0023] 9. The DOA estimation method based on self-supervised contrastive learning under non-ideal arrays as described in claim 2, characterized in that the data preprocessing in step S1 is as follows:

[0024] To simulate the amplitude and phase errors between arrays, the received signal x(t) is remodeled as an amplitude-phase enhancement signal x. q (t):

[0025] x q (t)=G(A(θ)s(t)+n(t)) (18)

[0026] in For the complex diagonal perturbation matrix, Indicates amplitude disturbance, φ i ~U[-Δ φ ,Δ φ The symbol ] represents phase perturbation. To simulate the possibility that some array elements may fail due to occlusion or damage, the outputs of random η∈M array elements are set to 0 using a binary diagonal matrix H, resulting in the array element mask enhancement signal x. k (t):

[0027] x k (t)=H(A(θ)s(t)+n(t)) (19)

[0028] Where H = diag(h1,h2,...,h) M ), h i ∈{0,1}.

[0029] In a further optimization of this technical solution, step S2 includes:

[0030] Step S2.1, Data Management and Labeling: Based on the signal samples generated in step S1 and their corresponding DOA ground truth values, divide the first-stage training dataset for self-supervised contrastive learning and the second-stage training dataset for supervised learning.

[0031] Step S2.1: Construct and train the contrast recovery network module: Build a network structure containing two covariance feature encoders with shared parameters. Using the dataset from the first stage, train the network with the goal of minimizing the contrast loss so that the network can recover a robust covariance matrix from signal samples disturbed by non-ideal conditions.

[0032] Step S2.3, Covariance Feature Encoder: Specifically configure the encoder-decoder structure, skip connections, and momentum update mechanism for maintaining feature consistency of the covariance feature encoder;

[0033] Step S2.4: Construct and train the DOA estimation network: Construct a deep neural network, take the reconstructed covariance matrix output by the contrast recovery network module in step S2.2 as input, use the second stage dataset, train it with the goal of minimizing the angle estimation error, and finally output the DOA estimate.

[0034] In a further optimization of this technical solution, step S2.1 sets the angle range, angle interval, and signal-to-noise ratio level, and generates a sample set at each signal-to-noise ratio level. For each received sample x... i (t), calculate the covariance matrix corresponding to equation (6). The covariance matrix corresponding to equation (7) Both are complex-valued N×N matrices; take their real and imaginary parts to represent... and It is a real-valued tensor of form 2×N×N, where the two channels represent the real and imaginary parts of the covariance matrix, respectively. as well as Therefore, the training dataset for the first stage consists of c1 samples. The second stage is a supervised learning task, which requires generating corresponding angle labels. Therefore, the training dataset for the second stage consists of c2 samples.

[0035] This technical solution is further optimized by refining step S2.2 to extract signals under different signal enhancement methods. and The directional information features are compared and recovered in the network module, which contains two covariance feature encoders with identical structures but different weight parameters, denoted as f.q (·) and f k (·), f q (·) and f k The inputs for (·) are respectively and After feature extraction by the covariance feature encoder, we obtain:

[0036]

[0037] in The recovered covariance matrix retains its two-dimensional structure, allowing it to be directly used for subsequent DOA estimation tasks and vectorized. and have to:

[0038]

[0039] Where vec(·) represents the vectorization operation. and The positive sample pairs that constitute the i-th sample;

[0040] When constructing the negative sample set, a dictionary mechanism is introduced. This dictionary is organized in the form of a queue with a fixed length of D, and follows a "first-in, first-out" update strategy to store historical f. k (·) Output feature representation As The source of the negative sample set, therefore, The negative sample set is represented by all the features in the queue. constitute;

[0041] The goal of the contrast recovery network module is to minimize the feature differences between positive sample pairs while maximizing the feature differences between negative samples. Therefore, the contrast loss used by the contrast recovery network module is as follows:

[0042]

[0043] Where τ>0 is the temperature coefficient, used to adjust the discrimination boundary between positive and negative samples, and sim(·) is the cosine similarity:

[0044]

[0045] A further optimization of this technical solution is that step 2.3 includes:

[0046] The covariance feature encoder adopts an encoder-decoder architecture. The encoding part uses convolution and max pooling to extract and compress features, while the decoding part gradually restores the resolution through deconvolution and combines skip connections to fuse shallow and deep information, thereby improving the accuracy and stability of covariance matrix reconstruction. The convolutional blocks used consist of a convolutional layer, a batch normalization layer, and a linear rectified activation function.

[0047] To ensure the stability and consistency of negative sample feature representations, f k The parameter ν of (·) k via f q The parameter ν of (·) q Updated using momentum, f k The parameter ν of (·) k The momentum update formula is:

[0048]

[0049] in This represents the momentum coefficient, and the mechanism ensures f k (·) While keeping the output characteristics stable, it also keeps them consistent with f q The distribution of the output features of (·) is consistent.

[0050] In a further optimization of this technical solution, step S2.4 includes:

[0051] The input to the DOA estimation network is the f of the contrast recovery network module. q (·) Output covariance matrix Feature extraction is performed through convolution and max pooling, followed by mapping through fully connected layers to finally output the DOA angle estimation result. The DOA estimation network module uses the mean squared error between the predicted DOA value and the true label as the loss function, i.e.:

[0052]

[0053] in For the predicted DOA, θ i This is a label for the actual angle.

[0054] Unlike existing technologies, the above technical solution has the following beneficial effects: First, it significantly improves robustness and estimation accuracy under non-ideal array conditions. By introducing data augmentation that simulates real defects and self-supervised contrastive learning, the model can directly learn robust features from damaged signals, effectively overcoming the dependence of traditional methods on ideal array models and the problem of performance drop-off in practical applications. Second, it greatly reduces the dependence on large-scale, accurately labeled data. The core contrastive learning module can be trained without angle labels, breaking through the bottleneck of strong dependence on expensive labeled data in existing deep learning methods, and improving its practicality and scalability in real-world scenarios with scarce data. Third, it adopts a two-stage cascaded decoupled training strategy to optimize the learning process and enhance generalization ability. By optimizing robust feature learning and angle estimation tasks in stages, it avoids the instability of joint training and ensures that the model maintains excellent performance under different interference and signal-to-noise ratios. Attached Figure Description

[0055] Figure 1 Here is a diagram of the cascaded DOA estimation structure;

[0056] Figure 2 This is a diagram of the covariance feature encoder structure.

[0057] Figure 3 RMSE performance graphs for different algorithms on the target;

[0058] Figure 4 The accuracy of different algorithms at the target angle. Detailed Implementation

[0059] To explain in detail the technical content, structural features, objectives, and effects of the technical solution, the following description is provided in conjunction with specific embodiments and accompanying drawings.

[0060] This invention proposes a DOA estimation method based on self-supervised contrastive learning for non-ideal arrays, specifically including the following steps:

[0061] Step S1: Signal model and data preprocessing.

[0062] Step S1.1: Constructing a signal model

[0063] Suppose that K narrowband far-field signals are incident on a ULA with M elements, and the element spacing is d. The DOA angles corresponding to the K signals are denoted as θ. k Where k = 1, 2, ..., K. The array-received signal x(t) at time t can be expressed as:

[0064] x(t)=A(θ)s(t)+n(t) (26)

[0065] Where t = 1, 2, ..., T is the number of snapshots. Let a(θ) represent the array manifold matrix. i ) represents the steering vector of the i-th signal, expressed as:

[0066]

[0067] Where λ represents the signal wavelength. s(t)=[s1(t),s2(t),...,s K (t)] T And n(t) = [n1(t), n2(t), ... n M (t)] T These represent the signal vector and the Gaussian white noise vector, respectively.

[0068] The covariance matrix of the received signal can be represented as:

[0069] R = E[x(t)x(t)] H ]=A(θ)R S A(θ) H +σ 2 I (28)

[0070] Where R S Let I represent the signal covariance matrix and the identity matrix, respectively. In practical applications, the covariance matrix is ​​approximated by L snapshots:

[0071]

[0072] At the same time, in order to improve training stability, Normalization using the Frobenius norm:

[0073]

[0074] Step 1.2, Data Preprocessing

[0075] In practical applications, various non-ideal factors can cause the array to deviate from its ideal value, affecting the accuracy of DOA estimation. Therefore, this embodiment simulates array element missingness and amplitude / phase errors in real-world scenarios by randomly masking the output signals of array elements and adding perturbations during training, thereby enhancing the network's robustness in complex scenarios. To simulate the amplitude and phase errors between arrays, the received signal x(t) is remodeled as follows:

[0076] x q (t)=G(A(θ)s(t)+n(t)) (31)

[0077] in For the complex diagonal perturbation matrix, Indicates amplitude disturbance, φ i ~U[-Δφ ,Δ φ The symbol ] represents phase perturbation. To simulate the possibility of some array elements failing due to occlusion or damage, the outputs of random η∈M array elements are set to 0 using a binary diagonal matrix H. That is:

[0078] x k (t)=H(A(θ)s(t)+n(t)) (32)

[0079] Where H = diag(h1,h2,...,h) M ), h i ∈{0,1}.

[0080] Step S2: Construct a cascaded DOA estimation framework.

[0081] See Figure 1 The diagram shows the cascaded DOA estimation structure. The DOA estimation framework consists of two modules: a Contrastive Reconstruction Network (CRN) and a DOA Estimate Network (DEN). In the first stage, the CRN module is trained to reconstruct the covariance matrix. This module introduces a self-supervised contrastive learning (SSCL) framework, which eliminates the need for manual labeling and captures shared directional information features between samples under different signal enhancement methods to recover the covariance matrix under different disturbances. In the second stage, the covariance matrix reconstructed by the CRN module is used as input to train the DEN module, completing the DOA estimation task of the signal source.

[0082] Step S2.1, Data Management and Annotation

[0083] The angle range is set to [-60°, 60°], discrete in 1° intervals, for a total of 121 angle grids. Four signal-to-noise ratio (SNR) levels are set: {0dB, 5dB, 10dB, 15dB}, with 10,000 samples generated at each SNR. For each received sample x... i (t), calculate the covariance matrix corresponding to equations (6) and (7). and All are complex-valued N×N matrices. Taking their real and imaginary parts, we represent... and It is a real-valued tensor of form 2×N×N. The two channels represent the real and imaginary parts of the covariance matrix, respectively. as well as Therefore, the training dataset κ1 in the first stage consists of c1 samples. The second stage is a supervised learning task, which requires generating corresponding angle labels. Therefore, the training dataset κ2 for the second stage consists of c2 samples.

[0084] Step S2.1, CRN module

[0085] In order to extract different signal enhancement methods and Based on the directional information features, this embodiment proposes a Contrast Recovery Network (CRN), the structure of which is as follows: Figure 1 As shown in the upper middle section, within the dashed box labeled "Stage 1," the CRN contains two covariance feature encoders (CFEs) with identical structures but different weight parameters, denoted as f. q (·) and f k (·). f q (·) and f k The inputs for (·) are respectively and After feature extraction via CFE, we obtain:

[0086]

[0087] in The recovered covariance matrix retains its two-dimensional structure, allowing it to be directly used for subsequent DOA estimation tasks. Vectorization and Obtain amplitude and phase enhancement sample vector Enhanced sample vector with array element mask

[0088]

[0089] Where vec(·) represents the vectorization operation. and The positive sample pairs that constitute the i-th sample.

[0090] To ensure the diversity and stability of the negative sample set during construction, this embodiment introduces a dictionary mechanism. This dictionary is organized in the form of a queue with a fixed length D, and follows a first-in, first-out (FIFO) update strategy to store historical f. k (·) Output feature representation As The source of the negative sample set. Therefore, The negative sample set is represented by all the features in the queue. constitute.

[0091] The goal of CRN is to minimize the feature differences between positive sample pairs while maximizing the feature differences between negative samples. Therefore, inspired by InfoNCE loss, CRN employs a contrastive loss form L... contrast as follows:

[0092]

[0093] Where τ>0 is the temperature coefficient, used to adjust the discrimination boundary between positive and negative samples. sim(·) is the cosine similarity.

[0094] Step S2.3, Covariance Feature Encoder

[0095] The structure of the covariance feature encoder (CFE) is as follows: Figure 2 As shown, the network employs an encoder-decoder architecture, with the following specific structure: The encoder consists of multiple cascaded convolutional blocks, each containing a convolutional layer, a batch normalization layer, and a linear rectified activation function, interspersed with max-pooling layers for feature compression; the decoder gradually restores the feature map resolution through corresponding deconvolution operations. To improve reconstruction accuracy and stability, the network introduces skip connections between corresponding layers of the encoder and decoder to fuse shallow detail information with deep semantic information. For example, the convolutional blocks in the encoder can be configured sequentially as 3x3 convolutional layers with 32, 64, and 128 channels (e.g., ...). Figure 2 The blocks are labeled Conv Block1, Conv Block2, Conv Block3, etc., and the final reconstruction result is output through a fully connected layer. The encoding part uses convolution and max pooling to extract and compress features, while the decoding part gradually restores the resolution through deconvolution and combines skip connections to fuse shallow and deep information, improving the accuracy and stability of covariance matrix reconstruction. Each convolutional block consists of a convolutional layer, a batch normalization (BN) layer, and a rectified linear activation function (ReLU).

[0096] To ensure the stability and consistency of negative sample feature representations, f k The parameter ν of (·) k via f q The parameter ν of (·) q Updated using momentum. k The parameter ν of (·) k The momentum update formula is:

[0097]

[0098] in This represents the momentum coefficient. This mechanism ensures that f... k (·) While keeping the output characteristics stable, it also keeps them consistent with f qThe distribution of the output features of (·) is consistent.

[0099] Step S2.4, DOA estimation network

[0100] The structure of DEN is as follows Figure 1 As shown in the lower center, within the dashed box labeled "Stage 2," the DOA estimation network module consists of a convolutional feature extractor and a fully connected regressor. Its input is the reconstructed covariance matrix output by the contrast recovery network module. This matrix is ​​first processed through multiple cascaded convolutional blocks for feature extraction and compression. Each convolutional block also contains convolutional layers, batch normalization layers, and linear rectified activation functions, and its dimensionality can be reduced through max pooling layers. The extracted features are flattened and fed into one or more fully connected layers, and finally, the output layer regresses to obtain the estimated direction-of-arrival (DOA) angle of the target. The network input is f from the CRN. q (·) Output covariance matrix Feature extraction is performed through convolution and max pooling, followed by mapping through a fully connected layer to finally output the DOA angle estimation result. DEN uses the mean squared error (MSE) between the predicted DOA value and the true label as the loss function L. MSE .Right now:

[0101]

[0102] in For the predicted DOA, θ i This is a label for the actual angle.

[0103] Simulation results

[0104] Consider a ULA with N=7 elements, an element spacing d=λ / 4, where λ is the signal wavelength. The number of sampling snapshots T=100, and the number of signal sources K=1. Set the queue length D=65536, the temperature coefficient τ=0.07, and the momentum coefficient... η = 2 array elements were randomly masked. In all experiments, the root mean square error (RMSE) was used to measure the performance of the angle estimation.

[0105]

[0106] in The true angle of the k-th signal in the n-th sample. Here is the corresponding estimated value, and N is the total number of test samples.

[0107] Training strategy

[0108] This embodiment employs a two-stage training strategy, corresponding to the independent training processes of CRN and DEN, respectively. In the first stage, CRN is trained using dataset κ1 and optimized using contrastive loss. In the second stage, all parameters of CRN are frozen, and DEN is trained using training set κ2 to complete the DOA estimation task. Both training stages use the Adam optimizer, with a batch size of 64, 50 epochs, and a learning rate of 1×10⁻⁶. -4 To ensure fairness, all comparison methods were trained using the same training dataset κ2 and the same number of iterations.

[0109] DOA Estimation Performance

[0110] This embodiment compares the proposed method with the classic model-driven method MUSIC and two commonly used neural network methods, LTDDOA-Net and DRN. To evaluate the anti-interference capabilities of different methods, amplitude and phase perturbations and random array element shielding are applied simultaneously to the test samples.

[0111] Consider a signal source with a DOA of -27°. Figure 3 (a) shows the results of RMSE as a function of signal-to-noise ratio when the number of snapshots is fixed at 100; Figure 3 (b) shows the RMSE as a function of the number of snapshots when the signal-to-noise ratio (SNR) is fixed at 10 dB. Experimental results show that this method exhibits the lowest RMSE under all SNR and snapshot conditions, maintaining good accuracy even under low SNR (SNR = 0 dB) and low snapshot count (T = 15), significantly outperforming other methods. The accuracy threshold is set to 0.6°. Figure 4 (a) shows the results of Accuracy as a function of signal-to-noise ratio with a fixed number of snapshots of 100; Figure 4 (b) shows the results of accuracy as a function of snapshot number when the signal-to-noise ratio is fixed at 10dB. Figure 4 As shown in (a), the angle prediction accuracy of the proposed method gradually increases with the increase of the signal-to-noise ratio (SNR), and approaches 100% at SNR = 15 dB. Figure 4 In (b), the proposed method achieves an accuracy exceeding 90% at T=90, outperforming other algorithms. This demonstrates that the two-stage cascaded DOA estimation framework proposed in this invention exhibits stronger robustness under conditions of severe noise interference or limited data.

[0112] This invention proposes a two-stage cascaded DOA estimation framework based on self-supervised contrastive learning to enhance DOA estimation performance under non-ideal array conditions. The framework comprises two modules: a Continuous Regression Array (CRN) and a Dependency Array Encryption Array (DEN). In the first stage, the CRN is trained using contrastive learning to obtain a robust covariance representation under unlabeled conditions, reducing dependence on labeled samples and improving generalization ability. In the second stage, the covariance matrix recovered by the CRN is used as input to train the DEN to complete DOA estimation. Staged training avoids training conflicts caused by simultaneously optimizing two objectives, thus improving stability. Simulation results verify the superior performance of the proposed method. Simulation experiments show that the proposed two-stage framework exhibits higher estimation accuracy and stronger robustness under different signal-to-noise ratios and snapshot conditions.

[0113] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Unless otherwise specified, an element defined by the phrase "comprising..." or "including..." does not exclude the presence of additional elements in the process, method, article, or terminal device that includes said element. Additionally, in this document, "greater than," "less than," "exceeding," etc., are understood to exclude the stated number; "above," "below," "within," etc., are understood to include the stated number.

[0114] Although the above embodiments have been described, those skilled in the art, once they understand the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the above descriptions are merely embodiments of the present invention and do not limit the scope of patent protection of the present invention. Any equivalent structural or procedural transformations made using the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A DOA estimation method based on self-supervised contrastive learning under a non-ideal array, characterized in that, Comprising the following steps: Step S1, constructing a signal model and data preprocessing: based on the signal model of the receiving array, the original received signal is preprocessed, specifically, the received signal is converted into a covariance matrix, and a non-ideal array condition is simulated through a preset data enhancement strategy to generate a signal sample pair for network training; Step S2, constructing and executing cascaded DOA estimation: based on the signal model and the preprocessed data, a two-stage cascaded DOA estimation framework is constructed, which includes a contrast recovery network module and a DOA estimation network module connected in series; in the first stage, the data enhanced signal sample pair is used to train the contrast recovery network module in a self-supervised contrast learning manner, so that the robust covariance matrix is recovered from the disturbed signal; in the second stage, the reconstructed covariance matrix output by the contrast recovery network module is used as the input of the DOA estimation network module to train the module in a supervised learning manner to complete the final DOA angle estimation task.

2. The DOA estimation method based on self-supervised contrastive learning for non-ideal array according to claim 1, wherein, The step S1 constructs a signal model as follows: Suppose that there are K narrowband far-field signals incident on a ULA with M elements, the element spacing is d, and the DOA angles corresponding to the K signals are represented as θ k where k = 1, 2, …, K, the array receiving signal x(t) at time t can be represented as: x(t)=A(θ)s(t)+n(t) (1) where t = 1, 2,..., T is the snapshot number, denotes the array manifold matrix, a(θ i ) denotes the steering vector of the i-th signal and is given by: where λ denotes the signal wavelength, s(t) = [s1(t), s2(t),..., s K (t)] T and n(t) = [n1(t), n2(t),... n M (t)] T denote the signal vector and the Gaussian white noise vector, respectively, The covariance matrix R of the received signal is represented as: R = E[x(t)x(t) H ] = A(θ)R S A(θ) H + σ 2 I (3) wherein R S , I denote the signal covariance matrix and the identity matrix, respectively. In practical applications, the covariance matrix is approximated by L snapshots Meanwhile, in order to improve the training stability, the gradient is normalized by the Frobenius norm of the input data Normalization using the Frobenius norm:

3. The DOA estimation method based on self-supervised contrastive learning for non-ideal array according to claim 2, wherein, The data preprocessing in step S1 is as follows: To model the amplitude and phase errors between the arrays, the received signal x(t) is re-modeled as an amplitude and phase enhanced signal x q (t): x q (t) = G(A(0)s(t) + n(t)) (6) where is a complex diagonal perturbation matrix, denotes the amplitude perturbation, φ i ~ U[-Δ φ , Δ φ denotes the phase perturbation, is to simulate the situation that some array elements may be disabled due to occlusion or damage, and the outputs of random η ∈ M array elements are set to 0 by a binary diagonal matrix H, to obtain the array element mask enhanced signal x k (t): x k (t) = H(A(0)s(t) + n(t)) (7) where H = diag(h1, h2,..., hN) and h = (h1, h2,..., hN)T. M ), h i ∈{0, 1}.

4. The DOA estimation method based on self-supervised contrastive learning for non-ideal array of claim 3, wherein, The step S2 includes: Step S2.1, data management and labeling: based on the signal sample and its corresponding DOA true value generated in step S1, a first stage training data set for self-supervised contrast learning and a second stage training data set for supervised learning are divided; Step S2.1, constructing and training a contrast recovery network module: a network structure containing two parameter-shared covariance feature encoders is built, and the first stage data set is used to train the network to recover a robust covariance matrix from a signal sample disturbed by a non-ideal condition, with the goal of minimizing the contrast loss; Step S2.3, covariance feature encoder: the encoder-decoder structure, jump connection and momentum update mechanism for maintaining feature consistency of the covariance feature encoder are specifically configured; Step S2.4, constructing and training a DOA estimation network: a deep neural network is constructed, the reconstructed covariance matrix output by the contrast recovery network module in step S2.2 is taken as the input, and the second stage data set is used to train the network to minimize the angle estimation error, and finally the DOA estimation value is output.

5. The DOA estimation method based on self-supervised contrastive learning for non-ideal array of claim 4, wherein, The step S2.1 sets the angle range, the angle interval, the signal-to-noise ratio level, generates a sample set under each signal-to-noise ratio level, and calculates the covariance matrix corresponding to the formula (6) for each received sample x i The formula (6) corresponds to the covariance matrix The formula (7) corresponds to the covariance matrix Both are complex N×N matrices; taking the real part and the imaginary part, the formula (6) is expressed as And The real value tensor is in the form of 2×N×N, wherein two channels respectively represent the real part data and the imaginary part data of the covariance matrix, that is, And Therefore, the training data set κ1 of the first stage is composed of c1 samples The second stage belongs to a supervised learning task, and a corresponding angle label needs to be generated, so the training data set κ2 of the second stage is composed of c2 samples 6. The DOA estimation method based on self-supervised contrastive learning for non-ideal array of claim 5, wherein, The direction information features of the different signal enhancement modes in step S2.2 are extracted and The contrast recovery network module includes two covariance feature encoders with the same structure but different weight parameters, denoted as f q (·) and f k (·), and the inputs of f q (·) and f k (·) are and After the features are extracted by the covariance feature encoders, the following is obtained: wherein As the restored covariance matrix, the two-dimensional structure form of the covariance matrix is retained, which can be directly used for subsequent DOA estimation tasks, vectorization With Get amplitude and phase enhanced sample vector And array element mask enhanced sample vector where vec( ) denotes a vectorization operation, and a positive sample pair constituting the i-th sample; In constructing the negative sample set, a dictionary mechanism is introduced, which is organized in the form of a queue with a fixed length D, satisfying the "first in, first out" update policy, for storing historical f k (·) the output feature representation As the source of the negative sample set, therefore, the negative sample set of f is composed of all feature representations in the queue. The objective of the contrastive recovery network module is to minimize the feature difference between positive sample pairs while maximizing the feature difference between negative samples, thus, the contrastive loss L employed by the contrastive recovery network module is contrast is as follows: Wherein, τ>0 is the temperature coefficient for adjusting the discrimination boundary between positive and negative samples, and sim(·) is the cosine similarity.

7. The DOA estimation method based on self-supervised contrastive learning for non-ideal array of claim 6, wherein, The step 2.3 includes: The covariance feature encoder adopts an encoder-decoder architecture, the encoding part uses convolution and maximum pooling to extract and compress features, the decoding part gradually recovers the resolution through deconvolution, combines with jump connection to fuse shallow and deep information, and improves the accuracy and stability of covariance matrix reconstruction, and the convolution block used is composed of a convolution layer, a batch normalization layer and a linear rectifier activation function; To ensure the stability and consistency of the negative sample feature representation, f k the parameter v of f k Through the momentum update of f q the parameter v of f q is updated in a momentum manner, f k the parameter v of f k The momentum update formula of f wherein represents a momentum coefficient, the mechanism guarantees f k (·) output features remain stable while keeping them consistent with the distribution of the output features of f q (·).

8. The DOA estimation method based on self-supervised contrastive learning for non-ideal array of claim 7, wherein, The step S2.4 includes: The input of the DOA estimation network is f q (·) The output covariance matrix The features are extracted through convolution and max-pooling, and then mapped through a fully connected layer to finally output the DOA angle estimation result; the mean square error between the DOA prediction value and the true label is used as the loss function L of the DOA estimation network module MSE That is: wherein is the predicted DOA, θ i is the true angle label.

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