Subspace array direction finding method based on semi-supervised learning

Abstract

The invention provides a subspace array direction finding method based on semi-supervised learning. According to the method, the signal subspace is used as network input, the scale of a data set and the memory requirement of a processor are remarkably reduced, and application of a deep learning method in a super-large-scale antenna array scene becomes possible. In order to solve the problem that label data in an actual scene is difficult to obtain, a semi-supervised learning strategy is introduced, and high-precision model training is realized through combination of a small amount of label data and complex value operation of a convolutional layer. Simulation results show that the method is excellent in performance in a scene in which memory resources are limited but high time complexity is allowed, and an effective solution is provided for practical application.

Description

Technical Field

[0001] The present invention relates to a subspace array direction finding method based on semi-supervised learning, belonging to the technical field of antenna array signal processing. Background Art

[0002] As an important research direction in the field of array signal processing, source localization has been widely applied in scenarios such as wireless communication, radar detection, and mobile terminal positioning. This technology receives source signals through an array composed of multiple sensors or antennas, and then realizes the accurate estimation of the source position. Under far-field conditions, that is, when the distance between the source and the array is much larger than the array aperture, the incident wave can be approximated as a plane wave. At this time, the source localization problem can be transformed into a direction-of-arrival estimation problem. With the rapid development of technologies such as mobile communication, the requirements for positioning accuracy in various application scenarios are increasing day by day. Especially in the field of communication and sensing integration, high-precision positioning has become the focus of common concern in academia and industry. To meet the demand for ultra-high-precision positioning, researchers have proposed solutions based on ultra-large-scale antenna arrays, and the number of antenna elements can reach hundreds or even thousands. However, while ultra-large-scale antenna arrays improve performance, they also bring significant computational complexity problems and impose a huge computational burden on single-processor systems.

[0003] In recent years, deep learning methods have shown unique advantages in reducing computational complexity due to their data-driven characteristics, providing new ideas to make up for the deficiencies of distributed algorithms. However, it should be noted that the highly parameterized characteristics of deep learning models pose high requirements for the scale and quality of training data. As the array scale expands, the dimension of the input data increases exponentially, and the resulting high-dimensional matrix dataset will cause huge pressure on the device memory. Especially in the scenario of ultra-large-scale antennas, the memory requirement of the algorithm has become one of the main bottlenecks restricting its practical application. In addition, the performance of neural network models depends to a large extent on high-quality training datasets, and it is often difficult to obtain such data in actual application scenarios. To address the above problems, the method of constructing a training set based on the signal subspace shows significant advantages. This method performs well in application scenarios with limited memory resources but allowing relatively high computational complexity, providing a feasible technical path for solving the source localization problem under ultra-large-scale antenna arrays. Summary of the Invention

[0004] The present invention proposes a subspace array direction finding method based on semi-supervised learning. This method uses the signal subspace as the network input, significantly reducing the scale of the data set and the memory requirements of the processor, making it possible to apply deep learning methods in scenarios with ultra-large-scale antenna arrays. Aiming at the problem that labeled data is difficult to obtain in actual scenarios, the present invention introduces a semi-supervised learning strategy, and realizes high-precision model training through a small amount of labeled data combined with the complex-valued operation of the convolutional layer. The simulation results show that this method performs excellently in scenarios with limited memory resources but allowing a relatively high time complexity, providing an effective solution for practical applications.

[0005] The technical solution of the present invention is as follows:

[0006] A subspace array direction finding method based on semi-supervised learning, comprising the following steps:

[0007] S1. Construct a received signal model of a uniform linear array, preprocess the received signal to obtain the covariance matrix R of the received signal, perform eigenvalue decomposition on R to obtain the signal subspace U S ;

[0008] S2. Build a subspace covariance reconstruction ViT network (Semi-SCV C ) based on semi-supervised learning. The network consists of a feature extraction module and a post-processing module;

[0009] S3. Construct a training set for Semi-SCV C . The training set consists of input data and labels; among them, the signal subspace U of the received signal S is used as the input data of Semi-SCV C ; calculate the noise-free covariance matrix of the array received signal, and extract the first row element u as the label of the training set of Semi-SCV C ;

[0010] S4. Use the training set to train Semi-SCV C . U S obtains an output through the feature extraction module Take as the input of the post-processing module to obtain the output θ.

[0011] Further, in step S1, it is necessary to first establish a received signal model of a uniform linear array, specifically:

[0012] S11. The array used at the receiving end is a uniform linear array with M array elements, and the spacing between adjacent array elements is λ / 2, where λ is the wavelength of the signal. The reference array element is the central array element of the array, and its coordinates are set as (0,0);

[0013] S12. Assume K narrowband far-field signal sources Incident from θ = {θ1, θ2, …, θ K} onto a uniform linear array consisting of M array elements, the signal received by the d-th subarray at time t is expressed as follows,

[0014]

[0015] where n(t) represents Gaussian white noise, and ∑(·) represents the summation symbol. The array manifold A(θ) = [a(θ1), a(θ2), …, a(θ K )], where a(θ k ) represents the steering vector of the k-th signal source, and is specifically expressed as follows,

[0016]

[0017] where e represents the natural exponent, π is the circumference ratio. Perform eigenvalue decomposition on R to obtain

[0018] R = U S Σ S U S H + U N Σ N U N H

[0019] where U N represents the noise subspace.

[0020] Furthermore, in step S2, it is necessary to build a D-CRN composed of sub-processors and a fusion center, specifically,

[0021] S21. Build a feature extraction module of Semi-SCV C , specifically,

[0022] S21. Divide U S into N P-dimensional image blocks. Flatten each image block into a vector X P , and then map it to a D-dimensional embedding space through linear projection, specifically expressed as follows,

[0023] z P = EX P + b

[0024] where is the projection matrix, is the bias term, is the embedding representation of the image block.

[0025] Finally, all the image blocks form

[0026] S22. Embed positional encoding in the image patch, obtaining Z = Z + E pos , where is a learnable vector;

[0027] S23. To perform the image classification task, a learnable classification token is added at the beginning of the input sequence to aggregate the information of the entire image. The final input sequence is as follows

[0028] Z = [z class , z1, z2, …, z N

[0029] S24. Feature extraction is performed on the sequence, which includes complex-valued convolutional layers, complex-valued linear layers, and complex-valued activation functions;

[0030] S241. Assume that the complex-valued input of the l-th layer network is h l = m l + jn l , where m l and n l both represent real number vectors. The complex-valued weight matrix is denoted as The complex-valued bias matrix is denoted as where and represent the real parts of the weight matrix and bias matrix of the l-th layer respectively, and W I l and represent the imaginary parts of the weight matrix and bias matrix of the l-th layer respectively. At this time, the convolution operation can be expressed as follows

[0031]

[0032] S242. The complex-valued linear layer can integrate the class-discriminative local information in the convolutional layer. To ensure the integrity of complex numbers, complex arithmetic is used to connect the neurons between adjacent layers, and the process is as follows

[0033]

[0034] S243. The complex-valued LeakyReLU activation function can be expressed as follows

[0035] h l+1 = LeakyReLU(m l ) + jLeakyReLU(n l )

[0036] ​S25. The post - processing module uses the Toeplitz structure to restore u to a noise - free covariance matrix and accurately estimates the angle θ using the classical algorithm Root - MUSIC.

[0037] Furthermore, in step S3, construct the training set of Semi - SCV C . Among them, the amount of labeled data accounts for one - quarter of the total data volume. U S serves as the input data of the Semi - SCV C training set; u serves as the label of the Semi - SCV C training set, and its generation process is as follows.

[0038]

[0039] where R represents the covariance matrix of the received signals of the complete array, R s represents the covariance matrix of the signal source s(t), T(u) represents the Toeplitz matrix, and u is its first - row element.

[0040] Furthermore, in step S4, use the labeled training set and the unlabeled training set to train the Semi - SCV C . When the array receives K angles, the i - th data point is composed of the data pair , thus forming a data set of size , where Therefore, the data set is represented as follows.

[0041]

[0042] where represents the actual output of the k - th signal source in the i - th training set, and u (k,i) represents the label of the k - th signal source in the i - th training set. Take and as the input and expected output of the label data set and the pseudo - label data set to train the Semi - SCV C network, and use the mean - square error between the actual output and the expected output as the loss function, that is

[0043]

[0044] The beneficial effects of the present invention are as follows: On the premise of ensuring the array direction finding accuracy, taking the signal subspace as the network input significantly reduces the scale of the data set and the memory requirements of the processor. Aiming at the problem that label data is difficult to obtain in the actual scenario, a semi-supervised learning strategy is introduced in this paper, and high-precision model training is realized through a small amount of label data combined with the complex-valued operation of the convolutional layer. The simulation results show that this method performs excellently in scenarios with limited memory resources but allowing a relatively high time complexity, providing an effective solution for practical applications. Description of the Drawings

[0045] Figure 1 is a schematic flowchart of the subspace array direction finding method based on semi-supervised learning according to an embodiment of the present invention;

[0046] Figure 2 is the received signal model of the uniform linear array in the embodiment;

[0047] Figure 3 is the architecture diagram of Semi-SCV C in the embodiment;

[0048] Figure 4 is the flowchart of semi-supervised learning in the embodiment;

[0049] Figure 5 is the comparison of the direction-of-arrival estimation performance between the proposed method and the existing methods in the embodiment; where (a) is the comparison of the direction-of-arrival estimation performance with the existing methods under different signal-to-noise ratios, and (b) is the comparison of the direction-of-arrival estimation performance with the existing methods under different snapshots;

[0050] Figure 6 is the comparison of the minimum memory required between the proposed distributed deep learning method and the traditional centralized deep learning method in the embodiment.

[0051] Figure 7 is the performance comparison between the proposed method and the existing methods under the uniform linear array in the embodiment. Detailed Embodiment

[0052] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0053] Embodiment

[0054] As Figure 1-4 shown, the present invention proposes a subspace array direction finding method based on semi-supervised learning, including the following steps,

[0055] S1. Construct the received signal model of the uniform linear array, preprocess the received signal to obtain the covariance matrix R of the received signal, and perform eigenvalue decomposition on R to obtain the signal subspace U S ;

[0056] S2. Build the Subspace Covariance Reconstruction ViT Network Based on Semi-Supervised Learning (Semi-SCV C ), and the network consists of a feature extraction module and a post-processing module;

[0057] S3. Construct the training set of Semi-SCV C , where the training set consists of input data and labels; among them, the signal subspace U S of the received signal is used as the input data of Semi-SCV C ; calculate the noise-free covariance matrix of the array received signal, and extract the first row element u as the label of the training set of Semi-SCV C ;

[0058] S4. Use the training set to train Semi-SCV C , and U S obtains the output through the feature extraction module Take as the input of the post-processing module to obtain the output θ, that is, the required direction-of-arrival estimation.

[0059] In this embodiment, in step S1, it is necessary to first construct the received signal model of the uniform linear array. Specifically,

[0060] S11. The array used at the receiving end is a uniform linear array with M array elements, and the spacing between adjacent array elements is all λ / 2, where λ is the wavelength of the signal, and the reference array element is the central array element of the array, and its coordinates are set to (0,0);

[0061] S12. Suppose K narrowband far-field signal sources are incident from θ = {θ1, θ2,..., θ K} to the uniform linear array composed of M array elements. The signal received by the d-th sub-array at time t is expressed as follows,

[0062]

[0063] where n(t) represents Gaussian white noise, and ∑(·) represents the summation symbol. The array manifold A(θ) = [a(θ1), a(θ2),..., a(θ K )], where a(θ k ) represents the steering vector of the k-th signal source, and is specifically expressed as follows,

[0064]

[0065] where e represents the natural exponential, π is the circumference ratio. Perform eigenvalue decomposition on R to obtain

[0066] R = U S ΣS U S H +U N Σ N U N H

[0067] where U N represents the noise subspace.

[0068] In this embodiment, in step S2, a feature extraction module composed of Semi-SCV C needs to be built. Specifically,

[0069] S21. Divide U S into N P-dimensional image patches. Flatten each image patch into a vector X P , and then map it to a D-dimensional embedding space through linear projection, which is specifically expressed as follows,

[0070] z P = EX P + b

[0071] where is the projection matrix, is the bias term, is the embedded representation of the image patch.

[0072] Finally, all the image patches form

[0073] S22. Embed positional encoding in the image patches, and we can get Z = Z + E pos , where is a learnable vector;

[0074] S23. To perform the image classification task, a learnable classification token is added at the beginning of the input sequence to aggregate the information of the entire image. The final input sequence is as follows,

[0075] Z = [z class , z1, z2,..., z N

[0076] S24. Extract features from the sequence, which includes complex-valued convolutional layers, complex-valued linear layers, and complex-valued activation functions;

[0077] S241. Assume that the complex-valued input of the l-th layer network is h l = m l + jn l , where m l and n l both represent real-valued vectors. The complex-valued weight matrix is expressed as The complex-valued bias matrix is represented as where and represent the real parts of the weight matrix and the bias matrix of the l-th layer respectively, and W I l and represent the imaginary parts of the weight matrix and the bias matrix of the l-th layer respectively. At this time, the convolution operation can be represented as follows,

[0078]

[0079] S242. The complex-valued linear layer can integrate the class-discriminative local information in the convolutional layer. To ensure the integrity of complex data, complex operations are used to connect the neurons between adjacent layers. The process is as follows,

[0080]

[0081] S243. The complex-valued LeakyReLU activation function can be represented as follows,

[0082] h l+1 = LeakyReLU(m l ) + jLeakyReLU(n l )

[0083] S25. The post-processing module uses the Toeplitz structure to restore u to the noise-free covariance matrix and accurately estimates the angle θ using the classical Root-MUSIC algorithm.

[0084] In this embodiment, in step S3, a training set of Semi-SCV C is constructed. Among them, the amount of labeled data accounts for one-fourth of the total amount of data. U S is used as the input data of the training set of Semi-SCV C ; u is used as the label of the training set of Semi-SCV C , and its generation process is as follows,

[0085]

[0086] where R represents the covariance matrix of the received signals of the complete array, R s represents the covariance matrix of the signal source s(t), T(u) represents the Toeplitz matrix, and u is the first row element of it.

[0087] In this embodiment, in step S4, the Semi-SCV C is trained using the labeled training set and the unlabeled training set. When the array receives K angles, the i-th data point is composed of the data pair , thus forming a size of a data set, where Therefore, the data set is represented as follows

[0088]

[0089] where represents the actual output of the k-th source in the i-th training set, and u (k,i) represents the label of the k-th source in the i-th training set. Take and as the input and expected output of the label data set and the pseudo-label data set to train the Semi-SCV C network, and use the mean square error between the actual output and the expected output as the loss function, that is

[0090]

[0091] The simulation experiment of this embodiment is verified as follows:

[0092] Simulation Example 1: Assume that two far-field sources are incident on a uniform linear array of 7 elements, and the number of received snapshots is set to 200. The angles of the far-field sources are [-15.6, 2.3], and the signal-to-noise ratio range is set from -15 dB to 10 dB at intervals of 5 dB. The performance comparison between the method of the embodiment and the existing method under the uniform linear array is as Figure 5 shown, and the comparison of the memory required by the method of the embodiment and the existing deep learning methods is as Figure 6 shown. It can be seen from the figure that the method of the embodiment has better performance than the existing method.

[0093] Simulation Example 2: Assume that four far-field sources are incident on a uniform linear array of 40 elements, and the number of received snapshots is set to 200. The angles of the far-field sources are [-26.1, -8.4, 7.2, 22.6], and the signal-to-noise ratio range is set from -15 dB to 10 dB at intervals of 5 dB. The performance comparison between the method of the embodiment and the existing method under the uniform linear array is as Figure 7 shown. It can be seen from the figure that the method of the embodiment has better performance than the existing method.

[0094] Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A subspace array direction finding method based on semi-supervised learning, characterized in that: Including the following steps, S1. Construct the received signal model of a uniform linear array, preprocess the received signal to obtain the covariance matrix R of the received signal, perform eigenvalue decomposition on R to obtain the signal subspace U S ; S2. Build the Subspace Covariance Reconstruction ViT Network Based on Semi-Supervised Learning, Semi-SCV C , and the network consists of a feature extraction module and a post-processing module; S3. Construct the Semi-SCV C to obtain a training set, which consists of input data and labels; among them, the signal subspace U S of the received signal is used as the input data of the Semi-SCV C ; calculate the noise-free covariance matrix of the array received signal, and extract the first row element u as the label of the training set of the Semi-SCV C ; S4. Use the training set to train Semi-SCV C for training, U S Obtain the output through the feature extraction module Take as the input of the post-processing module to obtain the output θ.

2. The subspace array direction finding method based on semi-supervised learning according to claim 1, characterized in that: In step S1, construct the received signal model of a uniform linear array. Specifically, S11. The array used at the receiving end is a uniform linear array with M array elements. The spacing between adjacent array elements is λ / 2, where λ is the wavelength of the signal. The reference array element is the central array element of the array, and its coordinates are set as (0,0); S12. Assume K narrowband far-field signal sources incident from θ = {θ1, θ2, …, θ K} onto a uniform linear array composed of M array elements. The signal received by the d-th subarray at time t is expressed as follows: where \(n(t)\) represents Gaussian white noise, and \(\sum(\cdot)\) represents the summation symbol; the array manifold \(A(\theta)=[a(\theta_1),a(\theta_2),\ldots,a(\theta K )]\), where \(a(\theta k )\) represents the steering vector of the \(k\)th signal source, and is specifically expressed as follows. where e represents the natural exponential, π is the ratio of a circle's circumference to its diameter; performing eigenvalue decomposition on R gives R = U S Σ S U S H +U N Σ N U N H where U N represents the noise subspace.

3. The subspace array direction finding method based on semi-supervised learning according to claim 2, characterized in that: In step S2, build a feature extraction module of Semi-SCV C , specifically S21. Divide U S into N P-dimensional image patches; flatten each image patch into a vector X P , and then map it to a D-dimensional embedding space through linear projection, which is specifically expressed as follows z P = EX P + b wherein is the projection matrix, is the bias term, is the embedded representation of the image patch; finally, all the image patches form S22. Embed position encoding in the image block to obtain Z = Z + E pos , where is a learnable vector; S23. To perform the image classification task, a learnable classification token is added at the beginning of the input sequence to aggregate the information of the entire image; the final input sequence is as follows, Z = [z class , z1, z2, …, z N ​ S24. Extract features from the sequence, which includes a complex-valued convolutional layer, a complex-valued linear layer, and a complex-valued activation function; S241. Assume that the complex-valued input of the l-th layer network is h l = m l + jn l , where m l and n l both represent real-valued vectors; the complex-valued weight matrix is denoted as The complex-valued bias matrix is denoted as where and represent the real parts of the l-th layer weight matrix and bias matrix respectively, and represent the imaginary parts of the l-th layer weight matrix and bias matrix respectively; at this time, the convolution operation is expressed as follows, S242. The complex-valued linear layer can integrate the class-discriminative local information in the convolutional layer. To ensure the integrity of complex data, complex operations are used to connect the neurons between adjacent layers. The process is as follows, S243. The complex-valued LeakyReLU activation function is expressed as follows, h l+1 = LeakyReLU(m l ) + jLeakyReLU(n l ) S25. The post-processing module uses the Toeplitz structure to restore u to the noise-free covariance matrix, and estimates the accurate angle θ using the classical algorithm Root-MUSIC.

4. The subspace array direction finding method based on semi-supervised learning according to claim 3, characterized in that: In step S3, construct the training set of Semi-SCV C ; among them, the amount of labeled data accounts for one-fourth of the total data volume; U S is used as the input data of the training set of Semi-SCV C ; u is used as the label of the training set of Semi-SCV C The generation process is as follows where R represents the covariance matrix of the received signals of the complete array, and R s represents the covariance matrix of the signal source s(t), T(u) represents the Toeplitz matrix, and u is the elements of its first row.

5. The subspace array direction finding method based on semi-supervised learning according to claim 4, characterized in that: In step S4, the Semi-SCV is trained using the labeled training set and the unlabeled training set C When the array receives K angles, the i-th data point consists of the data pair to form a data set of size where Therefore, the data set is represented as follows Among them represents the actual output of the k-th information source in the i-th training set, u (k,i) represents the label of the k-th information source in the i-th training set; take and as the input and expected output of the label data set and the pseudo-label data set to train the Semi-SCV C network, and use the mean square error between the actual output and the expected output as the loss function, that is

Images