Method for near-field doa estimation based on cckan

Abstract

A near-field DoA estimation method based on CCKAN is proposed. In the offline stage, the received signals of array element channels are simulated. Based on the near-field propagation model, simulated signals affected by near-field effects are generated as a sample set. Feature data of the received signals of each array element channel are extracted from this sample set. Empirical autocorrelation is used to obtain the covariance features of the received signals, which are then used to train the constructed CCKAN. In the online stage, real-time DoA estimation is performed using the trained CCKAN. This invention introduces complex-valued convolution into the Kolmogorov-Arnold network (KAN). By simulating complex-valued operations in the convolution, the intrinsic relationship between signal amplitude and phase is enhanced. Simultaneously, the more interpretable KAN is introduced as a feature extraction method, achieving excellent DoA resolution under both far-field and near-field conditions.

Description

Technical Field

[0001] This invention relates to a technology in the field of wireless communication, specifically a method for near-field direction of arrival (DoA) estimation based on complex-valued convolution and Kolmogorov-Arnold network (CCKAN). Background Technology

[0002] Existing DoA estimation algorithms include the Capon algorithm and the Multiple Signal Classification (MUSIC) algorithm. Capon, an early DoA estimation algorithm, is a beamforming algorithm based on a linearly constrained minimum variance criterion. It estimates the angle of arrival by searching for peaks using a spatial spectral function related to the signal covariance matrix and the array direction vector. The MUSIC algorithm, on the other hand, utilizes the orthogonality of the signal and noise subspaces to construct a spectral function, achieving higher DoA resolution than Capon. By expanding the search space and performing joint estimation of angle and distance, both Capon and MUSIC algorithms can be applied to near-field DoA estimation. However, these traditional methods are based on statistics, and due to statistical instability, they exhibit significant errors when handling samples with low snapshot counts and closely spaced source signals. Existing neural network-based DoA techniques can only handle single signal sources and do not extend the experimental scenario to the near field, resulting in a lack of mechanisms to address the unique signal propagation characteristics of the near-field environment, such as the spherical wave characteristics and distance attenuation effects. Summary of the Invention

[0003] To address the aforementioned shortcomings of existing technologies, this invention proposes a near-field DoA estimation method based on CCKAN. By introducing complex-valued convolutions into the Kolmogorov-Arnold network (KAN), the intrinsic relationship between signal amplitude and phase is enhanced by simulating complex-valued operations in the convolutions. At the same time, the more interpretable KAN is introduced as a feature extraction method, achieving excellent DoA resolution under both far-field and near-field conditions.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a near-field DoA estimation method based on CCKAN. In the offline stage, the received signals of array element channels are simulated. After generating simulated signals affected by near-field effects based on the near-field propagation model as a sample set, the feature data of the received signals of each array element channel are extracted from them. The covariance features of the received signals are obtained by using empirical autocorrelation, and then used to train the constructed CCKAN. In the online stage, real-time DoA estimation is performed using the trained CCKAN.

[0006] The CCKAN comprises: a complex-valued convolutional network and a KAN connected in sequence, wherein: the complex-valued convolutional network performs simulated complex-valued operations based on the covariance feature information of the received signal to obtain intermediate complex-valued features; the KAN network performs feature fusion and regression processing based on the real part, imaginary part and argument information of the intermediate complex-valued features to obtain the DoA estimation result.

[0007] The training specifically includes:

[0008] S1: Load data and randomly select a portion of the test sample set as training data;

[0009] S2: Initialize the CCKAN structure: Set the number of complex-valued convolutional layers to 4, the intermediate output dimension of the KAN to 64, the number of KAN layers to 2, the number of grid intervals for each KAN layer to 5, and the order of the piecewise polynomial to 3.

[0010] S3: Convert the input layer data format, splitting the complex-valued data into real and imaginary parts as input; set the number of output categories for the output layer according to the dataset, and set the number of output categories to be the same as the number of categories in the DoA estimation model.

[0011] S4: CCKAN model training. Train CCKAN using the set parameters and store the model. Calculate the root mean square periodic error (RMSPE) as the evaluation criterion to complete the DoA estimation of the test data.

[0012] Preferably, the batch_size is set to 256, the initial learning rate is 0.001, and the maximum number of training rounds is 100.

[0013] Preferably, after training is completed, by loading data, a portion of the test sample set is randomly selected as validation data to validate the CCKAN model. Specifically, a test sample set is established using the covariance feature data of all received signals. The test sample set includes the training set, validation set, and test set, which are divided in a ratio of 7:1:2, and the training set, validation set, and test set are mutually exclusive. Technical effect

[0014] This invention employs a complex-valued neural network architecture specifically designed to process complex-valued signals received by array element channels. It comprehensively expands the experimental scenario to the near-field domain, specifically adapting to near-field conditions and optimizing the algorithm model and parameter settings. Compared to existing technologies, this invention can directly use the complete complex-valued signal as the input source, abandoning the previous practice of splitting the signal into unrelated real and imaginary parts, thus avoiding information loss caused by splitting and preserving and utilizing the rich information originally carried by the signal. Through in-depth research and optimization for near-field scenarios, it can fully adapt to the unique signal propagation characteristics of the near field, such as the spherical wave characteristics and distance attenuation effects, significantly improving DOA estimation performance under near-field conditions. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention;

[0016] Figure 2 This is a schematic diagram of the CCKAN structure of the present invention;

[0017] Figure 3 A schematic diagram comparing the RMSPE of DoA estimation results with different numbers of snapshots in a near-field environment;

[0018] Figure 4 A schematic diagram comparing the RMSPE of DoA estimation results for closely spaced sources in a near-field environment;

[0019] Figure 5 A schematic diagram comparing the RMSPE of DoA estimation results with different numbers of signal sources in a near-field environment;

[0020] Figure 6 This is a schematic diagram comparing the RMSPE of DoA estimation results for different numbers of signal sources in a far-field environment. Detailed Implementation

[0021] like Figure 1 As shown, this embodiment involves a near-field DoA estimation method based on complex-valued convolution and KAN, including:

[0022] Step 1, Sample Generation, specifically includes:

[0023] 1.1 Modeling of Received Signals: The near-field communication scenario of the simulated signal consists of N access points of uniform linear antennas, with each antenna spaced apart by a distance of 1 / 2. λ is the wavelength, and at each time t∈{1,...,T}, it originates from... and distance source signal vector M represents the number of target sources.

[0024] 1.2 The received signal acquired by the receiver at the t-th sampling snapshot Among them: x(t)=A(θ,r)s(t)+ω(t), The noise vector is (iid); the matrix A(θ,r) consists of the steering vector.

[0025] Step 2, Feature Extraction, specifically includes:

[0026] 2.1 When the sampling time is longer than the coherence time, the covariance matrix of the received signal obtained from a finite number of samplings Specifically: in:(·) HIt is the conjugate transpose; As expected.

[0027] 2.2 Convert the covariance matrix data format to obtain the input data. And input CCKAN, where: and These are the real and imaginary parts of a complex number, respectively.

[0028] like Figure 1 As shown, the CCKAN includes: a complex-valued convolutional network and a KAN, wherein: the complex-valued convolutional network performs complex-valued convolution, complex-valued batch normalization and activation operations on complex-valued inputs to simulate complex-valued operations, and the KAN decomposes complex high-dimensional functions into a series of simpler functions to effectively learn and approximate complex high-dimensional functions.

[0029] The complex-valued convolutional network comprises: a complex-valued convolutional layer, a complex-valued batch normalization layer, and a complex-valued ReLU layer. Specifically: the complex-valued convolutional layer performs complex-valued convolution processing on the input multi-dimensional feature information, extracting complex-valued features from different local regions to obtain intermediate feature results containing hierarchical complex-valued features; the complex-valued batch normalization layer, based on the intermediate feature information output by the complex-valued convolutional layer, performs whitening processing on the complex-valued data in each feature channel, and then uses learnable parameters and scale transformations and offsets to standardize the distribution of the complex-valued data; the complex-valued ReLU layer, based on the normalized complex-valued information output by the complex-valued batch normalization layer, performs element-wise activation operations on the real and imaginary parts of the complex-valued data to obtain the final complex-valued feature result that has been activated and highlights key features.

[0030] The KAN network comprises two KAN layers connected in sequence. The first KAN layer performs initial deep abstraction of the local information based on the complex-valued feature results output by the complex-valued convolutional network, using a function fitting strategy to obtain intermediate feature results with a more ordered function structure. The second KAN layer performs more refined function composition and optimization processing based on the intermediate feature results output by the first KAN layer to obtain the final DoA estimation result.

[0031] The shape of the KAN is [n0,...,n L Between the l-th layer and the (l+1)-th layer, there are n l n l+1 There are several activation functions, specifically: φ l,i,j ,l=0,...,L-1,i=1,...,n l j = 1, ..., n l+1 The calculation process for each KAN layer is as follows:

[0032] The output dimension of the first KAN layer is 64. For each KAN layer, the number of grid intervals is 5, and the order of the piecewise polynomial is 3.

[0033] The simulated complex value operation specifically includes: initial input Let be the empirical covariance matrix. The input, weight matrix, and bias vector of the network at layer l are: Where: u l , Corresponding to y l W l ,b l The real part, v l , Corresponding to y l W l ,b l The imaginary part.

[0034] The complex-valued convolution mentioned above refers to: Where: * represents the convolution operation.

[0035] The aforementioned complex-valued batch normalization refers to: first, whitening the complex-valued data to ensure that each component of the vector has zero mean and unit variance; then, using learnable parameters, scaling and shifting are performed, specifically: Where: γ is the scaling parameter, which is a 2×2 positive semi-definite matrix composed of three learnable components; β is a complex translation parameter composed of two learnable components.

[0036] The activation operation mentioned above refers to: application The activation function applies ReLU to the real and imaginary parts of the input vector, specifically: in: ReLU represents the complex value ReLU, while ReLU(·) represents the real value ReLU.

[0037] 2.3 Calculate the root mean square periodic error (RMSPE) as an evaluation criterion to complete the DoA estimation of the test data. Specifically, this involves using the output of the CCKAN model... Mapped to Use RMSPE to output the model. Compared to the true θ, specifically: in: It is the set of all M×M permutations.

[0038] Through specific practical experiments, under near-field environment settings of target source number M=2, access point N=8, wavelength λ=0.03m, the above model was trained with snapshot number T=2, batch size 256, and learning rate 0.01. The experimental data related to model estimation error and signal-to-noise ratio (SNR) are shown in Table 1. Specific experimental data under other environments are given in the form of figures.

[0039] Table 1. DoA estimation results under different signal-to-noise ratios in the near-field environment. SNR[dB] -20 -15 -10 -5 0 5 10 RMSPE[rad] 0.4947 0.4001 0.1171 0.0540 0.0410 0.0408 0.0352

[0040] like Figure 3 The figure shows the relationship between estimation error and the number of snapshots when M=5. The results show that traditional algorithms crash when the number of snapshots is less than 10, while CCKAN consistently achieves the best estimation, outperforming other neural network models.

[0041] like Figure 4 The figure shows the estimation error when M=2 and the distance between the two signal sources is Δθ. The results show that the error of the traditional algorithm increases significantly when Δθ=5, while the deep learning algorithm exhibits a constant low error for all Δθ values. The CCKAN model can achieve the lowest error in some scenarios, which demonstrates the high resolution of the deep learning algorithm for angle estimation.

[0042] Under near-field and far-field conditions, the relationship between estimation error and the number of sources is as follows: Figure 5 and Figure 6 As shown in the figure, the results indicate that traditional algorithms are significantly affected by the number of sources; as the number of sources increases, the error of traditional algorithms rises rapidly. Deep learning methods exhibit smaller errors when dealing with a large number of sources, and CCKAN achieves the minimum error in most scenarios. Figures 5-6 It also shows that the MUSIC algorithm degenerates under near-field conditions compared to far-field conditions, while CCKAN exhibits better robustness under these conditions.

[0043] Compared with existing technologies, this invention adopts a complex-valued neural network architecture, which is specifically designed to process complex-valued signals received by the pairwise channels; it incorporates key variables unique to the near field, such as spherical waves, distance, and complex interference terms, so that the algorithm fits the real near-field environment from the underlying logic.

[0044] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A method for near-field DoA estimation based on complex-valued convolution and KAN, characterized in that, In the offline phase, the received signals of the array element channels are simulated. The simulated signals affected by the near-field effect are generated as a sample set according to the near-field propagation model. The feature data of the received signals of each array element channel are extracted from them. The covariance features of the received signals are obtained by using empirical autocorrelation, and then used to train the constructed CCKAN. In the online phase, the DoA estimation is performed in real time through the trained CCKAN. The CCKAN comprises: a complex-valued convolutional network and a KAN connected in sequence, wherein: the complex-valued convolutional network performs simulated complex-valued operations based on the covariance feature information of the received signal to obtain intermediate complex-valued features; the KAN network performs feature fusion and regression processing based on the real part, imaginary part and argument information of the intermediate complex-valued features to obtain the DoA estimation result.

2. The method for complex-valued convolution and KAN based near-field DoA estimation according to claim 1, characterized in that, The complex-valued convolutional network comprises: a complex-valued convolutional layer, a complex-valued batch normalization layer, and a complex-valued ReLU layer. Specifically: the complex-valued convolutional layer performs complex-valued convolution processing on the input multi-dimensional feature information, extracting complex-valued features from different local regions to obtain intermediate feature results containing hierarchical complex-valued features; the complex-valued batch normalization layer, based on the intermediate feature information output by the complex-valued convolutional layer, performs whitening processing on the complex-valued data in each feature channel, and then uses learnable parameters and scale transformations and offsets to standardize the distribution of the complex-valued data; the complex-valued ReLU layer, based on the normalized complex-valued information output by the complex-valued batch normalization layer, performs element-wise activation operations on the real and imaginary parts of the complex-valued data to obtain the final complex-valued feature result that has been activated and highlights key features.

3. The method for complex-valued convolution and KAN based near-field DoA estimation according to claim 1, characterized in that, The KAN network includes two KAN layers connected in sequence. The first KAN layer uses a function fitting strategy to perform initial deep abstraction of the local information based on the complex-valued feature results output by the complex-valued convolutional network, and obtains intermediate feature results with a more ordered function structure. The second KAN layer performs more refined function composition and optimization processing based on the intermediate feature results output by the first KAN layer, and obtains the final DoA estimation result. The shape of the KAN is [n0,...,n L Between the l-th layer and the (l+1)-th layer, there are n l n l+1 There are several activation functions, specifically: φ l,i,j ,l=0,...,L-1,i=1,...,n l j = 1, ..., n l+1 The calculation process for each KAN layer is as follows:

4. The near-field DoA estimation method based on complex-valued convolution and KAN according to claim 1 or 2, characterized in that, The analog complex value operation specifically includes: initial input is an empirical covariance matrix, the input, weight matrix and bias vector of the network of the lth layer are in: Corresponding to y l W l ,b l The real part, Corresponding to y l W l ,b l The imaginary part.

5. The near-field DoA estimation method based on complex-valued convolution and KAN according to claim 1 or 2, characterized in that, The complex convolution refers to: wherein * is a convolution operation.

6. The near-field DoA estimation method based on complex-valued convolution and KAN according to claim 2, characterized in that, The aforementioned complex-valued batch normalization refers to: first, whitening the complex-valued data to ensure that each component of the vector has zero mean and unit variance; then, using learnable parameters, scaling and shifting are performed, specifically: Where: γ is the scaling parameter, which is a 2×2 positive semi-definite matrix composed of three learnable components; β is a complex translation parameter composed of two learnable components.

7. The near-field DoA estimation method based on complex-valued convolution and KAN according to claim 2, characterized in that, The activation operation mentioned above refers to: application The activation function applies ReLU to the real and imaginary parts of the input vector, specifically: in: ReLU represents the complex value ReLU, while ReLU(·) represents the real value ReLU.

8. The near-field DoA estimation method based on complex-valued convolution and KAN according to claim 1, characterized in that, The training specifically includes: S1: Load data and randomly select a portion of the test sample set as training data; S2: Initialize the CCKAN structure: Set the number of complex-valued convolutional layers to 4, the intermediate output dimension of KAN to 64, the number of KAN layers to 2, the number of grid intervals for each KAN layer to 5, and the order of the piecewise polynomial to 3. S3: Convert the input layer data format, splitting the complex-valued data into real and imaginary parts as input; set the number of output categories for the output layer according to the dataset, and set the number of output categories to be the same as the number of categories in the DoA estimation model; S4: CCKAN model training. Train CCKAN using the set parameters and store the model. Calculate the root mean square periodic error (RMSPE) as the evaluation criterion to complete the DoA estimation of the test data.

9. The near-field DoA estimation method based on complex-valued convolution and KAN according to claim 8, characterized in that, Once training is complete, the CCKAN model is validated by loading data and randomly selecting a portion of the test sample set as validation data. Specifically, a test sample set is established using the covariance feature data of all received signals. The test sample set includes the training set, validation set, and test set, which are divided in a 7:1:2 ratio and are mutually exclusive.

10. The near-field DoA estimation method based on complex-valued convolution and KAN according to any one of claims 1-9, characterized in that, specifically include: Step 1, Sample Generation, specifically includes: 1.1 Modeling of Received Signals: The near-field communication scenario of the simulated signal consists of N access points of uniform linear antennas, with each antenna spaced apart by a distance of 1 / 2. λ is the wavelength, and at each time t∈{1,...,T}, it originates from... and distance source signal vector M represents the number of target sources; 1.2 The received signal acquired by the receiver at the t-th sampling snapshot in: Let i be the noise vector; matrix A(θ,r) is composed of steering vectors. Step 2, Feature Extraction, specifically includes: 2.1 When the sampling time is longer than the coherence time, the covariance matrix of the received signal obtained from a finite number of samplings Specifically: in:(·) H It is the conjugate transpose; For expectations; 2.2 Convert the covariance matrix data format to obtain the input data. And input CCKAN, where: and These are the real and imaginary parts of a complex number, respectively. 2.3 Calculate the root mean square periodic error (RMSPE) as an evaluation criterion to complete the DoA estimation of the test data. Specifically, this involves using the output of the CCKAN model... Mapped to Use RMSPE to output the model. Compared to the true θ, specifically: in: It is the set of all M×M permutations.

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