A cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method

Abstract

The application relates to the technical field of direction of arrival estimation, and specifically discloses a cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method, which comprises the following steps: firstly, a complex domain CVSIMO learning model is constructed; sampling data is preprocessed; forward propagation of the CVSIMO learning model is carried out; backward propagation and parameter optimization of the CVSIMO learning model are carried out; data reconstruction and signal separation are carried out; cross-platform super-resolution DOA estimation is carried out; and finally, model simulation experiments are carried out. The cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method can realize feature mining of multiple point source signals, converts a multi-source estimation problem into a single point source DOA estimation problem by using a complex domain neural network model, enhances the features of coherent signals by using the advantages of the complex domain neural network, improves the performance and precision of the super-resolution DOA estimation algorithm, can also realize data separation of multiple coherent signals and cross-platform DOA estimation, and realizes real angle estimation through ingenious feature solving.

Description

Technical Field

[0001] This invention relates to the field of direction-of-arrival (DOA) estimation technology, and in particular to a cross-platform complex-domain feature-enhanced coherent super-resolution DOA estimation method. Background Technology

[0002] Direction of arrival (DOA) refers to the direction of arrival of a spatial signal (the direction angle at which each signal arrives at the array reference element, abbreviated as DOA). It is an important concept in spatial spectrum estimation theory, which is one of the two major research directions in array signal processing.

[0003] Typical DOA estimation methods include monopulse angle measurement (amplitude-comparison monopulse, phase-comparison monopulse) and array super-resolution angle measurement. Monopulse angle measurement technology has low computational cost and strong real-time performance, but its accuracy is not high, making it unsuitable for multi-source DOA estimation; it is more suitable for angle estimation problems of coherent sources. Currently, for DOA estimation of coherent signals, array signal processing methods are mainly used. For DOA estimation of coherent sources, classic super-resolution algorithms include Multiple Signal Classification (MUSIC) and Maximum Likelihood (ML). The ML algorithm, which takes into account the statistical distribution characteristics of noise, exhibits superior performance. For single-source signals, the Machine Learning (ML) algorithm can usually be used directly for angle estimation. However, for multi-source estimation problems, the ML algorithm involves multi-dimensional projection matrix calculations, resulting in high computational cost and poor real-time performance. Multi-dimensional iterative optimization algorithms can be used to reduce computational complexity, but the iterative process cannot always optimize to the global optimum, leading to a slight performance loss. If the Music algorithm is used, decoherence processing must be performed first to restore the rank of the covariance matrix. The classic rank restoration method is to use subarray smoothing, i.e., the Spatial Smoothing Music (SSMUSIC) algorithm. Clearly, smoothing causes array aperture loss and degrades angle measurement performance. Furthermore, the Music algorithm involves eigenvalue decomposition, which is computationally intensive. For these super-resolution algorithms, under the ideal far-field plane wave model, good estimation performance can be achieved when the number of snapshots and the signal-to-noise ratio (SNR) are high. However, when the actual received signal model does not meet the requirement of a high degree of matching between the far-field plane wave model and the number of snapshots is small, the performance of the super-resolution algorithm is greatly reduced.

[0004] Artificial intelligence has become one of the hottest topics in society today, mainly due to the rapid development of deep learning. Neural networks are an important model in deep learning, primarily applied in the field of computer vision, where they have achieved many outstanding results. While existing deep learning-based super-resolution algorithms offer high performance, they only utilize the spatial characteristics of the target, i.e., spatial sparsity, learning the mapping relationship between the array's received data and the target's elevation angle through deep neural networks. They lack analysis of the data characteristics of the array's received data itself and require a high number of snapshots from the array's received data.

[0005] However, most neural networks are based on real-number representations, and very few are based on complex-number representations. Recent studies have shown that networks based on complex-number representations have better expressive power than those based on real-number representations. In 2010, Haensch R and Hellwich O applied complex neural networks to classify fully polarimetric synthetic aperture radar images, and experimental results showed that complex networks outperformed fully connected complex networks. In 2016, Danihelka et al. proposed complex long short-term memory networks, achieving better performance than real-number long short-term memory networks. In 2017, Popa et al. proposed multilayer complex neural networks and achieved better performance than real-number neural networks on the MNIST and CIFAR-10 datasets. In 2018, Trabelsi et al. proposed complex-valued residual networks (CResNet), whose core module is the cResNet block. In 2019, Cheng Huitao applied complex neural networks to the reconstruction of MRI data, achieving better results than traditional methods. In 2020, Dang Ze applied cResNet to the identification of wireless communication interference signals, and the identification performance of cResNet was better than that of rResNet.

[0006] Complex-valued neural networks (CV-NN) have a significant advantage in recognition compared to real-valued neural networks (RV-NN). In the case of low-altitude targets, multipath signals can cause amplitude and phase distortion of the target's direct signal, reducing the performance of existing methods in direction-of-arrival (DOA) estimation.

[0007] Therefore, there is an urgent need for a phase enhancement method that utilizes supervised deep neural networks (DNNs) to reduce phase distortion and improve the accuracy of DOA estimation. Summary of the Invention

[0008] The purpose of this invention is to provide a cross-platform coherent super-resolution DOA estimation method with enhanced complex domain features. This method combines supervised deep neural networks (DNNs) with super-resolution DOA estimation techniques. By enhancing the phase of the received signal through a trained DNN network, the accuracy of DOA estimation can be improved. This technique can then be applied to different platforms to solve practical problems.

[0009] To achieve the above objectives, this invention provides a cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method, comprising the following steps:

[0010] S1. Construct a CVSIMO learning model for the complex field;

[0011] S2. Preprocess the sampled data;

[0012] Forward propagation of the S3 and CVSIMO learning models;

[0013] S4, Backpropagation and Parameter Optimization of CVSIMO Learning Model;

[0014] S5, Data Reconstruction and Signal Separation;

[0015] S6, cross-platform super-resolution DOA estimation;

[0016] S7. Conduct model simulation experiments.

[0017] Preferably, in step S1, the complex domain CVSIMO learning model includes a complex-valued input layer, four hidden layers, and K independent complex-valued output layers.

[0018] Preferably, in step S2, the specific process of preprocessing the sampled data is as follows:

[0019] Assume the training set consists of N samples, represented as: Where y(t) represents the t-th sampled data, Let represent the k-th labeled data. Complex Gaussian normalization is applied to the real and imaginary parts of the features of the N samples, as shown below:

[0020] y(t)=A(θ,λ)s(t)+n(t),t=1,2,…,L(1)

[0021] Where R(·) and I(·) are the real and imaginary parts of the complex number, respectively; μ R and μ I σ represents the statistical average of the real and imaginary parts of the training set, respectively; R and σ I The statistical standard deviations of the real and imaginary parts of the training set are respectively expressed as:

[0022]

[0023] Preferably, the specific process of step S3 is as follows:

[0024] Both the hidden layer and the output layer are fully connected layers. Assume the input of the l-th layer is o. l-1 The complex weight matrix is ​​W l The hidden layer is activated by the complex activation function σ. C The output after activation is represented as:

[0025] o l =σ C (z l )=σ(R(z l ))+i·σ(I(Z l (3)

[0026] Where z l =W l o l-1 ;

[0027] For an L-layer fully connected neural network, the output layer consists of K independent fully connected layers. Let W be the weighting matrix of the k-th output layer. L,k Then the output of the k-th output layer is represented as:

[0028] o L,k =σ C (z L,k )=σ C (W L,k o l-1 (4)

[0029] Therefore, the forward propagation of the CVSIMO learning model is represented as:

[0030]

[0031] Preferably, in step S4, the loss of the CVSIMO learning model is expressed as:

[0032]

[0033] Let the parameter update formula for the complex weight matrix W in row p and column q of the l-th layer be:

[0034]

[0035] Where η represents the learning rate, obtained from the chain rule:

[0036]

[0037]

[0038] in, Represents vector z l The p-th element, Represents vector o l-1 Substituting equation (9) into equation (8) for the q-th element, we get:

[0039]

[0040] Among them, let the error term be... Therefore, equation (7) can be expressed as:

[0041]

[0042] When l = L, the error term Represented as:

[0043]

[0044] When l = L-1, the m-th element of the error term is represented as:

[0045]

[0046] in,

[0047]

[0048] Substituting equation (14) into equation (13), we get:

[0049]

[0050] Combining equations (12) and (15), the error term for the l-th layer is summarized as follows:

[0051]

[0052] Next, the Adam algorithm for adaptive moment estimation is used to optimize the weights of the CVSIMO learning model until the learning error converges.

[0053] Preferably, in step S5, after optimizing the CVSIMO model learning model, the CVSIMO model is used to separate the coherent signals of the given data: assuming any test data is y′(t)|λ2 and λ1≠λ2, the test samples are Gaussian normalized using the mean and standard deviation in equation (2), and the processed samples are:

[0054]

[0055] Normalized data The input is fed into the trained SIMO learning model, and through the model's forward propagation process, the K separated signal data outputs are obtained. The K independent outputs are:

[0056]

[0057] Where s′(t) and n′(t) represent the separate signal data and noise data.

[0058] Preferably, in step S6, the array data separated by the CVSIMO model contains only one signal source. The complex domain feature enhancement coherent super-resolution DOA estimation technique is used to enhance the phase of the separated signal through a DNN network to remove noise and other interference before DOA estimation is performed.

[0059] For DOA estimation when the frequency changes across different platforms, the following principle applies:

[0060] Assume the wavelength of the training set samples is λ1, and the angular range of the coherent signal is θ. k ∈[φ1,φ2], the test set is cross-platform sampled data, the wavelength of the test set samples is λ2, which is different from the training set samples, and the angular range of the coherent signal is... and

[0061] The phase features of the training and test set samples are represented as follows:

[0062]

[0063] The phase characteristics of test set Φ2 are obtained by equivalent substitution of λ1:

[0064]

[0065] make in The phase characteristic Φ2 is represented as:

[0066]

[0067] The above variation is consistent with Φ1, which means that changes in wavelength across platforms will cause changes in the angle measured by the DOA, and satisfy the following relationship:

[0068]

[0069] Therefore, DOA under cross-platform conditions is estimated in the following way:

[0070]

[0071] Analyze equation (23) and discuss the range of values ​​for λ1 and λ2. get:

[0072]

[0073] therefore, The range of values ​​for is:

[0074]

[0075] Data separated by the CVSIMO learning network DOA estimation is achieved using classic DBF, MUSIC, and ML algorithms:

[0076] Let the measured angle be θ′. Based on the above correction principle and according to equation (23), the cross-platform DOA estimation result for wavelength λ2 is expressed as follows:

[0077]

[0078] Where θ′ is the angle measurement result of the training set sample, and θ is the expected angle measurement result for the cross-platform output.

[0079] Therefore, the present invention employs the aforementioned cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method, with the following beneficial effects:

[0080] (1) This invention solves the phase distortion problem caused by multipath signals in low-altitude target scenarios by using a supervised deep neural network (DNN) to enhance the phase of the received signal. The phase enhancement method is targeted and accurate, and can improve the accuracy of direction of arrival (DOA) estimation.

[0081] (2) This invention can be applied to different real-world scenarios to solve the problem of cross-platform DOA estimation. By constructing and training a supervised deep neural network model, and then using the trained DNN network to achieve phase enhancement on different platforms, DOA estimation can be performed with high accuracy.

[0082] (3) Traditional coherent signal processing methods may be affected by mutual interference and coupling when there are multiple coherent sources, resulting in inaccurate DOA estimation results. This invention improves the accuracy of DOA estimation by deeply analyzing the coupling effect of coherent signals, mining the potential features of the signal model, and realizing feature mining of multiple point source signals.

[0083] (4) Traditional super-resolution algorithms typically have high computational complexity and are not suitable for real-time applications. This invention utilizes a complex-domain neural network model to transform the multi-source estimation problem into a single-source DOA estimation problem, thereby achieving fast DOA estimation. Complex-domain neural networks have faster learning speeds and richer expressive capabilities, which can improve the real-time performance and overall performance of the algorithm.

[0084] (5) The present invention introduces a complex domain neural network, which, compared with a real domain neural network, can better preserve the information of the array aperture and has a stronger feature extraction and expression capability. By utilizing the advantages of the complex domain neural network, the features of coherent signals are enhanced, and the performance and accuracy of the super-resolution DOA estimation algorithm are improved.

[0085] (6) This invention addresses the problem of mismatched phase distribution characteristics caused by the difference in the frequency (wavelength) of radar signals during actual wartime and non-wartime, and the wavelength difference between training samples and test samples. This technology uses a complex domain data feature separation model to separate the data of multiple coherent signals and perform DOA estimation, and achieves true angle estimation through ingenious feature solving.

[0086] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0087] Figure 1 This is an overall flowchart of an embodiment of a cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method according to the present invention;

[0088] Figure 2 This invention provides a cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method embodiment, which describes the phase characteristics of array received signals at different wavelengths.

[0089] Figure 3 This is a schematic diagram illustrating the impact of wavelength error on algorithm performance in an embodiment of a cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method of the present invention.

[0090] Figure 4 This is an embodiment of the CVSIMO model separating array data of a cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method according to the present invention;

[0091] Figure 5 This is a DNN network architecture diagram of an embodiment of a cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method according to the present invention.

[0092] Figure 6 This is the cross-platform DOA estimation accuracy under the matched signal-to-noise ratio condition in experimental scenario 1 of the embodiment of the cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method of the present invention;

[0093] Figure 7 This is an analysis diagram of the real and imaginary parts of the CVSIMO learning model output under experimental scenario 1 of an embodiment of a cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method of the present invention, where (a) is the real and imaginary parts of the first output of the CVSIMO learning model, and (b) is the real and imaginary parts of the second output of the CVSIMO learning model.

[0094] Figure 8 This is a phase analysis diagram of the CVSIMO learning model output under experimental scenario 1 of an embodiment of a cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method of the present invention, where (a) is the phase distribution of the first output of the CVSIMO learning model; and (b) is the phase distribution of the second output of the CVSIMO learning model.

[0095] Figure 9 This is a spatial spectrum analysis diagram of the CVSIMO learning model output under experimental scenario 1 of an embodiment of a cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method of the present invention, where (a) is the spatial spectrum of the first output of the CVSIMO learning model and (b) is the spatial spectrum of the second output of the CVSIMO learning model.

[0096] Figure 10 This is the cross-platform DOA estimation accuracy under the mismatched signal-to-noise ratio condition in experimental scenario 2 of the embodiment of the cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method of the present invention.

[0097] Figure 11 This is the cross-platform DOA estimation accuracy under the matched channel error condition in experimental scenario 3 of the embodiment of the cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method of the present invention;

[0098] Figure 12 This is an analysis diagram of the real and imaginary parts of the CVSIMO learning model output under experimental scenario 3 of an embodiment of a cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method of the present invention, where (a) is the real and imaginary parts of the first output of the CVSIMO learning model, and (b) is the real and imaginary parts of the second output of the CVSIMO learning model.

[0099] Figure 13 This is a phase analysis diagram of the CVSIMO learning model output under experimental scenario 3 of an embodiment of a cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method of the present invention, where (a) is the phase distribution of the first output of the learning model and (b) is the phase distribution of the second output of the CVSIMO learning model.

[0100] Figure 14 This is a spatial spectrum analysis diagram of the CVSIMO learning model output under experimental scenario 3 of an embodiment of a cross-platform complex domain feature enhancement coherent super-resolution DOA estimation method of the present invention, where (a) is the spatial spectrum of the first output of the CVSIMO learning model and (b) is the spatial spectrum of the second output of the CVSIMO learning model.

[0101] Figure 15This is a cross-platform DOA estimation accuracy diagram under the mismatched channel error condition in experimental scenario 4 of an embodiment of the cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method of the present invention. Detailed Implementation

[0102] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0103] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0104] A cross-platform coherent super-resolution DOA estimation method with complex-domain feature enhancement is proposed. First, training and testing data of multipath signals with low-altitude targets are collected. This data includes the amplitude and phase information of the received signal, as well as the corresponding Direction of Arrival (DOA) labels. Then, a supervised deep neural network (DNN) model is constructed using the training data. During training, the DNN learns the mapping relationship between the original phase difference distribution of the received signal and the desired phase difference distribution. The parameters of the DNN are adjusted through backpropagation and gradient descent optimization to accurately predict the phase enhancement results.

[0105] Next, the phase of the test data is augmented using a trained DNN. The phase of the test data is used as input, and the augmented output is obtained through forward propagation of the DNN model. The augmented phase is then used as input for DOA estimation. Various DOA estimation algorithms, such as the method of arrival (POA) or maximum likelihood estimation, can be used to infer the target's direction of arrival based on the phase information. Applying this trained DNN network to real-world scenarios can solve DOA estimation problems on different platforms, enhancing the applicability of this technique.

[0106] Assume the receiving array is a uniform linear array with M elements, the incident signal wavelength is λ, the element spacing is d = λ / 2, the number of snapshots is L, and K signals originate from angles θ1, θ2, ..., θ k If the signal is incident at a certain point and its model satisfies the far-field plane wave model, then the array-received signal can be expressed as:

[0107] y(t)=A(θ,λ)s(t)+n(t),t=1,2,…,L(1)

[0108] Among them, the array flow pattern matrix A(θ,λ)=[a(θ1,λ),a(θ2,λ),…,a(θ K The complex envelope of the array received signal is s(t) = [s1(t), s2(t), ..., sλ). K (t)] T If the i-th signal source is coherent with the j-th signal source, then the complex envelope of the signal satisfies s.i (t)=ρs j n(t) represents a variable with a mean of zero and a variance of 0. For complex Gaussian white noise, under far-field conditions, the steering vector a(θ) is related to the incident direction of the signal and can be expressed as:

[0109]

[0110] Observing the signal model, it can be seen that the array-received signal y(t) is actually the superposition of K signals at the array, that is:

[0111]

[0112] For the far-field coherent signal given by equation (1), the phase distribution of the array-received data y with a coherence factor of 1 can be expressed as:

[0113]

[0114] For given θ1 and θ2, the phase distribution of Φ is related to the element spacing d and the signal wavelength λ, while the characteristic length is related to the number of elements M. The number of elements M and the element spacing d are array parameters, which remain unchanged in peacetime and wartime, but the wavelength parameters differ between peacetime and wartime. Therefore, for the same radar equipment, even if the location and environment remain unchanged, the signal characteristics received by radar arrays at different wavelengths will be different. Figure 2 Phase characteristics under different wavelengths and different coherent DOAs are given. The array parameters are M = 24, d = 0.5m, θ1 = 0°, θ2 ∈ [2°, 4°, 6°], λ ∈ [1m, 1.2m].

[0115] Depend on Figure 2 As can be seen, even with the same DOA, the wavelength determines the phase characteristics of the signal received by the array. Therefore, the effectiveness and accuracy of phase characterization directly determine the accuracy and performance of DOA estimation.

[0116] For classic super-resolution algorithms, different wavelength errors have a certain impact on the algorithm's performance, such as Figure 3 As shown, the estimation performance of both the ML and MUSIC algorithms improves significantly with increasing SNR. However, the performance of these algorithms degrades significantly when the wavelength error is between 0% and 100%. This means that differences in radar transmitted signal wavelengths across platforms can cause many existing DOA estimation algorithms to fail. Therefore, it is necessary to consider the negative impact of cross-platform signal wavelengths on the characteristics of array received data in order to improve the performance of data-driven DOA estimation algorithms.

[0117] A cross-platform method for coherent super-resolution DOA estimation with complex domain feature enhancement, specifically including the following steps:

[0118] S1. Construct a CVSIMO learning model for the complex field;

[0119] For the problem of DOA estimation of coherent signals, the classic super-resolution algorithm requires a K-dimensional search to estimate the angle of the K signals, which is computationally intensive and has poor real-time performance. Therefore, this invention constructs a complex-domain CVSIMO learning model, such as... Figure 4 As shown, the complex domain CVSIMO learning model includes a complex-valued input layer, four hidden layers, and K independent complex-valued output layers.

[0120] The algorithm proposed in this invention combines a Complex-Valued Neural Network (CV-NN) model with the angle estimation problem of multi-source signals. It learns the mapping relationship between the array-received signal y(t) and the K signals received by the array, achieving the separation and angle estimation of the K mixed coherent signals. For the CV-NN model, its network input is the real and imaginary parts of the array-received data y(t), and the K output label features of the CV-NN model are a(θ). k ,λ)s k The real and imaginary parts of (t) are used to update the network parameters using the backpropagation algorithm, so that the actual output of the network approximates the label, and the sum of the K outputs is... Approximating y(t). When the network training error converges, the CV-NN model achieves the separation and extraction of K information sources. For the K outputs of the CV-NN model, the array received data is reconstructed, and the angle estimation of the K information sources can be achieved using conventional algorithms such as DBF.

[0121] S2. Preprocess the sampled data, the specific process is as follows:

[0122] Assuming the training set consists of N samples, it can be represented as: Where y(t) represents the t-th sampled data, Representing the k-th labeled data, to eliminate the influence of the size of each dimension of features on the learning of the neural network model, the real and imaginary parts of the N sample features are subjected to complex-valued Gaussian normalization, as shown below:

[0123]

[0124] Where R(·) and I(·) are the real and imaginary parts of the complex number, respectively; μ R and μ I σ represents the statistical average of the real and imaginary parts of the training set, respectively; R and σ I The statistical standard deviations of the real and imaginary parts of the training set, respectively, can be expressed as:

[0125]

[0126] The forward propagation of the S3 and CVSIMO learning models is as follows:

[0127] Both the hidden layer and the output layer are fully connected layers. Assume the input of the l-th layer is o. l-1 The complex weight matrix is ​​W l The hidden layer is activated by the complex activation function σ. C The output after activation can be represented as:

[0128] o l =σ C (z l )=σ(R(z l ))+i·σ(I(Z l (7)

[0129] Where z l =W l o l-1 ;

[0130] For an L-layer fully connected neural network, the output layer consists of K independent fully connected layers. Let W be the weighting matrix of the k-th output layer. L,k Then the output of the k-th output layer can be expressed as:

[0131] o L,k =σ C (z L,k )=σ C (W L,k o l-1 (8)

[0132] Therefore, the forward propagation of the CVSIMO learning model can be expressed as:

[0133]

[0134] S4. Backpropagation and parameter optimization of the CVSIMO learning model. The loss of the CVSIMO learning model is expressed as:

[0135]

[0136] Let the parameter update formula for the complex weight matrix W in row p and column q of the l-th layer be:

[0137]

[0138] Where η represents the learning rate, we can obtain the following based on the chain rule:

[0139]

[0140] in, Represents vector z l The p-th element, Represents vector o l-1 The q-th element. Substituting equation (13) into equation (12) yields:

[0141]

[0142] Among them, let the error term be... Therefore, equation (11) can be expressed as:

[0143]

[0144] When l = L, the error term It can be represented as:

[0145]

[0146] When l = L-1, the m-th element of the error term can be represented as:

[0147]

[0148] in,

[0149]

[0150] Substituting equation (18) into equation (17), we get:

[0151]

[0152] Combining equations (16) and (19), the error term for the l-th layer can be summarized as follows:

[0153]

[0154] Next, the Adam algorithm for adaptive moment estimation is used to optimize the weights of the CVSIMO learning model until the learning error converges.

[0155] S5, Data Reconstruction and Signal Separation;

[0156] After optimizing the CVSIMO model, the coherent signal separation for any given data is achieved using the CVSIMO model: assuming any test data is y′(t)|λ2 and λ1≠λ2. To ensure that the test samples and training samples have the same feature distribution, the test samples are Gaussian normalized using the mean and standard deviation in equation (6). The processed samples are:

[0157]

[0158] Normalized data The input is fed into the trained SIMO learning model. Through the model's forward propagation process, the outputs of the separated K signal data can be obtained. The K independent outputs are:

[0159]

[0160] Where s′(t) and n′(t) represent the separate signal data and noise data.

[0161] The goal of the data reconstruction process is to restore the original array data representation from the data after normalization and CVSIMO model processing, and then use this data for DOA estimation.

[0162] S6, cross-platform super-resolution DOA estimation;

[0163] Since the array data separated by the CVSIMO model contains only one signal source, complex domain feature enhancement coherent super-resolution DOA estimation can be used. This involves first passing the separated signal through a DNN network for phase enhancement and noise removal before DOA estimation, effectively improving estimation accuracy. The phase-enhanced DNN network architecture is as follows: Figure 5 As shown.

[0164] For DOA estimation when the frequency changes across different platforms, the following principle can be used for correction:

[0165] Assume the wavelength of the training set samples is λ1, and the angular range of the coherent signal is θ. k ∈[φ1,φ2]. The test set is cross-platform sampled data. The wavelength of the test set samples is λ2, which differs from that of the training set samples. The angular range of the coherent signal is... and

[0166] The phase features of the training and test set samples can be represented as:

[0167]

[0168] The phase characteristics of test set Φ2 can be obtained by equivalent substitution of λ1:

[0169]

[0170] make in The phase characteristic Φ2 can be expressed as:

[0171]

[0172] The above variation is consistent with Φ1, which means that changes in wavelength across platforms will cause changes in the angle measured by the DOA, and satisfy the following relationship:

[0173]

[0174] Therefore, DOA under cross-platform conditions can be estimated in the following way:

[0175]

[0176] Analyze equation (27) and discuss the range of values ​​for λ1 and λ2. get:

[0177]

[0178] therefore, The range of values ​​for is:

[0179]

[0180] The wavelength λ1 of the training set samples is usually fixed, so accurate DOA estimation can be achieved by adjusting the wavelength λ2 of the test set samples.

[0181] Data separated by the CVSIMO learning network DOA estimation can be achieved using classic algorithms such as DBF, MUSIC, and ML.

[0182] Let the measured angle be θ′. Based on the above correction principle and according to equation (27), the cross-platform DOA estimation result for wavelength λ2 can be expressed as:

[0183]

[0184] Where θ′ is the angle measurement result of the training set sample, and θ is the expected angle measurement result for the cross-platform output.

[0185] Using this transformation formula, phase-enhanced super-resolution DOA estimation technology can still be applied as long as the cross-platform frequency relationship is known. Simply separate the original platform echo data using a CVSIMO learning model, perform phase enhancement and DOA estimation using a DNN network, and then correct it according to the transformation formula to achieve accurate phase-enhanced super-resolution DOA estimation.

[0186] S7. Conduct model simulation experiments.

[0187] The technology model is simulated and enhanced through training, and then applied in practice to solve the DOA estimation problem on different platforms.

[0188] To verify the effectiveness and robustness of the cross-platform complex domain feature enhancement coherent super-resolution DOA estimation technique of this invention, the following simulation experiments were conducted.

[0189] In this experiment, the array structure was a uniform linear array with 24 elements and a spacing of 0.5m, containing two coherent signals. The wavelength of the signal in the training sample was λ1 = 1m, and the wavelength of the signal in the test sample was λ2 = 1.2m. A feature mismatch existed between the training and test samples. Beamwidth θ 3dB The asymptotic value is 4.2°. The CVSIMO model is as follows: Figure 4 As shown, the learning model consists of one complex-valued input layer, four complex-valued hidden layers, and K independent complex-valued output layers. The non-linear activation function used is the CReLU function, with a learning rate of 0.00005, β1 = 0.9, β2 = 0.99, and ε = 10. -8 The Adam optimizer. The expression for the CReLU activation function is:

[0190] CReLU(x)=ReLU(R(x))+i·ReLU(I(x))(31)

[0191] The performance of this technique can be evaluated using the root mean square error of the angle, as follows:

[0192]

[0193] Where P is the number of Monte Carlo experiments. and This represents the DOA estimation result of the p-th test sample of two coherent signals. and These represent their actual angle values.

[0194] Experimental Scenario 1: Cross-platform DOA estimation accuracy analysis when matching SNR of test and training samples

[0195] In this scenario, the performance of a cross-platform DOA estimation algorithm under the condition of matching signal-to-noise ratio (SNR) parameters for training and test samples is analyzed. Assume there are two coherent signals, and the DOA satisfies θ1~U(2°,5°) and θ2~U(-3°,0°), considering both cases within and outside the beamwidth. A 50% channel error is also considered, with the SNR variation range of the training and test sets being 0dB-10dB and the sampling interval being 2dB. 6000 randomly generated samples are used as the training set to train the CVSIMO learning network, and 6000 samples are generated as the test set to evaluate the proposed algorithm's performance on DOA estimation. The RMSE relationship curve between SNR and DOA estimation is shown below. Figure 6 As shown.

[0196] As can be seen, even if the wavelength parameters of the training set and the test set do not match, the proposed algorithm can still perform DOA estimation effectively and outperforms the classic digital beamforming (DBF) algorithm, ML algorithm and MUSIC algorithm. The model performance is better than the RVSIMO learning model in the real domain.

[0197] Furthermore, the proposed algorithm was compared with existing Support Vector Regression (SVR), Real-Imaginary Part Learning (REMLE), and Phase Enhancement Learning (PEMLE) algorithms. The results show that the proposed algorithm outperforms existing machine learning algorithms. With increasing signal-to-noise ratio (SNR), the angle error of the three algorithms decreased from 0.8° to 0.5° after CVSIMO model separation, and their performance was roughly equivalent. This is because the separated data contains only a single signal source, and the three algorithms exhibit similar estimation performance in single-source estimation. This also implies that for coherent source scenarios, after CVSIMO model separation, the computationally inefficient DBF algorithm can be used to achieve super-resolution DOA estimation.

[0198] To verify the effectiveness of the proposed CVSIMO learning model in coherent source signal separation, samples with θ1 = 3.4° and θ2 = -2.8° were randomly selected to compare the data distribution of the separated signal and the real signal. Since the CVSIMO learning model contains two independent signal output layers, such as... Figure 7 As shown, the distribution of the real and imaginary features of the two signals output by the CVSIMO learning model is presented.

[0199] It can be seen that although the data features output by CVSIMO contain errors, the trend of feature changes is similar to that of the real data. This means that the CVSIMO learning model can effectively mine the distribution features of the data and can separate coherent source data into two single-source data. The corresponding phase distribution is as follows: Figure 8 As shown.

[0200] The separated signal satisfies the far-field plane wave model, and its phase distribution exhibits good linearity, with its variation trend basically consistent with the ideal phase. Similarly, the separated data are analyzed using the DBF and MUSIC algorithms, and their spatial spectra are shown below. Figure 9 As shown, after the echo signal is separated by the CVSIMO model, the spatial spectrum peak positions of the DBF algorithm and the MUSIC algorithm are closer to the true values, and the error is smaller.

[0201] Experimental Scenario 2: Cross-Platform Generalization Analysis of SNR

[0202] Typically, the signal-to-noise ratio (SNR) of the test set samples differs from that of the training set samples. Therefore, it is necessary to analyze the reliability of the proposed algorithm under SNR mismatch conditions. Thus, with the training set sample parameters unchanged, the SNR of the test set samples is varied from -3dB to 13dB in a step of 2dB, ensuring that the SNR difference between the training and test set samples is greater than 1dB. The curve between the SNR estimated by DOA and RMSE is shown below. Figure 10 As shown.

[0203] Even with imperfect signal-to-noise ratio (SNR) parameters, the algorithm proposed in this invention can still effectively achieve DOA estimation across platforms. Furthermore, its performance surpasses that of classic DBF, MUSIC, and ML algorithms, and its model performance outperforms the RVSIMO learning model, as well as existing support vector regression (SVR), real-imaginary learning, and phase enhancement learning algorithms. Therefore, the proposed algorithm exhibits excellent generalization ability for the SNR parameters of samples.

[0204] Experimental Scenario 3: Cross-Platform DOA Estimation Accuracy and Channel Error

[0205] In this scenario, the impact of array channel error on the performance of the proposed algorithm will be further analyzed. It is assumed that the signal-to-noise ratio (SNR) of both the training and test sets is 10 dB, and the channel error of both sets varies from 0% to 50% in 10% increments. 6000 samples are randomly generated for training the CVSIMO learning model, and another 6000 samples are generated for testing. The relationship between channel error and DOA estimation error is shown in the curve below. Figure 11 As shown.

[0206] As channel error increases, the performance of various algorithms degrades significantly, but the algorithm proposed in this invention still exhibits optimal performance. For the classic ML algorithm, the error increases from 0.4° to 0.67°; using a real-domain SIMO learning model, the performance of the three algorithms increases from 0.28° to 0.32°; and when employing existing SVR, real-imaginary learning, and phase-enhancing learning algorithms, the error increases significantly. Specifically, the error of the phase-enhancing learning algorithm increases from 1.00° to 1.40°; the SVR learning algorithm from 0.77° to 0.90°; and the real-imaginary learning algorithm from 0.70° to 0.73°. However, the complex-domain SIMO learning model proposed in this invention increases the performance of the three algorithms from 0.25° to 0.29°. Therefore, the algorithm proposed in this invention is also applicable to the DOA estimation problem under imperfect array conditions.

[0207] Furthermore, this invention also randomly selected a data sample with a channel error of 50%, and the angles of the coherent sources were 3.3° and -2.3°, respectively. The real / imaginary part features and phase features of the data separated by the CVSIMO learning model are as follows: Figure 12 and Figure 13 As shown, the CVSIMO learning model can accurately separate data from two coherent sources. The real and imaginary features of the data can approximate the ideal values, and the corresponding phase distribution features have a high degree of agreement with the ideal phase distribution features.

[0208] Figure 14 The spatial spectra of the DBF and MUSIC algorithms are presented. It can be seen that the data spatial spectrum separated by the CVSIMO learning model is clearer and has a smaller error compared to the true DOA.

[0209] Experimental Scenario 4: Cross-Platform Generalization Analysis of Channel Error

[0210] Furthermore, the general applicability of the proposed algorithm to channel error was analyzed. The parameters of the training set remained unchanged, while the channel error of the test set increased from 5% to 65% in 10% increments, and the channel errors of both the training and test sets were kept greater than 5%. Figure 15 The DOA estimation error curve for channel error mismatch is given.

[0211] As can be seen, the algorithm proposed in this invention still exhibits the best generalization performance. Even under channel error mismatch, the proposed algorithm has the smallest angle error, while the error of the classic ML algorithm increases from 0.41° to 0.85°. If a real-domain SIMO learning model is used, the performance of the three algorithms increases from 0.29° to 0.36°. If existing support vector regression (SVR), real-imaginary learning, and phase enhancement learning algorithms are used, the algorithm errors will increase significantly. Specifically, the estimation error of the phase enhancement learning algorithm increases from 0.97° to 1.55°; the error of the SVR learning algorithm increases from 0.77° to 0.92°; and the estimation error of the real-imaginary learning algorithm increases from 0.69° to 0.75°. However, using the complex-domain SIMO learning model proposed in this paper, the performance of the three algorithms increases from 0.25° to 0.33°.

[0212] In summary, the technology provided by this invention can fully solve the DOA estimation problem on different platforms and has good generalization ability for parameters such as signal-to-noise ratio and channel error.

[0213] Therefore, this invention employs a cross-platform complex-domain feature-enhanced coherent super-resolution DOA estimation method. By training a DNN to learn the mapping relationship between the original phase difference distribution and the desired phase difference distribution of the received signal, the phase of test data from different platforms (different frequency signals) can be enhanced. The enhanced phase is then applied to DOA estimation. Simulation experiments demonstrate the effectiveness and superiority of this method. Experimental results show that this technique exhibits better performance than existing methods such as physics-driven DOA estimation, feature inversion, and support vector regression (SVR) in terms of estimation error and goodness of fit.

[0214] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A cross-platform method for coherent super-resolution DOA estimation with complex domain feature enhancement, characterized in that, Includes the following steps: S1. Construct a complex-domain CVSIMO learning model; the complex-domain CVSIMO learning model includes a complex-valued input layer, four hidden layers, and K independent complex-valued output layers; S2. Preprocess the sampled data; The forward propagation of the S3 and CVSIMO learning models is as follows: Both the hidden layer and the output layer are fully connected layers. Assume the first... l The input of the layer is The complex weight matrix is The hidden layer is activated by a complex activation function. The output after activation is represented as: （3） in , and These are used to solve for the real and imaginary parts of a complex number, respectively. For a L A fully connected neural network with layers, the output layer consisting of... K It consists of several independent fully connected layers, assuming the first... k The weighting matrix of each output layer is: Then the first k The output of each output layer is represented as follows: （4） Therefore, the forward propagation of the CVSIMO learning model is represented as: （5）； in, Representing the t One sampled data; S4, Backpropagation and Parameter Optimization of CVSIMO Learning Model; S5, Data Reconstruction and Signal Separation; S6. Cross-platform super-resolution DOA estimation: The array data separated by the CVSIMO model contains only one signal source. The complex domain feature enhancement coherent super-resolution DOA estimation technique is used to enhance the phase of the separated signal through a DNN network to remove noise interference before DOA estimation. For DOA estimation when the frequency changes across different platforms, the following principle applies: Assume the wavelength of the training set samples is The angular range of the coherent signal is The test set consists of cross-platform sampled data, and the wavelength of the test set samples is... Unlike the training set samples, the angular range of the coherent signal is ,and ; The phase features of the training and test set samples are represented as follows: （19） test set The phase characteristics are obtained by analyzing the phase characteristics of ... Equivalent substitution yields: （20） make ,in Phase characteristics Represented as: （21） The above variations and Consistency means that changes in wavelength across platforms will cause changes in the angle measured by the DOA, and the following relationship must be satisfied: （22） Therefore, DOA under cross-platform conditions is estimated in the following way: （23） Analysis (23), Discussion and The range of values ​​for , due to ,get: （24） therefore, The range of values ​​for is: （25） Data separated by the CVSIMO learning network DOA estimation is achieved using classic DBF, MUSIC, and ML algorithms: Record the measured angle as... Based on the above correction principle, according to equation (23), the wavelength is obtained as The cross-platform DOA estimation results are expressed as follows: （26） in, The angle measurement results for the training set samples, To obtain the desired angle measurement results across platforms, the separated angles are obtained through the forward propagation process of the CVSIMO model. K The output of each signal data, K Each independent output is , ; S7. Conduct model simulation experiments.

2. The cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method according to claim 1, characterized in that, In step S2, the specific process of preprocessing the sampled data is as follows: Assume the training set consists of N Composed of 10 samples, represented as: ,in Representing the t One sampled data, Representing the k-th labeled data, for N The real and imaginary parts of each sample feature are subjected to complex-valued Gaussian normalization, as shown below: （1） in, and These are used to solve for the real and imaginary parts of a complex number, respectively. and represent the statistical averages of the real and imaginary parts of the training set, respectively; and The statistical standard deviations of the real and imaginary parts of the training set are respectively expressed as: （2）。 3. The cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method according to claim 1, characterized in that, In step S4, the loss of the CVSIMO learning model is expressed as follows: （6） Let the first l layer p OK q Complex weight matrix of columns W The parameter update formula is: （7） in The learning rate, derived from the chain rule, is: （8） （9） in, Representing vectors The p One element, Representing vectors The q Substituting equation (9) into equation (8) for each element, we get: （10） Among them, let the error term be... Therefore, equation (7) can be expressed as: （11） when l=L At that time, the error term Represented as: （12） when l=L-1 When, the first error term m Each element is represented as: （13） in, （14） Substituting equation (14) into equation (13), we get: （15） Combining equations (12) and (15), the first... l The layer error term is summarized as follows: （16） Next, the Adam algorithm for adaptive moment estimation is used to optimize the weights of the CVSIMO learning model until the learning error converges.

4. The cross-platform complex domain feature-enhanced coherent super-resolution DOA estimation method according to claim 3, characterized in that, In step S5, after optimizing the CVSIMO model, the CVSIMO model is used to separate the coherent signals of the given data: assuming any test data is... and The test sample was normalized using the mean and standard deviation from equation (2) using Gaussian normalization. The processed sample is as follows: （17） Normalized data The input is fed into the trained SIMO learning model, and through the model's forward propagation process, the separated... K The output of each signal data, K Each independent output is: （18） in, and This represents the separated signal data and noise data.

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