A Broadband Signal Direction-of-Arrival Estimation Method Based on Virtual Interference Suppression

Abstract

This invention belongs to the field of broadband array signal processing technology, specifically relating to a broadband signal direction-of-arrival (DOA) estimation method based on virtual interference suppression. The method comprises the following steps: Dataset construction: Based on simulation data, array observation covariance matrices with different signal-to-noise ratios and directions, along with corresponding virtual interference matrices, are generated. These matrices are then preprocessed and post-processed, and the processed matrices are used as samples and labels in the dataset. Model training: A machine learning model is trained using the constructed dataset. DOA estimation: The preprocessed array output vector covariance matrix is ​​input into the trained machine learning model. The virtual interference matrix is ​​obtained from the machine learning model's output and then rank-1 covariance matrix is ​​obtained through loading. Finally, the spatial spectrum is estimated using a subspace orthogonality method, and the direction corresponding to the peak position of the spatial spectrum is the DOA.

Description

Technical Field

[0001] This invention belongs to the field of broadband array signal processing technology, specifically relating to a broadband signal direction-of-arrival estimation method based on virtual interference suppression. Background Technology

[0002] Wideband array signal processing has broad application prospects in military and civilian fields such as high-resolution radar, phased array radar, sonar, wireless communication (spread spectrum, orthogonal frequency division multiplexing, massive MIMO), earthquake monitoring, teleconferencing, intelligent voice interaction-automatic guidance, and smart security. One of the main problems in wideband array signal processing is determining the direction of arrival (DOA) of the signal. In some cases, it is also necessary to consider the estimation of signal power spectral density, average power, waveform parameters, and polarization state.

[0003] Under broadband conditions, the components corresponding to the same signal in the outputs of different sensors are not perfectly correlated (incoherent), meaning they do not satisfy the rank-1 model assumption (under noiseless, single-polarization, and single-signal conditions, the rank of the array output covariance matrix is ​​greater than 1). Signal direction-of-arrival (DOA) estimation methods based on the narrowband assumption and the rank-1 model generally cannot be directly applied. Currently, most broadband array signal DOA estimation methods are based on rank-1 analysis / operations of array observations (using approximations or transformations, or making special assumptions about the signal), and are combined with methods originally designed for narrowband models, such as maximum likelihood estimation, beam scanning, subspace separation (orthogonal subspace projection spectrum search, rotation-invariant closed-form solution, etc.), and sparse reconstruction.

[0004] Depending on the processing domain, methods for estimating the direction of arrival (DOA) of broadband signals can be broadly classified into two categories: frequency domain methods and time domain methods.

[0005] Frequency domain methods refer to estimation methods performed partially or entirely in the frequency domain. Examples include the frequency domain sub-band method proposed in the 2008 paper "An Improved RSS Algorithm for Broadband Signal Direction of Arrival Estimation" (Journal: Communication Technology, pp. 27-29) by Li Feng et al., and the 2022 patent application "A Broadband DOA Estimation Method Based on Microphone Array" (Patent No.: CN114639398A) by Huang Jiyan et al. This method transforms the array's time-domain observations to multiple frequency domain sub-bands using finite-time Fourier transform or narrowband filter banks. When the array observation time is much longer than the signal correlation time and the propagation delay of the signal wave sweeping across the entire array, the sub-band data received by each array element tends to be asymptotically uncorrelated. That is, when each sub-band data satisfies the rank-1 model, beam scanning or subspace decomposition methods can be used for direction of arrival estimation. Another example is the frequency domain delay compensation algorithm for broadband DOA estimation proposed in the 2018 paper "Frequency Domain Delay Compensation Algorithm for Broadband DOA Estimation" by Zhang Xingliang et al. The frequency domain alignment method proposed in (Journal: Journal of Electronics, Pages: 1633-1638) involves frequency shifting of the output of each array element in the frequency domain according to each scanning angle to achieve time delay compensation. This ensures that when the scanning angle equals the true direction of arrival (DOA) of a signal, the signal in that direction is approximately aligned, degenerating into a rank-1 model. A class of frequency domain sparse reconstruction methods proposed in the patents filed by Xie Shuguo et al. in 2021, namely "A Broadband Signal DOA Estimation Method Based on L1 Norm Sparse Representation" (Patent No.: CN112924924A) and Wu Xiaohuan et al. in 2021, namely "A Weighted Broadband Direction of Arrival Estimation Method Based on Group Sparseness" (Patent No.: CN113267746A), transform array observations into multiple sub-bands in the frequency domain. Sparse representation is performed on the data of each sub-band, and then parallel or joint sparse reconstruction techniques are used for DOA estimation. The English literature "Multisnapshot" further supports this approach. The frequency domain probabilistic inference method proposed in "Sparse Bayesian learning for DOA[J].IEEE Signal Processing Letters,2016,23(10):1469-1473" assumes that the signal model of each sub-band in the frequency domain follows a probabilistic model with a known structure. It uses the joint maximum likelihood function or the joint posterior probability density function as the optimization objective and solves for the unknown direction-of-arrival parameters through an iterative inference algorithm. The frequency domain modeling methods mentioned above all have approximations and errors in nature, and are also computationally cumbersome and complex.

[0006] The time-domain method refers to the estimation method performed entirely in the time domain, without the need for subband decomposition or other operations. Its core idea is to use the time delay information of the same incident signal between array elements, and to construct the array manifold matrix by using the signal sampling theorem or normalized autocorrelation function as a bridge. Then, it combines a mathematical model similar to narrowband to design subsequent estimation algorithms. For example, the temporal subspace decomposition method, as proposed in the English paper "Wideband modal orthogonality: A new approach for broadband DOAestimation[J].Signal Processing,2020,176:107696", uses the time delay information of the signal between array elements and the normalized autocorrelation function of the signal to fit the spatiotemporal covariance matrix. Its principal eigenvector is the steering vector of the signal, and finally the spatial spectrum is constructed by utilizing the orthogonality between the steering vector and the noise subspace. The temporal sparse reconstruction method, proposed by Liu Zhangmeng et al. in their 2011 paper "Direction-of-arrival estimation of wideband signals via covariance matrix sparse representation", uses the array covariance matrix vector as the observation, the normalized autocorrelation coefficient matrix as the complete matrix, and the signal power vector as the sparse vector to construct a sparse representation model. Finally, it is solved using a relaxation optimization method to achieve direction-of-arrival estimation. The temporal probabilistic inference method, as proposed in the English paper "Wideband arraysignal processing using MCMC methods[J].IEEE Transactions on The paper "SignalProcessing, 2005, 53(2):411-426" proposes a method based on signal sampling and reconstruction, using the time delay information of the signal between array elements and the interpolation sinc function to construct the array manifold matrix, and finally using the Markov chain Monte Carlo method to estimate the direction of arrival.

[0007] The problem of direction-of-arrival (DOA) estimation for broadband array signals under multi-source conditions faces several unique constraints. For example, the array aperture, the number of spatially uniform sampling elements, and the processing capacity are limited by the finite correlation time of the signal being processed. The propagation delay of the signal across the entire observation array cannot exceed the signal's own correlation time, ensuring that components corresponding to the same signal in different sensor outputs have a certain degree of correlation. This guarantees a certain degree of spatial aperture effectiveness and a small mismatch in the frequency domain rank-1 model. This requirement significantly limits the application of existing mainstream methods when the signal itself has a wide bandwidth (small correlation time), leading to a sharp decline in algorithm performance. Summary of the Invention

[0008] In view of this, the present invention aims to address the problem that the performance of existing broadband direction-of-arrival estimation methods under finite aperture conditions is limited by the bandwidth of the signal itself. It provides a broadband signal direction-of-arrival estimation method based on virtual interference suppression, which uses a machine learning model to reconstruct the virtual interference matrix to achieve rank-1 operation of broadband array time-domain observation, thereby solving the rank expansion problem of broadband array time-domain observation as the signal bandwidth increases.

[0009] The technical solution for implementing the present invention is as follows:

[0010] A broadband signal direction-of-arrival estimation method based on virtual interference suppression is described below:

[0011] Dataset Construction: Generating array observation covariance matrices with different signal-to-noise ratios and orientations based on simulation data. and the corresponding virtual interference matrix right and Preprocessing and postprocessing are performed to process the resulting... and As samples and labels for the dataset;

[0012] Model training: Training machine learning models using the constructed dataset;

[0013] Direction of arrival (DOA) estimation: This involves estimating the actual measured array output vector covariance matrix. After preprocessing, the data is input into a trained machine learning model, and a virtual interference matrix is ​​obtained based on the model's output. pass load The rank-1 covariance matrix is ​​obtained by means of the subspace orthogonal method, and finally the direction corresponding to the peak position of the spatial spectrum is estimated as the direction of arrival.

[0014] Furthermore, the preprocessing described in this invention is as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] The real and imaginary parts of the top diagonal elements are vectorized by row and then stacked together to form a vector. Remove vector middle The simplified vector z is obtained by taking the imaginary part of the diagonal element.

[0015] Further, the post-processing described in this invention is as follows: ... The real and imaginary parts of the top diagonal elements are vectorized by row and then stacked together to form a vector. Remove vector middle The imaginary part of the diagonal elements yields the simplified target vector d.

[0016] Furthermore, the present invention constructs a dataset for training. For the input sample space, For the real number field, y n Let N be an element of the target vector d, and N be the number of samples.

[0017] Furthermore, the machine learning model of this invention is an SVR model, a feedforward neural network model, a radial basis function network model, a long short-term memory network model, or a convolutional neural network model.

[0018] Furthermore, the machine learning model described in this invention comprises multiple SVR models, with a total number of L. 2 indivual.

[0019] Furthermore, during the training process, this invention transforms the convex optimization problem of the SVR model into a dual problem:

[0020]

[0021] Where, α n and α′ n For Lagrange multipliers, κ(z) n ,z m )=[φ(z n )] T φ(z m ) is the kernel function.

[0022] Furthermore, the present invention describes the method of... load The rank-1 covariance matrix is ​​obtained in this way. Finally, the spatial spectrum is estimated using the subspace orthogonality method. The direction corresponding to the peak position of the spatial spectrum is the direction of arrival. The specific process is as follows:

[0023] Based on the output of the virtual interference matrix calculate

[0024] Regarding the Perform eigenvalue decomposition;

[0025]

[0026] Where V is a unitary matrix, and its columns are... M larger eigenvalues ​​λ l The eigenvector v corresponding to (l=1,…,M) l (l=1,…,M), Σ is a diagonal matrix with M large eigenvalues ​​as its diagonal elements; U is a unitary matrix with columns of... The (LM) smaller eigenvalues ​​λ l The eigenvector u corresponding to (l=M+1,…,L) l(l=M+1,…,L),Φ is a diagonal matrix with (LM) smaller eigenvalues ​​as its diagonal elements.

[0027] Then, calculate the spatial spectrum based on the unitary matrix U.

[0028] Furthermore, the spatial spectrum described in this invention is:

[0029]

[0030] Where, τ opt To optimize latency parameters, This is the steering vector corresponding to the scanning signal in the θ direction.

[0031] Furthermore, the optimized delay parameter τ described in this invention opt for:

[0032]

[0033] Where, τ l,θ Let L be the propagation delay of the scanning signal in the θ direction from the reference element to the l-th element, where L is the number of elements.

[0034] Beneficial effects

[0035] First, this invention is based on the array observation covariance matrix. and virtual interference matrix There exists a non-linear mapping relationship. Based on the above findings, this relationship is learned from the data using a machine learning model, and thus... Reconstructed Then through load This method achieves virtual interference suppression by employing a model- and data-driven approach, thus addressing the performance degradation issue that arises as signal bandwidth increases.

[0036] Second, this method provides a new approach to joint model and data-driven approaches. Compared with traditional model-driven methods, it has higher tolerance, and compared with purely data-driven methods, it has stronger interpretability, reliability, and accuracy. Attached Figure Description

[0037] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0039] Figure 2 This is a schematic diagram of SVR nonlinear mapping;

[0040] Figure 3 This is a spatial spectrum. Detailed Implementation

[0041] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0042] It should be noted that, in the absence of conflict, the following embodiments and features can be combined with each other; and, based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0043] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0044] Suppose a uniform linear array consisting of L elements receives M uncorrelated broadband incoming signals. The entire environment conforms to the far-field assumption and the background noise is white noise. Then the complex analytic output vector of the array is:

[0045]

[0046]

[0047] Among them, s m (t) represents the complex analytical form of the m-th incoming wave signal, τ l,m = (l-1)d sinθ m / c represents the propagation delay between the m-th incoming signal and the first array element (i.e., the reference array element) and the l-th array element, d represents the element spacing, and θ represents the propagation delay. m Let be the direction of arrival of the m-th signal, c be the signal propagation speed, and n(t) be the additive noise vector of the array elements. Assume that both the incoming signal and the additive noise of the array elements are statistically independent zero-mean stationary random processes, all incoming signals have the same or similar correlation coefficients, and the propagation delay τ... l,m Less than the correlation time of the signal.

[0048] Based on the above assumptions, we have

[0049]

[0050] Where τ and τ0 are two variable time delay parameters, and ρ(τ) is the correlation coefficient of the incoming signal, which can be defined as...

[0051]

[0052] Where “E” represents the expected value and “*” represents the complex conjugate. Let be the power of the m-th signal.

[0053] According to equation (3), we can deduce It is a zero-mean random process and is statistically orthogonal to s. m (t+τ0), therefore the following s m Orthogonal representation of (t+τ):

[0054]

[0055] in, This is defined as virtual interference. Also according to equation (3), the power ratio of the signal to the virtual interference (Signal to Virtual Interference Ratio, SVIR) is...

[0056]

[0057] Therefore, given the time delay parameters τ and τ0, |ρ(τ-τ0)| increases with the increase of the incoming signal bandwidth, thereby reducing SVIR.

[0058] Combined with equation (5), s m (t) can be rewritten as:

[0059]

[0060] The steering vector defined by formula (7) above contains the correlation function information of the signal, and the correlation function of the signal is related to its correlation time. Therefore, the correlation time factor of the signal is taken into account. This provides a solution to the constraints of mainstream methods.

[0061] Similarly, the array's output vector can be rewritten as:

[0062]

[0063] According to equation (9), the output vector covariance matrix of the array has the following form:

[0064]

[0065] R ss =E{s(t+τ0)s H (t+τ0)}=E{s(t)s H (t)} (13)

[0066] s(t)=[s1(t),s2(t),…,s M (t)] T (14)

[0067]

[0068] R nn =E{n(t)n H (t)}=σ 2 I L (16)

[0069] Where, σ 2 For noise power, I L It is an L×L dimensional identity matrix. It is defined as the Virtual Interference Covariance Matrix (VICM).

[0070] According to equation (11), if the VICM is removed, equation (11) can be degenerated into a standard rank-1 model, that is, each incoming signal contributes rank-1 to the signal subspace, which means the dimension of the signal subspace is equal to the number of incoming signals, thus allowing the introduction of a narrowband arrival estimation method for processing. Therefore, suppressing the virtual interference defined in equation (5) is particularly important. To remove the randomness of virtual interference, the second-order statistical property (VICM) of virtual interference is chosen for suppression. The virtual interference covariance matrix (VICM) can be estimated using the following formula in a finite snapshot:

[0071]

[0072] It can be observed that, It is related not only to the direction of the incoming signal, but also to the signal power and correlation coefficient. However, this information is often unavailable in non-cooperative scenarios. Combining equation (17), it can also be found that in different scenarios, and There must exist some kind of non-linear mapping relationship between them. Based on the above findings, this relationship can be learned from the data using machine learning models (such as SVR), and thus... Reconstructed Then through load Virtual interference suppression is achieved through a method described above. Based on the above derivation, an orthogonal representation technique is introduced to transform the rank extension problem of the broadband signal time-domain model into a virtual interference suppression problem. This eliminates the need for frequency domain transformation, avoids approximation and focusing errors, and achieves higher computational efficiency.

[0073] Based on the above analysis, the embodiments of this application use a broadband signal direction-of-arrival estimation method based on virtual interference suppression, the entire process of which is shown in the attached figure. Figure 1 As shown, the specific steps are as follows:

[0074] (1) Dataset Construction

[0075] Based on simulation data, array observation covariance matrices with different signal-to-noise ratios and orientations are generated. and the corresponding virtual interference matrix From the simulation data and These are used as samples and labels in the dataset, respectively, and for... and Preprocessing and postprocessing are performed.

[0076] Data sets are constructed using simulation data. and These can be used as samples and labels for the dataset, respectively. Considering that most machine learning models are built in the real number domain, complex matrices need to be processed. and Preprocessing and postprocessing are performed to adapt the data to the input and output of the machine learning model.

[0077] The preprocessing process is as follows: First, ... The real and imaginary parts of the top diagonal elements are vectorized by row and then stacked together to form a vector. Secondly, remove vectors middle The simplified vector z is obtained by taking the imaginary part of the diagonal element.

[0078]

[0079] The post-processing process is the same as the pre-processing process, through... The target vector d is obtained through post-processing. The entire pre-processing and post-processing process is shown in the attached figure. Figure 2 As shown.

[0080] Based on the processed vector z and the target vector d, a training dataset is constructed. For the input sample space, For the real number field, y n Let N be an element of the target vector d, and N be the number of samples.

[0081] (2) Model Training

[0082] Use step (1) to build a dataset and train a machine learning model.

[0083] The machine learning model used in this step can be an SVR model, a feedforward neural network model, a radial basis function network model, a long short-term memory network model, a convolutional neural network model, etc.

[0084] In this embodiment, the SVR model is selected as the machine learning model for training. The basic idea of ​​SVR is to find a function f(·) such that the deviation between the function value after applying it to all training data and its corresponding target value is at most ε, while also being as flat as possible. It is worth noting that a single SVR can only achieve the mapping between a vector and a single value. To achieve the mapping between vector z and vector d, L is needed. 2 One SVR.

[0085] The nonlinear function f(z) learned by SVR has the following form:

[0086]

[0087] Where w and b are the weight vector and bias, respectively, and φ(·) is the input sample space. to feature space The nonlinear mapping function.

[0088] The entire SVR training process can then be transformed into a convex optimization problem, namely:

[0089]

[0090]

[0091] Where C is the regularization parameter, ξ n and ξ′ n These are slack variables.

[0092] From (21), only points outside the feasible region contribute to the objective function. To simplify the above convex optimization problem, it can be transformed into a dual problem, i.e.:

[0093]

[0094] Where, α n and α′ n For Lagrange multipliers, k(z) n ,z m )=[φ(z n )] T φ(z m Let be the kernel function. The dual problem described above is a quadratic programming problem, which can be solved using the sequential gradient descent method. The optimal solution can then be expressed as:

[0095]

[0096] Furthermore, this method selects the radial basis function (RBF) as the kernel function. For the calculation of the bias b, then for all non-boundary Lagrange multipliers (i.e., α... n ,α′ n The average of the biases corresponding to (≠-C, 0, C) is taken.

[0097] (3) Direction of arrival estimation

[0098] The actual measured array output vector covariance matrix After preprocessing, the data is input into a trained machine learning model, and a virtual interference matrix is ​​obtained based on the model's output. pass load The rank-1 covariance matrix is ​​obtained in this way. Finally, the spatial spectrum is estimated using the subspace orthogonal method, and the direction corresponding to the peak position of the spatial spectrum is the direction of arrival.

[0099] In this embodiment, after the SVR model is trained, the VICM can be reconstructed and loaded using the actually measured array output vector covariance matrix. The loaded array output vector covariance matrix has the following approximate form:

[0100]

[0101] According to equation (25), it can be found that It approximates a rank-1 model, and the steering vector is related to the time delay parameter τ0. If the time delay parameter τ0 is fixed, Given a positive definite Hermitian matrix, it has the following eigenvalue decomposition:

[0102]

[0103] Where V is a unitary matrix, and its columns are... M larger eigenvalues ​​λ l The eigenvector ν corresponding to (l=1,…,M) l (l=1,…,M), where ∑ is a diagonal matrix with M large eigenvalues ​​as its diagonal elements; U is a unitary matrix with columns of... The (LM) smaller eigenvalues ​​λ l The eigenvector u corresponding to (l=M+1,…,L) l (l=M+1,…,L),Φ is a diagonal matrix with (LM) smaller eigenvalues ​​as its diagonal elements.

[0104] According to the subspace orthogonality theory,

[0105]

[0106] According to equation (27), the equation holds true regardless of the value of the delay parameter τ0. This method selects the optimal delay parameter.

[0107]

[0108] Where, τ l,θ Let θ be the propagation delay of the scanning signal from the reference element to the l-th element.

[0109] Finally, the spatial spectrum estimate is obtained as J. OR-OP (θ), the position of the spatial spectrum peak corresponds to the direction of arrival.

[0110]

[0111] Appendix Figure 3 Spatial spectra of broadband BPSK signals in the -30° and 30° directions at a signal-to-noise ratio of 0 dB.

[0112] This application's embodiments generate array observation covariance matrices and corresponding virtual interference matrices with different signal-to-noise ratios and directions based on simulation data. These matrices are preprocessed to adapt to the input and output of the SVR (Signal-to-Video Response) system, and a training dataset is ultimately constructed to train the SVR model. For the actual array observation covariance matrix, a virtual interference matrix is ​​reconstructed through SVR model mapping. Rank-1 transformation is achieved through loading, and then the subspace orthogonality method is combined to estimate the direction of arrival (DOA) of the broadband signal.

[0113] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for estimating the direction of arrival (DOA) of a broadband signal based on virtual interference suppression, characterized in that, The specific process is as follows: Dataset Construction: Generating array observation covariance matrices with different signal-to-noise ratios and orientations based on simulation data. and the corresponding virtual interference covariance matrix right and Preprocessing and postprocessing are performed to process the resulting... and As samples and labels for the dataset; Model training: Training machine learning models using the constructed dataset; Direction of arrival estimation: This involves estimating the actual measured array observation covariance matrix. After preprocessing, the data is input into a trained machine learning model, and the virtual disturbance covariance matrix is ​​obtained based on the output of the machine learning model. pass load The rank-1 covariance matrix is ​​obtained by means of the subspace orthogonal method, and the spatial spectrum is estimated by means of the subspace orthogonal method. The direction corresponding to the peak position of the spatial spectrum is the direction of arrival. The preprocessing is as follows: The real and imaginary parts of the top diagonal elements are vectorized by row and then stacked together to form a vector. Remove vector middle The simplified vector z is obtained from the imaginary part of the diagonal elements; The post-processing is as follows: The real and imaginary parts of the top diagonal elements are vectorized by row and then stacked together to form a vector. Remove vector middle The imaginary part of the diagonal elements yields the simplified target vector d; During training, the convex optimization problem of the SVR model is transformed into a dual problem: Where, α n and α′ n For Lagrange multipliers, κ(z) n ,z m )=[φ(z n )] T φ(z m ) is the kernel function; The passage load The rank-1 covariance matrix is ​​obtained in this way. Finally, the spatial spectrum is estimated using the subspace orthogonality method. The specific process is as follows: Based on the output of the virtual interference matrix calculate Regarding the Perform eigenvalue decomposition; Where V is a unitary matrix, and its columns are... M larger eigenvalues ​​λ l The eigenvector ν corresponding to (l=1,…,M) l (l=1,…,M), where ∑ is a diagonal matrix with M large eigenvalues ​​as its diagonal elements; U is a unitary matrix with columns of... The (LM) smaller eigenvalues ​​λ l The eigenvector u corresponding to (l=M+1,…,L) l (l=M+1,…,L),Φ is a diagonal matrix with (LM) smaller eigenvalues ​​as diagonal elements; Then, calculate the spatial spectrum based on the unitary matrix U.

2. The broadband signal direction-of-arrival estimation method based on virtual interference suppression according to claim 1, characterized in that, Constructing a dataset for training For the input sample space, For the real number field, y n Let N be an element of the target vector d, and N be the number of samples.

3. The broadband signal direction-of-arrival estimation method based on virtual interference suppression according to claim 1, characterized in that, The machine learning model can be an SVR model, a feedforward neural network model, a radial basis function network model, a long short-term memory network model, or a convolutional neural network model.

4. The broadband signal direction-of-arrival estimation method based on virtual interference suppression according to claim 3, characterized in that, The machine learning model consists of multiple SVR models, with a total number of L. 2 indivual.

5. The broadband signal direction-of-arrival estimation method based on virtual interference suppression according to claim 1, characterized in that, The spatial spectrum is: Where, τ opt To optimize latency parameters, This is the steering vector corresponding to the scanning signal in the θ direction.

6. The broadband signal direction-of-arrival estimation method based on virtual interference suppression according to claim 5, characterized in that, The optimized delay parameter τ opt for: Where, τ l,θ Let L be the propagation delay of the scanning signal in the θ direction from the reference element to the l-th element, where L is the number of elements.

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