Broadband signal direction of arrival estimation method based on virtual interference suppression

Abstract

The invention belongs to the technical field of broadband array signal processing, and particularly relates to a broadband signal direction-of-arrival estimation method based on virtual interference suppression. The method comprises the following steps of: constructing a data set: generating array observation covariance matrixes # imgabs0 # with different signal-to-noise ratios and different directions and corresponding virtual interference matrixes # imgabs1 # based on analogue simulation data to perform preprocessing and post-processing on # imgabs2 # and # imgabs3 #, and taking the processed # imgabs4 # and # imgabs5 # as samples and labels of the data set; model training: performing machine learning model training by using the constructed data set; and estimating the direction of arrival: preprocessing an actually measured array output vector covariance matrix # imgabs6 #, inputting the preprocessed array output vector covariance matrix # imgabs6 # into the trained machine learning model, obtaining a virtual interference matrix # imgabs7 # according to the output of the machine learning model, obtaining a rank-1 covariance matrix in a manner of loading # imgabs9 # by # imgabs8 #, and finally estimating a spatial spectrum by combining a subspace orthogonal method. The direction corresponding to the peak position of the spatial spectrum is the direction of arrival.

Description

Technical Field

[0001] The invention belongs to the technical field of broadband array signal processing, and in particular relates to a broadband signal direction of arrival estimation method based on virtual interference suppression. Background Art

[0002] Broadband 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, large-scale multiple-input multiple-output), earthquake monitoring, remote conferencing, intelligent voice interaction-automatic guidance, and smart security. One of the main problems in broadband array signal processing is to determine the direction of arrival of the signal. In some cases, it is also necessary to consider the estimation of signal power spectrum density, average power, waveform parameters, and polarization state.

[0003] Under broadband conditions, the components corresponding to the same signal in different sensor outputs are not completely correlated (incoherent), that is, they do not satisfy the rank-1 model assumption (under noise-free, single-polarization, single-signal conditions, the rank of the array output covariance matrix is ​​greater than 1). Signal direction of arrival estimation methods based on narrowband assumptions and rank-1 models are generally not directly applicable. At present, the main idea of ​​broadband array signal direction of arrival estimation methods is mostly based on rank-1 analysis / operation of array observations (using approximation or transformation, or making special assumptions about the signal), and combined with maximum likelihood, beam scanning, subspace separation (orthogonal subspace projection spectrum search, subspace rotation invariant closed-form solution, etc.), sparse reconstruction and other methods originally designed for narrowband models.

[0004] According to the different processing domains, the DOA estimation methods for broadband signals can be roughly divided into two categories: frequency domain methods and time domain methods.

[0005] The frequency domain method refers to an estimation method that is performed partially or completely in the frequency domain, such as the frequency domain subband method proposed in the paper "An Improved RSS Algorithm for Direction of Arrival Estimation of Wideband Signals" (Journal: Communication Technology, Pages: 27-29) published by Li Feng et al. in 2008 and the patent "A Wideband DOA Estimation Method Based on Microphone Array" (Patent No.: CN114639398A) applied for by Huang Jiyan et al. in 2022, that is, the array time domain observation is transformed into multiple subbands in the frequency domain through a finite-time Fourier transform or a narrowband filter group. 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 subband data received by each array element tends to be asymptotically uncorrelated, that is, when each subband data satisfies the rank-1 model, beam scanning or subspace decomposition methods can be used for direction of arrival estimation; Zhang Xingliang et al. published the paper "Frequency Domain Delay Compensation Algorithm for Wideband DOA Estimation" in 2018 The frequency domain alignment method proposed in (Journal: Journal of Electronics, Pages: 1633-1638) is to approximately perform frequency shift on the output of each array element in the frequency domain according to each scanning angle to achieve time delay compensation, so that when the scanning angle is equal to the true direction of arrival of a certain signal, the signal in that direction is approximately aligned and degenerated into a rank-1 model; the frequency domain sparse reconstruction method proposed in the patent "A method for DOA estimation of broadband signals based on l1-norm sparse representation" (Patent No.: CN112924924A) applied for by Xie Shuguo et al. in 2021 and the patent "Weighted broadband direction of arrival estimation method based on group sparsity" (Patent No.: CN113267746A) applied for by Wu Xiaohuan et al. in 2021 transforms the array observations into the form of multiple sub-bands in the frequency domain, sparsely represents the data of each sub-band, and then uses parallel sparse reconstruction or joint sparse reconstruction technology to estimate the direction of arrival; the English literature "Multisnapshot The frequency domain probability inference method proposed in "Sparse Bayesian learning for DOA [J]. IEEE Signal Processing Letters, 2016, 23 (10): 1469-1473" assumes that each subband signal model in the frequency domain obeys a probability model with a known structure, takes the joint maximum likelihood function or the joint posterior probability density function as the optimization target, and solves the unknown direction of arrival parameters through an iterative inference algorithm. The above frequency domain model methods are essentially approximated and have errors, and are computationally cumbersome and complex.

[0006] The time domain method refers to an estimation method that is performed entirely in the time domain, without the need for operations such as sub-band decomposition. The core idea is to utilize the time delay information of the same incident signal between array elements, using the signal sampling theorem or the normalized autocorrelation function as a bridge to construct the array popular matrix, and then combine it with a mathematical model similar to that of narrowband to design subsequent estimation algorithms. For example, the time domain subspace decomposition method, the English literature "Wideband modal orthogonality: A new approach for broadband DOAestimation [J]. Signal Processing, 2020, 176: 107696" proposed to use the delay information of the signal between array elements and the normalized autocorrelation function of the signal to fit the space-time covariance matrix, whose main eigenvector is the steering vector of the signal, and finally use the orthogonality of the steering vector and the noise subspace to construct the spatial spectrum; the time domain sparse reconstruction method, Liu Zhangmeng et al. proposed in the paper "Direction-of-arrival estimation of wideband signals via covariance matrix sparse representation" in 2011 to use 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, and finally solve it through the relaxation optimization method to realize the direction of arrival estimation; the time domain probabilistic reasoning method, the English literature "Wideband array signal processing using MCMC methods [J]. IEEE Transactions on Signal Processing, 2005, 53(2): 411-426” proposed to use signal sampling and reconstruction as the theoretical basis, use the signal delay information between array elements and the interpolation sinc function to construct the array popularity matrix, and finally use the Markov chain Monte Carlo method to estimate the direction of arrival.

[0007] There are some unique constraints in the problem of estimating the direction of arrival of broadband array signals under multi-source conditions, such as the array aperture / number of spatially uniformly sampled array elements / processing capacity are subject to the limited correlation time of the signal to be processed: the propagation delay of the signal sweeping across the entire observation array cannot exceed the correlation time of the signal itself, so that the components corresponding to the same signal in different sensor outputs have a certain correlation, thereby ensuring a certain degree of spatial aperture effectiveness and a small frequency domain rank-1 model mismatch. This requirement greatly limits the application scope of existing mainstream methods when the bandwidth of the signal to be processed itself is wide (small correlation time), resulting in a sharp decline in algorithm performance. Summary of the invention

[0008] In view of this, the present invention aims to solve 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, and provides a broadband signal direction of arrival estimation method based on virtual interference suppression. The virtual interference matrix is ​​reconstructed by a machine learning model to achieve rank-1 operation of broadband array time domain observations, thereby solving the rank expansion problem of broadband array time domain observations 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, the specific process is as follows:

[0011] Dataset construction: Generate array observation covariance matrices with different signal-to-noise ratios and different directions based on simulation data And the corresponding virtual interference matrix right and Perform pre-processing and post-processing to and As samples and labels of the dataset;

[0012] Model training: Use the constructed data set to train the machine learning model;

[0013] Direction of Arrival Estimation: The actual measured array output vector covariance matrix After preprocessing, it is input into the trained machine learning model, and the virtual interference matrix is ​​obtained according to the output of the machine learning model. pass load The rank-1 covariance matrix is ​​obtained by combining the subspace orthogonal method, and finally the direction corresponding to the peak position of the spatial spectrum is estimated as the arrival direction.

[0014] Furthermore, the pretreatment of the present invention is: The real and imaginary parts of the upper diagonal elements of are vectorized row by row and stacked together to form a vector Remove Vector middle The imaginary part of the diagonal elements of is used to obtain the simplified vector z.

[0015] Furthermore, the post-processing of the present invention is: The real and imaginary parts of the upper diagonal elements of are vectorized row by row and stacked together to form a vector Remove Vector middle The imaginary part of the diagonal elements is used to obtain the simplified target vector d.

[0016] Furthermore, the present invention constructs a data set for training is the input sample space, is the field of real numbers, y n is an element of the target vector d, and N is the number of samples.

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

[0018] Furthermore, the machine learning model of the present invention is a plurality of SVR models, the total number of which is L 2 indivual.

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

[0020]

[0021] Among them, α n and α′ n is the Lagrange multiplier, κ(z n ,z m )=[φ(z n )] T φ(z m ) is the kernel function.

[0022] Furthermore, the present invention is load The rank-1 covariance matrix is ​​obtained by Finally, the subspace orthogonal method is combined to estimate the spatial spectrum. The direction corresponding to the peak position of the spatial spectrum is the direction of arrival. The specific process is:

[0023] According to the output of the virtual interference matrix calculate

[0024] Regarding the Perform eigenvalue decomposition;

[0025]

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

[0027] Then, the spatial spectrum is calculated according to the unitary matrix U.

[0028] Furthermore, the spatial spectrum of the present invention is:

[0029]

[0030] Among them, τ opt To optimize the delay parameters, is the steering vector corresponding to the scanning signal in the θ direction.

[0031] Furthermore, the optimized delay parameter τ of the present invention opt for:

[0032]

[0033] Among them, τ l,θ is the propagation delay of the scanning signal in the θ direction from the reference array element to the lth array element, and L is the number of array elements.

[0034] Beneficial Effects

[0035] First, the present invention is based on the array observation covariance matrix and virtual interference matrix There is a nonlinear mapping relationship between them. Based on the above findings, the machine learning model is used to learn this relationship from the data. Reconstruct Then through load This method uses a model and data-driven approach to achieve virtual interference suppression and solve the problem that the algorithm performance decreases as the signal bandwidth increases.

[0036] Second, this method provides a new idea for the joint driving of models and data. Compared with traditional model methods, it has higher tolerance and stronger interpretability, reliability and accuracy than pure data-driven methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0038] Figure 1 It is the overall flow chart of the method of the present invention;

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

[0040] Figure 3 It is a spatial spectrum. DETAILED DESCRIPTION

[0041] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0042] It should be noted that the following embodiments and features in the embodiments may be combined with each other in the absence of conflict; and, based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making any creative work are within the scope of protection of the present disclosure.

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

[0044] Assuming that a uniform linear array consisting of L array elements receives M uncorrelated broadband incoming signals, the entire environment conforms to the far-field assumption and the noise background is white noise, then the complex analytical output vector of the array is

[0045]

[0046]

[0047] Among them, s m (t) is the complex analytical form of the mth incoming signal, τ l,m =(l-1)d sinθ m / c is the propagation delay of the mth incoming signal incident on the first array element (i.e., the reference array element) and the lth array element, d is the array element spacing, θ m is the direction of the mth signal, c is the propagation speed of the signal, and n(t) is the array element additive noise vector. Assume that the incoming signal and the array element additive noise 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 is smaller than the correlation time of the signal.

[0048] Based on the above assumptions,

[0049]

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

[0051]

[0052] Among them, "E" is the mathematical expectation, "*" is the complex conjugate, is the power of the mth signal.

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

[0054]

[0055] in, is defined as virtual interference. According to formula (3), the signal to virtual interference power ratio (Signal to Virtual Interference Ratio, SVIR) is

[0056]

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

[0058] Combining formula (5), s m (t) can be rewritten as:

[0059]

[0060] The steering vector defined by the above formula (7) contains the signal correlation function information, and the signal correlation function has a certain relationship with its correlation time, so the signal correlation time factor is taken into account. This provides a solvable way to solve the constraints of mainstream methods.

[0061] Likewise, the output vector of the array 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] Among them, σ 2 is the noise power, I L is the L×L dimensional identity matrix, It is defined as the Virtual Interference Covariance Matrix (VICM).

[0070] According to formula (11), if VICM is removed, formula (11) can be degenerated into a standard rank-1 model, that is, each incoming signal contributes rank 1 in the signal subspace, that is, the dimension of the signal subspace is equal to the number of incoming signals, so that a quasi-narrowband wave arrival estimation method can be introduced for processing. To this end, it is particularly important to suppress the virtual interference defined in formula (5). In order to remove the randomness of virtual interference, the second-order statistical characteristics of virtual interference (VICM) are selected for suppression. The virtual interference covariance matrix (VICM) can be estimated by finite snapshots using the following formula:

[0071]

[0072] It can be found that It is not only related to the direction of the signal, but also to the power and correlation coefficient of the signal. However, this information is often not available in non-cooperative scenarios. Combining formula (17), it can be found that in different scenarios, and There must be some nonlinear mapping relationship between them. Based on the above findings, machine learning models (such as SVR) can be used to learn this relationship from data, so as to Reconstruct Then through load Based on the above derivation, the orthogonal representation technology is introduced to transform the rank expansion problem of the broadband signal time domain model into a virtual interference suppression problem. There is no need for frequency domain conversion, which avoids approximation error and focusing error and has higher computational efficiency.

[0073] Based on the above analysis, the broadband signal direction of arrival estimation method based on virtual interference suppression in the embodiment of the present application is as shown in the attached figure. Figure 1 As shown, the specific steps are as follows:

[0074] (1) Dataset construction

[0075] Generate array observation covariance matrices with different signal-to-noise ratios and different directions based on simulation data And the corresponding virtual interference matrix The simulation data and As samples and labels of the dataset respectively, and Perform pre-processing and post-processing.

[0076] Constructing a dataset by simulating data, and can be used as samples and labels of the data set respectively. Considering that most machine learning models are built in the real number domain, complex matrices need to be and Perform pre-processing and post-processing to adapt it 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 upper diagonal elements of are vectorized row by row and stacked together to form a vector Next, remove the vector middle The imaginary part of the diagonal elements of is used to obtain the simplified vector z.

[0078]

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

[0080] Based on the processed vector z and target vector d, construct a data set for training is the input sample space, is the field of real numbers, y n is an element of the target vector d, and N is the number of samples.

[0081] (2) Model training

[0082] Step (1) constructs a data set to train the machine learning model.

[0083] The machine learning model in this step can be an SVR model, a feedforward neural network model, a radial basis 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 function value after the function is applied to all training data has a maximum deviation from its corresponding target value of ε and is as flat as possible. It is worth noting that a single SVR can only realize the mapping between a vector and a single value. To realize the mapping between vector z and vector d, L is required. 2 SVR.

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

[0086]

[0087] Among them, w and b are weight vector and bias respectively, φ(·) is the input sample space To feature space Non-linear mapping function.

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

[0089]

[0090]

[0091] Among them, C is the regularization parameter, ξ n and ξ′ n is the slack variable.

[0092] From (21), only points outside the feasible region contribute to the objective function. In order to more easily handle the above convex optimization problem, it can be transformed into a dual problem, namely:

[0093]

[0094] Among them, α n and α′ n is the Lagrange multiplier, k(z n ,z m )=[φ(z n )] T φ(z m ) is the kernel function. The above dual problem is a quadratic programming problem, which can be solved by the sequential gradient descent method. The optimal solution can be expressed as:

[0095]

[0096] In addition, this method selects the radial basis function (RBF) as the kernel function. For the calculation of the bias b, all non-boundary Lagrange multipliers (i.e., α n ,α′ n ≠-C,0,C) the corresponding biases are averaged.

[0097] (3) Direction of Arrival Estimation

[0098] The actual measured array output vector covariance matrix After preprocessing, it is input into the trained machine learning model, and the virtual interference matrix is ​​obtained according to the output of the machine learning model. pass load The rank-1 covariance matrix is ​​obtained by Finally, the subspace orthogonal method is combined to estimate the spatial spectrum, and the direction corresponding to the peak position of the spatial spectrum is the direction of arrival.

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

[0100]

[0101] According to formula (25), we can find that It is approximately a rank-1 model, and the steering vector is related to the delay parameter τ0. If the delay parameter τ0 is fixed, is a positive definite Hermitian matrix with the following eigenvalue decomposition:

[0102]

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

[0104] According to the subspace orthogonality theory,

[0105]

[0106] According to formula (27), no matter what the delay parameter τ0 is, the equation holds true. This method selects the optimal delay parameter

[0107]

[0108] Among them, τ l,θ is the propagation delay of the scanning signal in the θ direction from the reference array element to the lth array element.

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

[0110]

[0111] Attached Figure 3 It is the spatial spectrum of broadband BPSK signal in -30° and 30° directions under 0dB signal-to-noise ratio.

[0112] The embodiment of the present application generates array observation covariance matrices with different signal-to-noise ratios and different directions and corresponding virtual interference matrices based on simulation data, preprocesses them respectively to adapt to the input and output of SVR, and finally constructs a training data set to train the SVR model. For the actual array observation covariance matrix, the virtual interference matrix is ​​reconstructed through SVR model mapping, and the rank-1 operation is realized by loading, and then the direction of arrival estimation of the broadband signal is realized by combining the subspace orthogonal method.

[0113] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for estimating the direction of arrival of a broadband signal based on virtual interference suppression, characterized in that: The specific process is: Dataset construction: Generate array observation covariance matrices with different signal-to-noise ratios and different directions based on simulation data And the corresponding virtual interference matrix right and Perform pre-processing and post-processing to and As samples and labels of the dataset; Model training: Use the constructed data set to train the machine learning model; Direction of Arrival Estimation: The actual measured array output vector covariance matrix After preprocessing, it is input into the trained machine learning model, and the virtual interference matrix is ​​obtained according to the output of the machine learning model. pass load The rank-1 covariance matrix is ​​obtained by combining the subspace orthogonal method, and finally the spatial spectrum is estimated. The direction corresponding to the peak position of the spatial spectrum is the direction of arrival.

2. The method for estimating the direction of arrival of a broadband signal based on virtual interference suppression according to claim 1, characterized in that: The pre-processing is: The real and imaginary parts of the upper diagonal elements of are vectorized row by row and stacked together to form a vector Remove Vector middle The imaginary part of the diagonal elements of is used to obtain the simplified vector z.

3. The broadband signal direction of arrival estimation method based on virtual interference suppression according to claim 1 or 2, characterized in that: The post-processing is: The real and imaginary parts of the upper diagonal elements of are vectorized row by row and stacked together to form a vector Remove Vector middle The imaginary part of the diagonal elements is used to obtain the simplified target vector d.

4. The method for estimating the direction of arrival of a broadband signal based on virtual interference suppression according to claim 3, characterized in that: Constructing a dataset for training is the input sample space, is the field of real numbers, y n is an element of the target vector d, and N is the number of samples.

5. The method for estimating the direction of arrival of a broadband signal based on virtual interference suppression according to claim 1, characterized in that: The machine learning model is an SVR model, a feedforward neural network model, a radial basis network model, a long short-term memory network model or a convolutional neural network model.

6. The method for estimating the direction of arrival of a broadband signal based on virtual interference suppression according to claim 5, characterized in that: The machine learning model is a plurality of SVR models, the total number of which is L 2 indivual.

7. The method for estimating the direction of arrival of a broadband signal based on virtual interference suppression according to claim 6, characterized in that: During the training process, the convex optimization problem of the SVR model is transformed into a dual problem: Among them, α n and α′ n is the Lagrange multiplier, κ(z n ,z m )=[φ(z n )] T φ(z m ) is the kernel function.

8. The method for estimating the direction of arrival of a broadband signal based on virtual interference suppression according to claim 1, characterized in that: Said through load The rank-1 covariance matrix is ​​obtained by Finally, the subspace orthogonal method is combined to estimate the spatial spectrum. The specific process is as follows: According to the output of the virtual interference matrix calculate Regarding the Perform eigenvalue decomposition; Where V is a unitary matrix whose columns are The M largest eigenvalues ​​λ of l (l=1,…,M) corresponding to the eigenvector v l (l=1,…,M), ∑ is a diagonal matrix, the diagonal elements are M larger eigenvalues; U is a unitary matrix, its columns are The (LM) smaller eigenvalues ​​λ l (l=M+1,…,L) corresponding eigenvector u l (l=M+1,…,L), Φ is a diagonal matrix, and the diagonal elements are (LM) smaller eigenvalues; Then, the spatial spectrum is calculated according to the unitary matrix U.

9. The method for estimating the direction of arrival of a broadband signal based on virtual interference suppression according to claim 8, characterized in that: The spatial spectrum is: Among them, τ opt To optimize the delay parameters, is the steering vector corresponding to the scanning signal in the θ direction.

10. The method for estimating the direction of arrival of a broadband signal based on virtual interference suppression according to claim 9, characterized in that: The optimized delay parameter τ opt for: Among them, τ l,θ is the propagation delay of the scanning signal in the θ direction from the reference array element to the lth array element, and L is the number of array elements.

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