A Robust Adaptive Beamforming Method

Abstract

The present invention discloses a robust adaptive beamforming method. First, a linear array is divided into two sub-arrays, and the initial arrival directions of the desired signal and interference and the nominal steering vector are obtained by using the rotational invariant subspace algorithm. A projection matrix 1 is constructed to obtain the optimal steering vector of the desired signal. A projection matrix 2 is constructed to remove the desired signal component and estimate the power of the interference. The noise power is estimated by using the eigenvalue matrix corresponding to the noise subspace. Based on the nominal steering vector of the interference and the estimated power, the interference-plus-noise covariance matrix is reconstructed by using the zero broadening method of virtual interference. Based on the optimal steering vector of the desired signal and the interference-plus-noise covariance matrix, robust beamforming is performed on the array received data. The present invention can obtain a more accurate steering vector of the desired signal, and the reconstructed interference-plus-noise covariance matrix is used to calculate the weight vector, which has a stronger suppression effect on the interference and improves the robustness of the beamformer.

Description

Technical Field

[0001] The present invention relates to the field of beamforming research in the field of array signal processing. Especially in a non-ideal situation where various errors may exist, by more accurately estimating the steering vector of the desired signal and reconstructing a more robust interference plus noise covariance matrix to perform adaptive beamforming, the robustness of the beamformer under various errors can be better improved. Background Art

[0002] Although traditional beamforming methods can improve the robustness of the beamformer to a certain extent, in real situations, when there are large deviations between the sampled covariance matrix and the ideal covariance matrix of the signal due to various errors, the performance of the beamformer will decline, and even the "self-cancellation" phenomenon will occur. At present, although covariance matrix reconstruction-based algorithms can improve the performance of the beamformer to a certain extent, on the one hand, the steering vector of the desired signal is often estimated by solving a convex optimization problem, which has a high complexity problem. On the other hand, most covariance matrix reconstruction methods are based on the Capon spatial power spectrum. Affected by the low estimation accuracy of the Capon power spectrum, there are still certain errors after reconstruction, and the computational complexity of the MUSIC spatial spectrum search is relatively high. In contrast, the method based on rotational invariance of the space is relatively impressive in terms of estimation accuracy and computational complexity.

[0003] In view of the above analysis, it is necessary to study new robust methods to improve the robustness of the beamformer. Summary of the Invention

[0004] The technical problem to be solved by the present invention is: overcoming the deficiencies of the prior art, providing a robust adaptive beamforming method. Based on the fact that the space where the projection matrix is located is the complementary space of the space where the desired signal is located, an error vector is constructed to achieve accurate estimation of the steering vector of the desired signal; by projecting the data covariance matrix, the signal component is removed to estimate the interference power; and a more robust interference plus noise covariance matrix is reconstructed through the zero-point broadening method based on virtual interference to achieve robustness under different array errors, further improving the performance of the beamformer.

[0005] The object of the present invention is achieved by the following technical solutions: A robust adaptive beamforming method, including:

[0006] Step 1: Divide the uniform linear array in space into two sub-arrays with exactly the same structure, respectively perform eigenvalue decomposition on the received data covariance matrices of the two sub-arrays to obtain the eigenvalue matrix corresponding to the noise subspace and the signal subspace; use the rotational invariance subspace algorithm to respectively obtain the initial arrival directions of the desired signal and interference, the nominal steering vector of the desired signal, and the nominal steering vector of the interference;

[0007] Step 2: Construct projection matrix 1 based on the nominal steering vector of the desired signal obtained in Step 1 to obtain the error vector; use the error vector to iteratively update the nominal steering vector of the desired signal to obtain the estimated optimal steering vector of the desired signal.

[0008] Step 3: Construct projection matrix 2 using the optimal steering vector of the desired signal obtained in Step 2; project the received data covariance matrix to remove the desired signal component to obtain the interference projection matrix; transform the interference projection matrix to obtain the power estimate value of the interference.

[0009] Step 4: Estimate the noise power using the eigenvalue matrix corresponding to the noise subspace obtained in Step 1.

[0010] Step 5: Reconstruct the interference covariance matrix based on the initial direction of arrival of the interference obtained in Step 1 and the power estimate value of the interference obtained in Step 3; and reconstruct the interference plus noise covariance matrix using the noise power estimated in Step 4.

[0011] Step 6: Calculate the weight vector of the beamformer based on the optimal steering vector of the desired signal obtained in Step 2 and the interference plus noise covariance matrix obtained in Step 5, and perform robust beamforming on the array received data.

[0012] The method provided by the present invention is applicable to any array configuration. For the convenience of description, taking an M-element uniform linear array as an example, with the element spacing of d, receiving L far-field narrowband uncorrelated signal sources, including one desired signal and L - 1 interferences, the data received by the array at time k can be expressed as:

[0013]

[0014] where, s0(k) represents the waveform of the desired signal at time k, a0 represents the steering vector of the desired signal, s l (k), l = 1, 2, …, L - 1 represents the waveform of the l-th interference source at time k, a l represents the steering vector of the l-th interference source, x n (k) represents the noise received by the array at time k. It is assumed that the means of the desired signal, interference, and noise are all zero.

[0015] Further, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, Step 1 includes the following steps:

[0016] Step 11: There are L far-field narrowband signal sources including one desired signal and L - 1 interferences incident on an M-element uniform linear array with the element spacing of d. Among them, the M-element uniform linear array is divided into two sub-arrays with exactly the same number of elements of M - 1. The sampling covariance matrices of the received data of the two sub-arrays are expressed as:

[0017]

[0018] Among them, x1(k) and x2(k) respectively represent the data vectors received by two sub-arrays 1 and 2 at time k, K represents the number of snapshots, H represents the conjugate transpose operation of a matrix or vector. For the received data sampling covariance matrix perform eigen-decomposition to obtain:

[0019]

[0020] Among them, represents the eigenvalues arranged in descending order, is the eigenvalue corresponding eigenvector; further, the received data sampling covariance matrix is expressed as:

[0021]

[0022] Among them, represents the eigenvector matrix, represents the diagonal matrix composed of eigenvalues, and diag represents diagonalization of elements; represents the eigenvector matrix corresponding to the first L eigenvalues, and it is called the signal subspace, is the eigenvalue matrix corresponding to the signal subspace; is the eigenvector matrix corresponding to the remaining M - L - 1 eigenvalues, and it is called the noise subspace, is the eigenvalue matrix corresponding to the noise subspace;

[0023] Step 12. According to the two signal subspaces obtained in Step 11 use the least squares method to solve and obtain the rotation invariance relationship matrix:

[0024]

[0025] Perform eigen-decomposition on the rotation invariance relationship matrix Ψ LS to obtain L eigenvalues. From the rotation invariance, the initial direction of arrival is Among them, is the phase angle of the l-th eigenvalue, and λ is the wavelength of the signal. Obtain the corresponding initial directions of arrival of the desired signal and interference, which are respectively and According to the known shape of the uniform linear array, obtain the nominal steering vector corresponding to the initial angle

[0026] Furthermore, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, Step 2 includes the following steps:

[0027] Step 21: Using the initial direction of arrival of the desired signal obtained in Step 1 and the corresponding nominal steering vector to obtain a nominal steering vector matrix of the desired signal composed of J surrounding angles:

[0028]

[0029] where Δθ represents the adjacent angle interval, and the space spanned by the nominal steering vector matrix of the desired signal contains the subspace where the true desired signal is located. Construct a projection matrix 1 such that the space where the projection matrix is located is the complementary space of the space spanned by the matrix The projection matrix 1 is:

[0030]

[0031] where I is the identity matrix;

[0032] Project the nominal steering vector of the desired signal to obtain an error vector perpendicular to :

[0033]

[0034] where || ||2 represents the vector l2 norm operator;

[0035] Step 22: By setting a certain step size, correct and iteratively update the nominal steering vector of the desired signal to estimate the optimal steering vector of the desired signal:

[0036]

[0037] where is the result of correcting the nominal steering vector of the desired signal using the error vector e0 at the nth iteration, b represents the nth value at an interval of η in the interval [-b, b], n represents the total number of searches, represents the received data covariance matrix of the array receiving the data vector x(k) at time k.

[0038] Furthermore, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, Step 3 includes the following steps:

[0039] Step 31: Using the optimal steering vector of the desired signal obtained in Step 2, construct a projection matrix 2 as:

[0040]

[0041] Step 32: Project the received data covariance matrix of the array, calculate the projected data covariance matrix, which is:

[0042]

[0043] where, is the interference plus noise covariance matrix, is the interference covariance matrix, is the noise power. The space where the projection matrix is located is the complementary space of the desired signal. The projected data covariance matrix after projection removes the signal component. Perform eigenvalue decomposition on the projected data covariance matrix to obtain:

[0044]

[0045] where, represents the eigenvalues arranged in descending order, is the eigenvector corresponding to the eigenvalue. The interference projection matrix can be expressed as:

[0046]

[0047] Step 33: Transform the obtained interference projection matrix to obtain the estimated interference matrix where, represents the pseudo-inverse. Use the transformed matrix to obtain the power estimate value of the interference:

[0048]

[0049] where, is the nominal steering vector of the interference obtained in Step 1, is the estimated interference matrix, represents the operation of taking the diagonal elements of the matrix to form a diagonal matrix, is the diagonal matrix, and the diagonal element is the power estimate value of the interference.

[0050] Furthermore, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, Step 4 includes the following steps:

[0051] Use the eigenvalue matrix corresponding to the noise subspace in Step 1 to estimate the noise power by taking the average value of the diagonal elements

[0052]

[0053] Furthermore, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, step 5 includes the following steps:

[0054] Step 51: Using the initial arrival directions of the interferences obtained in step 1, in the null broadening process, two virtual interferences with equal power are arranged on both sides of each interference direction, and the arrival directions of the virtual interferences are and reconstruct the interference covariance matrix using the interference power estimation value obtained in step 3:

[0055]

[0056] where Δ is the angular separation between the arrival direction of the added virtual interference and the initial arrival direction of the interference and is the power estimation value of the interference, is the nominal steering vector of the interference, and

[0057] is the nominal steering vector obtained according to the known uniform linear array shape;

[0058]

[0059] where is the reconstructed interference covariance matrix, is the estimated noise power, and I is the identity matrix.

[0060] Furthermore, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, step 6 includes the following steps:

[0061] Step 61: Based on the optimal desired signal steering vector obtained in step 2 and the interference-plus-noise covariance matrix obtained in step 5, calculate the weight vector according to the following formula:

[0062]

[0063] where is the optimal desired signal steering vector, is the reconstructed interference-plus-noise covariance matrix, and w is the obtained weight vector;

[0064] Step 62: Weight the weight vector w with the data x(k) received by the array at time k to obtain the output signal y(k) = wH x(k) to achieve robust adaptive beamforming.

[0065] The advantages of the present invention compared with the prior art are as follows:

[0066] (1) The space spanned by the projection matrix 1 constructed in the present invention is the complementary space of the nominal steering vector space of the desired signal. After projection, the error vector is in the complementary space. A more accurate desired signal steering vector will enable spatial power spectrum estimation, avoiding the solution of the convex optimization problem regarding steering vector estimation in traditional beamforming, reducing the computational complexity, and saving time costs.

[0067] (2) The present invention constructs a projection matrix 2 to project the received data matrix to remove the signal components, and transforms the projected covariance matrix to achieve accurate estimation of the interference power.

[0068] (3) The present invention uses the zero-width expansion method based on virtual interference to reconstruct the interference plus noise covariance matrix. Beamforming can have a stronger suppression effect on interference and achieve performance improvement under different array errors.

[0069] The differences between the present invention and the prior art are as follows: differences in the accurate estimation method of the steering vector: the present invention constructs the error vector of the steering vector through projection for accurate estimation of the steering vector, reducing the computational complexity; differences in the interference power estimation method: the signal components are removed by constructing a projection matrix, and accurate estimation of the interference power is achieved by transforming the projected covariance matrix; differences in the method of reconstructing the interference plus noise covariance matrix: the interference plus noise covariance matrix is reconstructed by the zero-width expansion method based on virtual interference, which has stronger robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0071] Figure 1 It is a flowchart of a robust adaptive beamforming method of the present invention;

[0072] Figure 2 It is a schematic diagram of a linear array signal reception model provided by an embodiment of the present invention;

[0073] Figure 3 It is a performance curve graph provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0074] The following clearly and completely describes the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0075] As Figure 1 shown, the embodiment of the present invention provides a robust adaptive beamforming method for reconstructing the interference plus noise covariance matrix based on projection, constructs two projection matrices, uses the space where projection matrix 1 is located as the complementary space of the space where the desired signal is located, constructs an error vector, and realizes the accurate estimation of the desired signal steering vector; uses projection matrix 2 to project and remove the signal component, estimates the interference power; and reconstructs a more robust interference plus noise covariance matrix through the zero broadening method based on virtual interference. The robust performance of the beamformer against any type of array error is improved.

[0076] It mainly includes the following steps:

[0077] Step 1: Divide the uniform linear array in space into two sub-arrays with exactly the same structure, respectively perform eigenvalue decomposition on the covariance matrices of the received data of the two sub-arrays to obtain the eigenvalue matrix corresponding to the noise subspace and the signal subspace; use the rotational invariance subspace algorithm to obtain the initial arrival directions of the desired signal and interference, the nominal steering vector of the desired signal, and the nominal steering vector of the interference;

[0078] Step 2: Construct projection matrix 1 according to the nominal steering vector of the desired signal obtained in Step 1 to obtain an error vector; use the error vector to iteratively update the nominal steering vector of the desired signal to obtain the estimated optimal steering vector of the desired signal;

[0079] Step 3: Construct projection matrix 2 using the optimal steering vector of the desired signal obtained in Step 2; project the received data covariance matrix to remove the desired signal component to obtain an interference projection matrix; transform the interference projection matrix to obtain the power estimate value of the interference;

[0080] Step 4: Estimate the noise power using the eigenvalue matrix corresponding to the noise subspace obtained in Step 1;

[0081] Step 5: Reconstruct the interference covariance matrix based on the initial arrival direction of the interference obtained in Step 1 and the interference power estimate value obtained in Step 3; and reconstruct the interference plus noise covariance matrix using the noise power estimated in Step 4;

[0082] Step 6: Calculate the weight vector of the beamformer based on the optimal steering vector of the desired signal obtained in Step 2 and the interference plus noise covariance matrix obtained in Step 5, and perform robust beamforming on the array received data.

[0083] As Figure 2 shown, for an M - element uniform array with element spacing d, receiving L far - field narrow - band uncorrelated signal sources, including one desired signal and L - 1 interferences, the data received by the array at time k can be expressed as:

[0084]

[0085] where s0(k) represents the waveform of the desired signal at time k, a0 represents the steering vector of the desired signal, s l (k), l = 1, 2, …, L - 1 represents the waveform of the l - th interference source at time k, a l represents the steering vector of the l - th interference source, and x n (k) represents the noise received by the array at time k. It is assumed that the means of the desired signal, interferences, and noise are all zero.

[0086] Step 11: There are L far - field narrow - band signal sources, including one desired signal and L - 1 interferences, incident on an M - element uniform linear array with element spacing d. The M - element uniform linear array is divided into two exactly identical sub - arrays with the number of elements being M - 1. The received data sampling covariance matrices of the two sub - arrays are expressed as:

[0087]

[0088] where x1(k) and x2(k) respectively represent the data vectors received by the two sub - arrays 1 and 2 at time k, K represents the number of snapshots, H represents the conjugate transpose operation of a matrix or vector. The received data sampling covariance matrix is eigen - decomposed to obtain:

[0089]

[0090] where, represents the eigenvalues arranged in descending order, is the eigen - value corresponding to the eigen - vector; further, the received data sampling covariance matrix is expressed as:

[0091]

[0092] where, represents the eigen - vector matrix, represents the diagonal matrix composed of eigenvalues, and diag represents diagonalizing the elements; represents the eigen - vector matrix corresponding to the first L eigenvalues and is called the signal subspace, is the eigenvalue matrix corresponding to the signal subspace; The eigenvector matrix corresponding to the remaining M - L - 1 eigenvalues is called the noise subspace. is the eigenvalue matrix corresponding to the noise subspace;

[0093] Step 12. According to the two signal subspaces obtained in Step 11 Use the least - squares method to solve for the rotation - invariant relationship matrix:

[0094]

[0095] Perform eigenvalue decomposition on the rotation - invariant relationship matrix Ψ LS to obtain L eigenvalues. From the rotation invariance, the initial direction of arrival is where is the phase angle of the l - th eigenvalue, and λ is the wavelength of the signal. The initial directions of arrival of the corresponding desired signal and interference are respectively and According to the known shape of the uniform linear array, obtain the nominal steering vector corresponding to the initial angle

[0096] Furthermore, in the above - mentioned robust adaptive beamforming method based on steering - vector estimation and covariance - matrix reconstruction, Step 2 includes the following steps:

[0097] Step 21. Use the initial direction of arrival of the desired signal obtained in Step 1 corresponding nominal steering vector to obtain the nominal steering - vector matrix of the desired signal composed of J angles around :

[0098]

[0099] where Δθ represents the adjacent - angle interval. The space spanned by the nominal steering - vector matrix of the desired signal contains the subspace where the true desired signal is located. Construct a projection matrix 1 such that the space where the projection matrix is located is the complementary space of the space spanned by the matrix The projection matrix 1 is:

[0100]

[0101] where I is the identity matrix;

[0102] Project the nominal steering vector of the desired signal to obtain an error vector perpendicular to :

[0103]

[0104] where, || ||2 represents the vector l2 norm operator;

[0105] Step 22: Modify the nominal steering vector of the desired signal by setting a certain step size and perform iterative update to estimate the optimal steering vector of the desired signal:

[0106]

[0107] where, is the result of modifying the nominal steering vector of the desired signal using the error vector e0 at the nth iteration, b represents the nth value at an interval of η in the interval [-b, b], n represents the total number of searches,

[0108]

[0109] Furthermore, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, step 3 includes the following steps:

[0110] Step 31: Construct the projection matrix 2 using the optimal steering vector of the desired signal obtained in step 2 as:

[0111]

[0112] Step 32: Project the array received data covariance matrix and calculate the projected data covariance matrix as:

[0113] where, is the interference plus noise covariance matrix, is the interference covariance matrix, is the noise power. The space where the projection matrix is located is the complementary space of the desired signal. The projected data covariance matrix after projection removes the signal component. Perform eigenvalue decomposition on the projected data covariance matrix

[0114] to obtain:

[0115] where, represents the eigenvalues arranged in descending order, is the eigenvector corresponding to the eigenvalue. The interference projection matrix

[0116] can be expressed as:

[0117] ​​Step 33. Transform the obtained interference projection matrix to obtain an estimated interference matrix wherein, represents the pseudo-inverse. Using the transformed matrix obtain the power estimation value of interference:

[0118]

[0119] wherein, is the nominal steering vector of interference obtained in Step 1, is the estimated interference matrix, represents the operation of taking the diagonal elements of the matrix to form a diagonal matrix, is a diagonal matrix, and the diagonal element is the power estimation value of interference.

[0120] Furthermore, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, Step 4 includes the following steps:

[0121] Use the eigenvalue matrix corresponding to the noise subspace in Step 1 to estimate the noise power by taking the average value of the diagonal elements

[0122]

[0123] Furthermore, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, Step 5 includes the following steps:

[0124] Step 51. Using the initial arrival direction of interference obtained in Step 1, in the null broadening process, arrange two virtual interferences with equal power on both sides of each interference direction. The arrival directions of the virtual interferences are and reconstruct the interference covariance matrix using the power estimation value of interference obtained in Step 3:

[0125]

[0126] where Δ is the angular interval between the arrival direction of the added virtual interference and the initial arrival direction of interference , is the power estimation value of interference, is the nominal steering vector of interference, is the nominal steering vector obtained according to the known shape of the uniform linear array;

[0127] Step 52: Reconstruct the interference plus noise covariance matrix by using the reconstructed interference covariance matrix in Step 51 and the noise power estimated in Step 4:

[0128]

[0129] where, is the reconstructed interference covariance matrix, is the estimated noise power, and I is the identity matrix.

[0130] Further, in the above robust adaptive beamforming method based on steering vector estimation and covariance matrix reconstruction, Step 6 includes the following steps:

[0131] Step 61: Calculate the weight vector according to the following formula based on the optimal desired signal steering vector obtained in Step 2 and the interference plus noise covariance matrix obtained in Step 5:

[0132]

[0133] where, is the optimal desired signal steering vector, is the reconstructed interference plus noise covariance matrix, and w is the obtained weight vector;

[0134] Step 62: Weight the weight vector w with the data x(k) received by the array at time k to obtain the output signal y(k) = w H x(k) of the beamformer, realizing robust adaptive beamforming.

[0135] As Figure 3 shown, it is a uniform linear array with M = 10 array elements provided by an embodiment of the present invention. The element spacing is half a wavelength. The desired signal comes from θ0 = 3°, the interference sources come from θ1 = -40° and θ2 = 30°, and there is an angle estimation error of 3°. In the method of the present invention, b = 0.01 and η = 10 -3。The comparison methods are as follows: the algorithm for reconstructing the interference plus noise covariance matrix based on line integral reconstruction (line integral reconstruction method), the algorithm for reconstructing the interference plus noise covariance matrix based on volume integral reconstruction (volume integral reconstruction method), the covariance matrix reconstruction method based on maximum entropy spectrum (maximum entropy spectrum method), the robust adaptive beamforming method based on subspace (subspace reconstruction-based method), and the robust adaptive beamforming method based on projection (projection reconstruction-based method). Under the condition of an interference-to-noise ratio of 20 dB, the direction-of-arrival error follows a uniform distribution on [-4°, 4°], the number of snapshots is fixed at 30, and the performance curves of the differences in the output signal-to-interference-plus-noise ratio between different methods and the theoretical optimal beamformer with respect to the signal-to-noise ratio (SNR) under 200 Monte Carlo experiments are shown. It can be seen from the figure that the method proposed in the present invention can achieve obvious performance improvement and is almost the same as the output signal-to-interference-plus-noise ratio of the theoretical optimal beamformer, indicating the effectiveness of the method proposed in the present invention. In addition, the method of the present invention does not involve the solution of any convex optimization problems, so the computational complexity is relatively low, and the present invention shows good robustness under different array errors.

[0136] Through the description of the above embodiments, those skilled in the art can clearly understand that the above embodiments can be implemented by software or by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solutions of the above embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.), including several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0137] The above is only a preferred 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 those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A robust adaptive beamforming method, characterized in that, It includes the following steps: Step 1: Divide the uniform linear array in space into two sub-arrays with exactly the same structure. Perform eigenvalue decomposition on the covariance matrices of the received data of the two sub-arrays respectively to obtain the eigenvalue matrix corresponding to the noise subspace and the signal subspace. Use the rotational invariance subspace algorithm to obtain the initial directions of arrival of the desired signal and interference, the nominal steering vector of the desired signal, and the nominal steering vector of the interference respectively; Step 2: Construct projection matrix 1 using the nominal steering vector of the desired signal obtained in Step 1 to obtain the error vector. Iteratively update the nominal steering vector of the desired signal using the error vector to obtain the estimated optimal steering vector of the desired signal; The projection matrix 1 is: Among them, is the identity matrix, is the vector matrix; Step 3: Construct projection matrix 2 using the optimal steering vector of the desired signal obtained in Step 2. Project the covariance matrix of the received data to remove the desired signal component to obtain the interference projection matrix. Transform the interference projection matrix to obtain the interference power estimate value; The projection matrix 2 is: is the optimal desired signal steering vector; Step 4: Estimate the noise power using the eigenvalue matrix corresponding to the noise subspace obtained in Step 1; Step 5: Reconstruct the interference covariance matrix based on the initial direction of arrival of the interference obtained in Step 1 and the interference power estimate value obtained in Step 3; And reconstruct the interference plus noise covariance matrix using the noise power estimated in Step 4; Step 6: Calculate the weight vector of the beamformer based on the optimal steering vector of the desired signal obtained in Step 2 and the interference plus noise covariance matrix obtained in Step 5, and perform robust beamforming on the array received data.

2. The robust adaptive beamforming method according to claim 1, characterized in that: The specific implementation of Step 1 is as follows: Step 11. There are far-field narrowband signal sources, including a desired signal and interference signals incident on an M-element uniform linear array with an element spacing of , where the M-element uniform linear array is divided into two exactly identical sub-arrays with the number of elements being . The received data sampling covariance matrices of the two sub-arrays are expressed as: Among them, and respectively represent the data vectors received by two sub-arrays 1 and 2 at time , represents the number of snapshots, represents the conjugate transpose operation of a matrix or vector. The received data sampling covariance matrix is subjected to eigenvalue decomposition to obtain: Among them, represents the eigenvalues arranged in descending order, is the eigenvalue corresponding eigenvector; further, the received data sampling covariance matrix is expressed as: Among them, represents the eigenvector matrix, represents the diagonal matrix composed of eigenvalues, represents diagonalizing the elements; represents the first eigenvector matrix corresponding to the eigenvalues, and it is called the signal subspace, is the eigenvalue matrix corresponding to the signal subspace; is composed of the eigenvector matrix corresponding to the remaining eigenvalues, and it is called the noise subspace, is the eigenvalue matrix corresponding to the noise subspace; Step 12. According to the two signal subspaces obtained in Step 11 , use the least squares method to solve and obtain the rotational invariance relation matrix: For the rotation-invariant relation matrix perform eigenvalue decomposition to obtain eigenvalues. From the rotation invariance, it can be known that the initial direction of arrival is , where is the phase angle of the -th eigenvalue, is the wavelength of the signal, and the initial directions of arrival of the corresponding desired signal and interference are obtained as and respectively. According to the known shape of the uniform linear array, the nominal steering vectors of the desired signal and interference corresponding to the initial angles are obtained as and the nominal steering vector of the interference .

3. The robust adaptive beamforming method according to claim 1, characterized in that: Step 2 includes the following steps: Step 21: Using the initial direction of arrival of the desired signal obtained in Step 1 the corresponding nominal steering vector , obtain the nominal steering vector matrix of the desired signal composed of angles around : Among them, , , represents the adjacent angular interval. The space spanned by the nominal steering vector matrix contains the subspace where the true desired signal is located. Construct the projection matrix 1 such that the space where the projection matrix is located is the complementary space of the space spanned by the matrix . The projection matrix 1 is: Among them, is the identity matrix; Project the nominal steering vector of the desired signal to obtain an error vector that is perpendicular to : Among them, represents a vector norm operator; Step 22, correct the nominal steering vector of the desired signal by setting a certain step size and perform iterative update to estimate the optimal steering vector of the desired signal: Among them, , is the result of correcting the nominal steering vector of the desired signal using the error vector at the -th iteration, represents the -th value in the interval with an interval of , represents the total number of searches, represents the received data covariance matrix of the array for the received data vector at time .​ 4. A robust adaptive beamforming method according to claim 1, wherein: Step 3 includes the following steps: Step 31: Construct projection matrix 2 using the optimal steering vector of the desired signal obtained in Step 2 as: Step 32: Project the covariance matrix of the array received data to calculate the projected data covariance matrix as: Among them, is the interference plus noise covariance matrix, is the interference covariance matrix, is the noise power. The space where the projection matrix is located is the complementary space of the desired signal. The covariance matrix of the projected data after projection removes the signal component. For the covariance matrix of the projected data perform eigenvalue decomposition to obtain: Among them, represents the eigenvalues arranged in descending order, is the eigenvector corresponding to the eigenvalue, and the interference projection matrix is expressed as: Step 33: Transform the obtained interference projection matrix to obtain an estimated interference matrix , where represents the pseudo-inverse. Using the transformed matrix , obtain the power estimate value of the interference: Among them, , is the nominal steering vector of the interference obtained in step 1, is the estimated interference matrix, represents the operation of taking the diagonal elements of the matrix to form a diagonal matrix, is a diagonal matrix, and the diagonal elements are the power estimates of the interference.

5. A robust adaptive beamforming method according to claim 1, wherein: Step 4 includes the following steps: Using the eigenvalue matrix corresponding to the noise subspace in Step 1 , the average value of the diagonal elements is taken to estimate the noise power : 。 6. A robust adaptive beamforming method according to claim 1, wherein: Step 5 includes the following steps: Step 51. Using the initial direction of arrival of interference obtained in Step 1, in the null broadening process, two virtual interferences with equal power are arranged on both sides of each interference direction, and the direction of arrival of the virtual interference is , and the interference covariance matrix is reconstructed using the interference power estimation value obtained in Step 3: Among them, is the direction of arrival of the added virtual interference wave and the initial direction of arrival of the interference The angular interval between them, is the power estimation value of the interference, is the nominal steering vector of the interference, , The nominal steering vector is obtained according to the known shape of the uniform linear array; Step 52: Reconstruct the interference plus noise covariance matrix using the reconstructed interference covariance matrix in Step 51 and the noise power estimated in Step 4: Among them, is the reconstructed interference covariance matrix, is the estimated noise power, is the identity matrix.

7. A robust adaptive beamforming method according to claim 1, wherein: Step 6 includes the following steps: Step 61: Based on the optimal steering vector of the desired signal obtained in Step 2 and the interference plus noise covariance matrix obtained in Step 5, calculate the weight vector according to the following formula: ； wherein, is the optimal desired signal steering vector, is the reconstructed interference plus noise covariance matrix, is the obtained weight vector; Step 62, weight the weight vector and the data received by the array at time to obtain the output signal of the beamformer, so as to achieve robust adaptive beamforming. ​

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