A Beam Synthesis Method Based on Eigenvalue Reconstruction

Abstract

A beamforming method based on eigenvalue reconstruction is implemented by the following steps: (1) defining parameters for a uniform linear array; (2) calculating the array covariance matrix; (3) performing eigenvalue decomposition on the covariance matrix to obtain normalized eigenvectors and their corresponding eigenvalues; (4) calculating the angle between the desired signal direction vector and each eigenvector; (5) determining the eigenvectors and eigenvalues ​​belonging to the desired signal subspace; (6) obtaining the eigenvalue index set of the interference signal subspace and the noise subspace; (7) calculating the inverse matrix of the covariance matrix after reconstructing the eigenvalues; (8) calculating the weight vectors used for beamforming; and (9) calculating the beamforming output signal. This invention calculates the weight vectors for beamforming using eigenvalue reconstruction, which effectively ensures beamforming performance under high signal-to-noise ratio. This invention can be applied to fields such as communication, radar, and telemetry that require beamforming.

Description

Technical Field

[0001] This invention relates to fields such as communication, radar, and telemetry and control that require beamforming, and specifically to a beamforming method based on eigenvalue reconstruction for synthesizing array received signals. Background Technology

[0002] Adaptive beamforming technology can adaptively adjust array weights and perform weighted synthesis based on the received signal, thereby ensuring distortion-free reception of the desired signal while creating spatial nulls for interfering signals, ultimately improving the anti-interference capability of the array system. Traditional adaptive beamforming technology typically uses the covariance matrix of the received signal to calculate the optimal weight vector. However, when the received signal contains a strong desired signal component, i.e., under high signal-to-noise ratio (SNR) conditions, the desired signal may be misjudged as interference and suppressed, resulting in a decrease in the output SNR and main lobe distortion, which seriously affects the performance of the beamformer in high SNR scenarios.

[0003] To this end, the covariance matrix is ​​first calculated and its eigenvalues ​​are decomposed. The correlation between the eigenvectors and the desired signal steering vector is calculated to determine the eigenvectors that constitute the desired signal subspace. Then, the eigenvalues ​​are reconstructed to directly obtain the inverse covariance matrix. Finally, the weights are calculated and the weighted output is performed to ensure the beamformer's performance under high signal-to-noise ratio. Summary of the Invention

[0004] The problem this invention aims to solve is how to improve beamforming performance when the received signal from the array contains a strong desired signal component. The method for solving this technical problem is a beamforming method based on eigenvalue reconstruction, the implementation steps of which are:

[0005] (1) For a uniform linear array, the number of array elements is The spacing between array elements is , No. The sampling sequence of the signal received by each array element is as follows ,in It is the sampling sequence number. It is less than The non-negative integer; the array receives the signal of the first... Each snapshot is composed of signals received by the array elements. dimensional column vector, i.e. , where the symbol " "" indicates transpose; if the desired signal incident angle is Its direction vector is defined as ,in Wave number;

[0006] (2) Using the array received A quick snapshot Calculate the array covariance matrix, i.e. The symbol "H" indicates the conjugate transpose.

[0007] (3) For the matrix Perform eigenvalue decomposition to obtain normalized eigenvectors and the corresponding eigenvalues ,in Not greater than Positive integers;

[0008] (4) Calculate the angle between the desired signal direction vector and each eigenvector. ,

[0009]

[0010] In the formula This represents finding the arccosine, with its range being... , This indicates the calculation of the 2-norm of a vector;

[0011] (5) At M included angles In the equation, if the index corresponding to the smallest included angle is determined to be t, then...

[0012]

[0013] Furthermore, the eigenvalue corresponding to the smallest included angle is The feature vector is , belongs to the expected signal subspace;

[0014] (6) Remove the eigenvalues ​​of the desired signal subspace Afterwards, the remaining eigenvalues ​​can be divided into an interference signal subspace and a noise subspace, and the corresponding set of indices for the two spaces can be represented as follows: ;definition To determine the minimum eigenvalue in both the interference signal subspace and the noise subspace, a threshold constant is determined. The set of eigenvalue indices for the interference signal subspace is: , The set of eigenvalue indices for the noise subspace is , ;

[0015] (7) Reset the eigenvalues ​​in the desired signal subspace and the noise subspace to 1; furthermore, since the eigenvalues ​​corresponding to the interference signal subspace are significantly larger, their contribution to the inverse operation can be ignored. Therefore, the inverse matrix of the covariance matrix after reconstructing the eigenvalues ​​is obtained as follows:

[0016]

[0017] (8) Calculate the weight vector used for beamforming according to the adaptive beamforming criterion.

[0018]

[0019] (9) Obtain the beamforming output signal based on eigenvalue reconstruction .

[0020] The beneficial effect of this invention is that, in an array signal processing system, beamforming is performed by calculating weight vectors using eigenvalue reconstruction, which can effectively avoid the desired signal being falsely suppressed under high signal-to-noise ratio and ensure beamforming performance under high signal-to-noise ratio. Attached Figure Description

[0021] Figure 1 This is a system block diagram for beamforming using eigenvalue reconstruction.

[0022] Figure 2 This is a schematic diagram of the geometric structure of a uniform linear phased array. Detailed Implementation

[0023] First, a uniform linear phased array model is established. The array covariance matrix is ​​calculated and its eigenvalues ​​are decomposed. The correlation between the eigenvectors and the desired signal steering vector is calculated to determine the eigenvectors constituting the desired signal subspace. Then, the inverse covariance matrix is ​​directly obtained by reconstructing the eigenvalues. Finally, the weights are calculated and the weighted output is performed. The overall steps are as follows: Figure 1 As shown. The specific implementation steps are as follows:

[0024] (1) Regarding such Figure 2 The uniform linear array shown has the following number of elements: The spacing between array elements is , No. The sampling sequence of the signal received by each array element is as follows ,in It is the sampling sequence number. It is less than The non-negative integer; the array receives the signal of the first... Each snapshot is composed of signals received by the array elements. dimensional column vector, i.e. , where the symbol " "" indicates transpose; if the desired signal incident angle is Its direction vector is defined as ,in For wave number.

[0025] (2) Using the array received A quick snapshot Calculate the array covariance matrix, i.e. The symbol “H” indicates the conjugate transpose.

[0026] (3) For the matrix Perform eigenvalue decomposition to obtain normalized eigenvectors and the corresponding eigenvalues ,in Not greater than Positive integers.

[0027] (4) Calculate the angle between the desired signal direction vector and each eigenvector. ,

[0028]

[0029] In the formula This represents finding the arccosine, with its range being... , This indicates the calculation of the 2-norm of a vector.

[0030] (5) At M included angles In the equation, if the index corresponding to the smallest included angle is determined to be t, then...

[0031]

[0032] Furthermore, the eigenvalue corresponding to the smallest included angle is The feature vector is It belongs to the expected signal subspace.

[0033] (6) Remove the eigenvalues ​​of the desired signal subspace Afterwards, the remaining eigenvalues ​​can be divided into an interference signal subspace and a noise subspace, and the corresponding set of indices for the two spaces can be represented as follows: ;definition To determine the minimum eigenvalue in both the interference signal subspace and the noise subspace, a threshold constant is determined. The set of eigenvalue indices for the interference signal subspace is: , The set of eigenvalue indices for the noise subspace is , .

[0034] (7) Reset the eigenvalues ​​in the desired signal subspace and the noise subspace to 1; furthermore, since the eigenvalues ​​corresponding to the interference signal subspace are significantly larger, their contribution to the inverse operation can be ignored. Therefore, the inverse matrix of the covariance matrix after reconstructing the eigenvalues ​​is obtained as follows:

[0035]

[0036] (8) Calculate the weight vector used for beamforming according to the adaptive beamforming criterion.

[0037]

[0038] (9) Obtain the beamforming output signal based on eigenvalue reconstruction .

Claims

1. A beamforming method based on eigenvalue reconstruction, the implementation steps of which are: (1) For a uniform linear array, the number of array elements is The spacing between array elements is , No. The sampling sequence of the signal received by each array element is as follows ,in It is the sampling sequence number. It is less than The non-negative integer; the array receives the signal of the first... Each snapshot is composed of signals received by the array elements. dimensional column vector, i.e. , where the symbol " "" indicates transpose; if the desired signal incident angle is Its direction vector is defined as ,in Wave number; (2) Using the array received A quick snapshot Calculate the array covariance matrix, i.e. The symbol "H" indicates the conjugate transpose. (3) For the matrix Perform eigenvalue decomposition to obtain normalized eigenvectors and the corresponding eigenvalues ,in Not greater than Positive integers; (4) Calculate the angle between the desired signal direction vector and each eigenvector. , In the formula This represents finding the arccosine, with its range being... , This indicates the calculation of the 2-norm of a vector; (5) At M included angles In the equation, if the index corresponding to the smallest included angle is determined to be t, then... Furthermore, the eigenvalue corresponding to the smallest included angle is The feature vector is , belongs to the expected signal subspace; (6) Remove the eigenvalues ​​of the desired signal subspace Afterwards, the remaining eigenvalues ​​can be divided into an interference signal subspace and a noise subspace, and the corresponding set of indices for the two spaces can be represented as follows: ;definition To determine the minimum eigenvalue in both the interference signal subspace and the noise subspace, a threshold constant is determined. The set of eigenvalue indices for the interference signal subspace is: , The set of eigenvalue indices for the noise subspace is , ; (7) Reset the eigenvalues ​​in the desired signal subspace and the noise subspace to 1; furthermore, since the eigenvalues ​​corresponding to the interference signal subspace are significantly larger, their contribution to the inverse operation can be ignored. Therefore, the inverse matrix of the covariance matrix after reconstructing the eigenvalues ​​is obtained as follows: (8) Calculate the weight vector used for beamforming according to the adaptive beamforming criterion. (9) Obtain the beamforming output signal based on eigenvalue reconstruction .

Images