Study On Array Spread Beamforming Based On Interpolation Transform

The virtual array beamforming algorithm plays an increasingly important role in the field of adaptive array signal processing,and the virtual array beamforming algorithm based on interpolation has the advantages that other virtual array expansions do not have.The advantages of the algorithm are as follows: firstly this algorithm successfully increased the number of array antenna array elements.Secondly,the virtual array antenna can effectively distinguish the number of sources beyond the actual number of elements or sources of interference more than the actual number of elements.Thirdly,narrower beam can be formed in the desired direction.However,the algorithm cannot form deep nulls in the interference direction,thus the transform error occurs inevitably,which makes the beam performance decrease.Therefore,this paper studies the algorithm of virtual array extended beamforming based on interpolation transform.The main work is discussed as follows:(1)A method to improve diagonal loading virtual array beamforming is proposed.The method solves the problem of shallow zeros and high grating lobes in the conventional virtual array antenna beamforming algorithm.The idea is to decompose the virtual covariance matrix by a singular value algorithm and use the virtual covariance matrix to determine diagonal loading values,new weights are constructed for subsequent beamforming.Simulation results show that the array element number is effectively increased,a deep zero-trap can be formed in the interference direction,good performance is achieved with fewer snapshots,and the robustness is better.(2)A method based on unitary matrix virtual array beamforming is proposed.The idea of this method is to construct a unitary matrix by using the virtual covariance matrix,form a matrix bundle according to the unitary matrix,and decompose the matrix bundle by the singular value decomposition algorithm to obtain the weight required for beamforming.Simulation results show that this algorithm improves the performance of the beam to a certain extent.(3)A generalized Singular Value Decompositon(GSVD)virtual array beamforming algorithm is proposed.In the algorithm,the noise subspace is obtained by decomposing the virtual covariance matrix by using the singular value decomposition,and then the virtual covariance matrix and the noise subspace are formed into a matrix bundle.Finally,the generalized singular value algorithm is used to decompose the matrix bundle to obtain the weight required for beamforming.The simulation results show that this algorithm has better beam performance than the traditional virtual antenna beamforming algorithm.(4)A virtual array beamforming algorithm based on improved orthogonal projection is proposed.This method is to solve the problem of small feature perturbation caused by transform error in the process of interpolation transform.First,the method decomposes the virtual array covariance matrix by eigenvalue decomposition to obtain the correspondingeigenvalues and eigenvectors,space and interference noise subspace.Then the desired signal steering vector is orthogonally projected to the interference signal subspace to obtain the projection matrix of the orthogonal complementary space in the interference signal subspace,and the reconstructed virtual covariance Matrix,using the singular value decomposition algorithm to decompose and reconstruct the covariance matrix to obtain the singular value of the covariance matrix and its corresponding eigenvector;and finally performing the beamforming by the MVDR algorithm.This variance can avoid the eigenvalue corresponding to the noise and the eigenvectors involved in the operation of the beamforming weight vector,thus avoiding the small eigenvalue perturbation and improving the performance of the beam.