Research On Virtual Covariance Matrix Reconstruction Algorithm For Sparse Array

In array signal processing,the array aperture is one of the key factors that determine the performance of the array,and the sparse array can use a few elements to construct a virtual uniform array,which improves the freedom of the array and realizes aperture extension.The sparse array manifold is ambiguity,but when its differential adjoint matrix is continuous and complete,the recognition and disambiguation of the sparse array manifold can be realized by the Toeplitz transform of the array covariance correlation sequence.When the adjoint matrix is non-continuously complete,it is necessary to estimate the missing related items in the virtual covariance matrix,and the Matrix Completion theory can realize the matrix recovery of some missing elements and complete the optimization processing of multi-dimensional data.The low-rank matrix completing can take advantage of the sparsity of the array signal and the low-rank nature of the covariance matrix to realize the completion of the virtual covariance matrix of the sparse array with a small amount of observation data and realize the disambiguation of the manifold.Therefore,This paper mainly combines the low-rank matrix completing theory and the virtual covariance matrix characteristics of sparse arrays to study the virtual covariance matrix completing and reconstruction algorithm of sparse arrays.The specific work is mainly as follows:(1)Introduce the basic knowledge of sparse array model,analyze uniform array and several common sparse array structures and the characteristics of each array model.From the perspective of the differential adjoint array,comprehensive analysis of the minimum redundancy array,nested array,minimum hole array,co-prime array's degree of freedom and mutual coupling and other characteristics.(2)Propose a positive definite Toeplitz completing algorithm with the minimum nuclear norm suitable for any sparse array.The algorithm first relaxes Toeplitz's positive definite constraint under the maximum entropy constraint to the matrix trace as positive,converts it to a nuclear norm constraint optimization problem,and uses the truncated mean singular value threshold method to solve the missing related items,and finally realizes the nearest neighbor Positive definite Teoplitz completing under the criterion and simulation verify that the reconstructed virtual array covariance matrix can effectively realize DOA estimation,and verify the effectiveness and stability of the algorithm in sparse arrays.(3)Aiming at the nonuniform weighting for covariance lags in virtual array interpolation,the covariance matrix reconstruction of the coprime array is modeled as the low-rank matrix completion and atomic norm reconstruction.A novel covariance matrix reconstruction algorithm based on atomic norm for coprime array is proposed.Firstly the generalized augmentation approach(GAA)is utilized to obtain a partial covariance matrix of the coprime array.Then the partial covariance matrix is completed with the truncated mean singular value threshold method and reconstructed through the atomic norm minimization.A robust positive definite Toeplitz covariance matrix is accomplished.