A mixed-field sources localization algorithm based on high-order cumulant matrix reconstruction for general symmetric array

Abstract

Sparse arrays are able to generate more lags to extend the array aperture, which is a distinct advantage in mixed-field localization. To exploit these lags, existing algorithms in the known literature can be mainly divided into two types: the subspace-based algorithm and the sparsity-based algorithm. However, the former algorithm cannot fully utilize the time delay information provided by sparse array, and the second algorithm has basis mismatch problem. In this paper, an interpolation processing method based on atomic norm is proposed to solve the sparse array localization problem. The high-order cumulant matrix is reconstructed by the interpolation method to generate an augmented cumulant matrix without holes, which can make full use of all the lags. Then, the atomic norm minimization method is used to recover the sparse matrix after interpolation in a gridless way. The matrix after recovery enables gridless direction-of-arrival (DOA) estimation. After the interpolation reconstruction, more lags can be exploited, the degrees of freedom are further increased. The proposed algorithm can not only make full use of the array receiving information but also avoid the base mismatch problem, and the accuracy of DOA estimation is improved. Numerical simulations verify the superiority of the proposed algorithm compared with the existing algorithms.