Reconstructing DOA Estimation in the Second-Order Statistic Domain by Exploiting Matrix Completion

It is known that the performance of classical direction-of-arrival (DOA) estimators may be deteriorated considerably in the presence of non-uniform noise and low signal-to-noise ratio (SNR). Focusing on this issue, based on the matrix completion theory, a sparse reconstruction algorithm combining second-order statistical vectors and weighted L1-norm is developed in this paper. In the proposed method, the elastic regularization factor is firstly introduced into the matrix completion model to reconstruct the signal covariance matrix as a noise-free covariance matrix. In what follows, the obtained multi-vector issue associated with the noise-free covariance matrix can be recast as a single vector one by exploiting matrix sum-average operation in the second-order statistical domain. With the constructed single vector, DOA estimation can be complemented by employing the sparse reconstruction weighted L1-norm (WL1) approach. Numerical simulation results show that the proposed algorithm has improved angle estimation accuracy and resolution effectively under low SNR and can suppress the effect of noise non-uniformity significantly.