Matrix Completion Based Second Order Statistic Reconstruction DOA Estimation Method

Focusing on the problem of poor accuracy and low resolution of traditional Direction Of Arrival (DOA) estimation algorithm in the presence of non-uniform noise, based on the Matrix Complement theory, a Weighted L1 Sparse Reconstruction DOA estimation algorithm is developed under the Second-order Statistical domain (MC-WLOSRSS) in this paper. Following the matrix completion approach, the regularization factor is firstly introduced to reconstruct the signal covariance matrix reconstruction as a noise-free covariance matrix. After that, the multi-vector problem of the noise-free covariance matrix can be transformed into a single vector one by exploiting sum-average operation for matrix in the second-order statistical domain. Finally, the DOA can be complemented by employing the sparse reconstruction weighted L1 norm. Numerical simulations show that the proposed algorithm outperforms the traditional DOA algorithms such as MUltiple SIgnal Classification (MUSIC), Improved L1-SRACV (IL1-SRACV), L1-norm-Singular Value Decomposition (L1-SVD) subspace and sparse reconstruction weighted L1 methods in the following respects: suppressing the influence of the non-uniform noise significantly, bettering DOA estimation performance, as well as improving estimation accuracy and resolution with low Signal-Noise Ratio (SNR).