$\ell _{0}$-Norm Minimization Based Robust Matrix Completion Approach for MIMO Radar Target Localization

Abstract

In this paper, we propose a robust matrix completion approach based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula> -norm minimization for target localization in sub-Nyquist sampled multiple-input multiple-output (MIMO) radar. Owing to the low-rank property of the noise-free MIMO radar transmit matrix, our approach is able to recover the missing data and resist impulsive noise from the receive matrix. We adopt proximal block coordinate descent and adaptive penalty parameter adjustment by complex Laplacian kernel and normalized median absolute deviation. We analyze the resultant algorithm convergence and computational complexity, and demonstrate through simulations that it outperforms existing methods in terms of pseudospectrum, mean square error, and target detection probability in non-Gaussian impulsive noise, even for the full sampling schemes. While in the presence of Gaussian noise, our approach performs comparably with other sub-Nyquist methods.