DOA estimation via shift-invariant matrix completion

Abstract

This paper presents a method to estimate the direction of arrival (DOA) of multiple sources received by a uniform linear array (ULA) with a reduced number of radio-frequency (RF) chains. The receiving array relies on antenna switching so that at every time instant only the signals received by a randomly selected subset of antennas are downconverted to baseband and sampled. Low-rank matrix completion (MC) techniques are then used to reconstruct the missing entries of the signal data matrix to keep the angular resolution of the original large-scale array. The proposed MC algorithm exploits not only the low-rank structure of the signal subspace, but also the shift-invariance property of ULAs, which results in a better estimation of the signal subspace. Further, the effect of MC on DOA estimation is discussed under the perturbation theory framework. The simulation results suggest that the proposed method provides accurate DOA estimates even in the small-sample regime with a significant reduction in the number of RF chains required for a given spatial resolution.