Sparsity-aware direction finding for strictly non-circular sources based on rank minimization

Abstract

Exploiting the statistical properties of strictly non-circular (NC) signals in direction of arrival (DOA) estimation has long been an active area of research due to its associated performance improvements. Recently, this concept has been introduced to DOA estimation via sparse signal recovery (SSR), where similar benefits from processing NC signals are achieved. However, the standard approach to NC SSR requires solving a two-dimensional (2-D) SSR problem in the spatial and the phase rotation domain, which is not only associated with a high computational complexity itself but also with a 2-D off-grid problem. In this paper, we propose an entirely new NC SSR approach based on nuclear norm (rank) minimization after lifting the original bilinear optimization problem to a linear optimization problem in a higher-dimensional space. Thereby, the SSR-based 2-D estimation problem is reduced to a 1-D estimation problem only in the sampled spatial domain, which automatically provides gridless estimates of the rotation phases. In our second contribution, we present a simple closed-form grid offset estimator for a single NC source and a numerical joint grid offset estimation procedure for two closely-spaced NC sources assuming a uniform linear array (ULA). Simulations validate the effectiveness of the new approach.