Sparsity-based direction-of-arrival estimation for strictly non-circular sources

Direction of arrival (DOA) estimation via sparse signal recovery (SSR) has recently attracted a considerable research interest due to its various advantages over the conventional DOA estimation methods. Yet, the performance of the SSR-based algorithms can be further enhanced by exploiting the structure of strictly non-circular (NC) signals. In this paper, we present a novel strategy to take the NC signal structure into account for the SSR, which results in a two-dimensional SSR problem. Thereby, the known benefits associated with NC sources can be achieved. Moreover, we address the 2-D off-grid problem by proposing a low-complexity procedure that estimates the sources' grid offset from the closest neighboring grid points. For a single off-grid source, we show analytically that the 2-D offset estimation problem is separable, allowing to perform the offset estimation in both dimensions independently. We also propose a numerical procedure for the joint estimation of the grid offsets of two closely-spaced sources. The effectiveness of the proposed methods is demonstrated via simulations.