Sparsity-Based Two-Dimensional DOA Estimation for Coprime Array: From Sum–Difference Coarray Viewpoint

Abstract

This paper addresses the issue of two-dimensional (2-D) direction of arrival (DOA) estimation with coprime planar arrays (CPPAs) via sparse representation. Our work differs from the partial spectral search approach [25] , which suppresses the phase ambiguity by searching the common peaks of two subarrays. We focus on the coprime property of CPPA, where the sparse array extension model with sum–difference coarray (SDCA) is derived for larger degrees of freedom (DOFs). Besides, to optimize the selection of regularization parameter, we also construct a new sparse representation algorithm by estimating the errors between the signal and noise parts. Further, an iterative scheme is presented to transform the 2-D grids searching to several times of 1-D searching, where the initial values are obtained by extracting one difference coarray from SDCA. So the proposed method can achieve aperture extension, high estimation performance, and low computational complexity. Besides, the sparse array extension model for multiple-input multiple-output radars is discussed and the Cramer–Rao bound for 2-D DOA estimation with CPPA is also derived in detail. Finally, simulation results demonstrate the effectiveness of proposed method compared to the state-of-the-art methods.