Generalized Three Dimensional Coprime Array for Two-Dimensional DOA Estimation

Abstract

In this paper, we extend the coprime planar array to coprime cubic array and propose a three dimensional coprime array (TDCA) for two-dimensional direction of arrival (DOA) estimation, which possesses larger inter-element spacing so that the mutual coupling effects can be effectively relieved. Moreover, due to the larger array aperture, better DOA estimation performance can be achieved. To obtain more degrees of freedom (DOFs), a generalized TDCA (G-TDCA) configuration is proposed, which has a flexible array geometry and can extend the array aperture to obtain performance improvement. The principle for optimal array design of G-TDCA is derived to achieve the maximum DOF. And the Cramer–Rao Bounds which denotes as a theoretical benchmark for the lower bound of unbiased estimate are derived. Then we propose Khatri–Rao estimation signal parameters via rotational invariance techniques (KR-ESPRIT) algorithm and obtain the close-form expression. The algorithm can achieve angles with automatic pairing and doesn’t need spectrum peak searching. In order to decrease the computational complexity, we propose KR-Unitary ESPRIT algorithm, which can achieve approximate DOA estimation performance of the KR-ESPRIT algorithm with the lower computational complexity. Numerical simulation results verify the superiority of G-TDCA with proposed algorithms.