Low-Complexity 2D DOA Estimation and Self-Calibration for Uniform Rectangle Array with Gain-Phase Error

Most subspace-based algorithms need exact array manifold for direction of arrival (DOA) estimation, while, in practical applications, the gain-phases of different array elements are usually inconsistent, degrading their estimation performance. In this paper, a novel low-complexity 2D DOA and gain-phase error estimation algorithm is proposed by adding auxiliary array elements in a uniform rectangular array (URA). Firstly, the URA is modeled as the Kronecker product of two uniform linear arrays (ULAs) to decouple the 2D DOA estimation. Then, several well-calibrated auxiliary array elements are added in the two ULAs, based on which the rotation invariant factor of the URA destroyed by the gain-phase error is reconstructed by solving constrained optimization problems. Lastly, ESPRIT is used to estimate the 2-D DOA and the gain-phase error coefficients. The closed-form expressions of the estimation CRBs are also derived, providing insight into the impact of gain-phase error on DOA estimation. Simulation results are used to validate the effectiveness of the proposed algorithm and the correctness of the theoretical analysis.