Calibration Nested Arrays for Underdetermined DOA Estimation Using Fourth-Order Cumulant

The application of a nonuniform nested array provides a simple way for underdetermined direction of arrival (DOA) estimation, enabling us to develop a suited self-calibration algorithm for perturbed nested array. The key points of this algorithm contain two steps: a first step is to obtain gain-phase errors estimation by utilizing partly calibrated array and properly choosing the elements of fourth-order cumulant matrix; a second step to form a small perturbed model after compensating the gain-phase errors as well as obtain DOA estimation using the sparse total east squares (STLS) technique. The proposed algorithm is very suited for underdetermined DOA estimation in the presence of gain-phase errors. Numerical simulations validate the effectiveness of the proposed algorithm.