Off‐grid direction‐of‐arrival estimation for nested arrays via uncertainty set extraction

Here, a novel off‐grid direction‐of‐arrival (DOA) estimation algorithm for nested arrays in the context of sparse recovery is proposed. The framework of existing off‐grid approaches is to correct the on‐grid parameter with a grid mismatch variable. From another perspective, we treat the direction‐of‐arrival deviation as the steering vector deviation equivalently, and the concept of steering vector uncertainty set is introduced to approximate the desired steering vector. Based on this idea, an optimization problem with respect to the uncertainty set for the purpose of steering vector reconstruction is formulated. After that, phase‐ambiguity resolving and phase‐difference approximation are orderly performed on the optimized uncertainty set to extract the off‐grid direction of arrival. Even though a coarse grid is given, simulation results are presented to demonstrate the performance advantage of the proposed direction‐of‐arrival estimation algorithm compared with several existing approaches.