A Heuristic Algorithm for Robust Adaptive Beamforming Design With Nonconvex Uncertainty Sets

This paper considers a robust adaptive beamforming (RAB) design problem based on the worst-case signal-to-interference-plus-noise ratio (SINR) maximization, where the steering vector has a nonconvex uncertainty set consisting of a similarity constraint anda double-sided ball constraint. This problem can be turned into a quadratic matrix inequality problem, and a linear matrix inequality relaxation is explored. Two sufficient conditions are given to ensure the validity of strong duality and existence of a rank-one solution to the relaxation problem, respectively. Combining with the perturbation method, we propose a heuristic algorithm to find an optimal/suboptimal solution to the original RAB problem. Finally, simulations demonstrate that the proposed method can improve the array output SINR.