Array Pattern Synthesis: A Tighter Robust Model and ADMM-Based Solution.

In most existing robust array beam pattern synthesis studies, the bounded-sphere model is used to describe the steering vector (SV) uncertainties. In this paper, instead of bounding the norm of SV perturbations as a whole, we explore the amplitude and phase perturbations of each SV element separately, and thus gives a tighter SV uncertainty set for better robust performance. Based on this model, we formulate the robust pattern synthesis problem from the perspective of the min-max optimization, which aims to minimize the maximum side lobe response, while preserving the main lobe response. However, this problem is difficult due to the infinitely many non-convex constraints. As a compromise, we employ the worst-case criterion and recast the problem as a convex second-order cone program (SOCP). To solve the SOCP, we further design an alternating direction method of multipliers (ADMM) based algorithm, which is computationally efficient by coming up with closed-from solutions in each step.