Optimal Synthesis of Robust Beamformer Weights Exploiting Interval Analysis and Convex Optimization

Abstract

An approach for the optimal design of linear arrays in the presence of tolerances on the amplitude weights is presented. Starting from the knowledge of the maximum deviations from the nominal values of the amplitude coefficients of the beam-forming network (BFN), an analytical tool based on interval analysis (IA) and integrating a convex programming (CP) method is exploited to maximize the minimum peak value of the main beam of the radiated power pattern along the boresight direction, while fitting an arbitrary user-defined bound on the secondary lobes in a globally optimal fashion. In order to analyze the behavior of the proposed approach also assessing its effectiveness, a set of representative numerical examples regarding arrays of ideal and realistic radiating elements is reported where different sidelobe constraints, array configurations, and tolerance errors are considered.