Space-Borne Hexagonal Array Element Failure Correction Using Iterative Convex Optimiztion

Abstract

Abstract-Element failure distorts the main-lobe pattern and increases side-lobe power level, which is almost impossible to be corrected artificially for space-borne array. It might be solved by redistributing the excitations of the left functional elements; however, this is a nonlinear, non-convex, and NP-hard problem. In this paper, two effective approaches are proposed for failure correction, which is performed for space-borne hexagonal array using digital beamforming (DBF). One method, a modified real-code genetic algorithm (RCGA), is employed that uses reinsertion and worst-elimination schemes, but it pays the high computation complexity. The other approach based on convex optimization chooses the excitations synthesized by RCGA as the initial points, and transforms the non-convex problem into a sequence of second-order cone programming (SOCP) problem, which can be solved iteratively by efficient optimization tool. Numerical results confirm that after the correction based on iterative convex optimization, the average root-mean-square error (RMSE) is reduced by 36%, and the relative side-lobe level (RSLL) is decreased by 6.7 dB, with respect to the RCGA-based correction pattern.