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 skillfully transforms the non-convex problem into a sequence of second-order cone programming (SOCP) problem, which is 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 improved by 6.7 dB, with respect to the RCGA-based correction pattern.
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