An effective hybrid approach for the synthesis of pencil beams and shaped beams through 4D linear antenna arrays with constrained DRR

In this work, a novel hybrid approach combining differential evolution (DE) algorithm and convex programming (CP) is proposed for the synthesis of four-dimensional (4D) antenna arrays. To achieve ultra-low sidelobe level while suppressing sideband radiations simultaneously, the hybrid approach is applied to optimize static excitation coefficients and switch-on duration time separately. In particular, the hybrid approach fully makes use of the partial convexity of the problem with respect to the static excitation coefficients. CP is used to optimize static excitation coefficients for each set of switch-on duration time generated by the DE algorithm, while the DE algorithm is used to optimize the switch-on duration time only. Consequently, fewer optimization variables are needed and less iterations are required. The approach converges faster as compared to stochastic algorithms including all the optimization variables, especially for large arrays. Several numerical examples of the 4D antenna arrays are presented to demonstrate the effectiveness of the proposed hybrid approach.