A Joint Optimization Approach for the Synthesis of Large 4-D Heterogeneous Antenna Arrays

Due to the inherent nonlinearity in the synthesis of large four dimensional (4-D) heterogeneous arrays, conventional pattern synthesis techniques are no longer suitable. In this paper, an effective joint optimization approach based on the combination of convex programming (CP) and differential evolution (DE) algorithm is proposed. By designing suitable time sequences of a 4-D heterogeneous array with uniform static amplitude excitations, the original synthesis problem is simplified into two independent small problems, which can be easily solved in two steps, respectively. In the first step, the approach takes definite advantages from the convexity of the problem with respect to the static phase excitations and the switch-on duration times. These optimization variables become known and are fixed in the second step. Then, the DE algorithm is used to optimize the switch-on time instants. Owing to the efficiency of the CP, only 2/3 of the optimization variables need be solved in the first step, while even fewer number of optimization variables are solved in the second step. Consequently, the joint optimization of CP and DE algorithm significantly improves the overall synthesis efficiency. Two numerical examples are presented to demonstrate the effectiveness of the proposed approach.