Pattern Synthesis of 4-D Irregular Antenna Arrays Based on Maximum-Entropy Model

The 4-D antenna arrays with the irregular array topology have great advantages in simplifying the beamforming network and reducing the cost. However, the complexity of such synthesis problems limited their development. An effective joint optimization approach based on the maximum-entropy model is proposed for the pattern synthesis of 4-D irregular arrays. By introducing the entropy concept into 4-D irregular arrays, the original synthesis problem is simplified into two problems, which can be solved in two steps separately. In the first step, the optimization of the topology of 4-D irregular arrays characterized by domino-shaped tiles is performed, based on the principle of entropy maximization. The genetic algorithm is introduced to solve the pure integer optimization problem. Then, the differential evolution algorithm is used to synthesize the desired radiation pattern based on the optimized array topology. Consequently, the joint optimization approach significantly improves the overall synthesis efficiency. Three numerical examples are presented to demonstrate the effectiveness of the proposed approach. Moreover, the numerical results show that the 4-D irregular arrays designed by the proposed approach have the excellent beam scanning ability.