7. Synthesis of Far Field Patterns

In this chapter, we will focus on the synthesis of antenna arrays and treat the problem from a slightly different perspective. We at first to synthesize the required radiation pattern with a continuous current distribution in free space, and then spatially sample the continuous current source and realize it with discrete radiation elements. We show that the effective number of degrees of freedom (NDF) can be adopted as a useful information to obtain the direct synthesis pattern, which can be used as a very good initial value for further optimization. The sidelobe levels and the ripples in the main beams can be effectively controlled using an efficient hybrid optimization algorithm, in which the extrema of the objective radiation pattern are assigned based on the properties of the entire function while their positions are flexibly adjusted. Meantime, we investigate the relationship between the radiation pattern of the continuous current and that of the spatially sampled current and discuss the aliasing effect on the radiation pattern due to spatial sampling. Eleven examples are provided to demonstrate that the sidelobe levels and the ripples in the main beams can be controlled much more effectively with the hybrid method.