Optimization of Embedded Element Patterns of Reactively Loaded Antenna Arrays

This paper introduces a framework for synthesizing reactively loaded antennas and antenna arrays. The framework comprises two main components: computing the fundamental bound using the semi-definite relaxation and finding a realizable solution via optimization on a Riemannian manifold. The embedded element patterns are subject to the optimization with two distinct goals under study: focusing the radiation in a single direction or synthesizing patterns with desired shapes. The reactive terminations of passive antenna elements serve as optimization variables. We demonstrate the framework using a connected bowtie-slot antenna and antenna array with both beam-focusing and beam-shaping targets. The tests show that the optimization on the Riemannian manifold yields superior results compared to existing methods, such as the genetic algorithm. This is particularly evident in the most complex and extensive problem, which requires the synthesis of shaped embedded element patterns for a sparse reactively loaded antenna array with a limited field of view.