A Convex Optimization Approach for the Design of Supergain Electrically Small Antenna and Rectenna Arrays Comprising Parasitic Reactively Loaded Elements

A convex optimization formulation is provided for antenna arrays comprising reactively loaded parasitic elements. The objective function consists of maximizing the array gain, while constraints on the admittance are provided in order to properly account for reactive loads. Topologies with two and three electrically small dipole arrays comprising one fed element and one or two parasitic elements, respectively, are considered and the conditions for obtaining supergain are investigated. The admittance constraints are formulated as linear constraints for specific cases as well as more general, quadratic constraints, which require the solution of an equivalent convex relaxation formulation. A design example for an electrically small superdirective rectenna is provided where an upper bound for the rectifier efficiency is computed.

Automated summary

This paper provides a convex optimization formulation for antenna arrays with reactively loaded parasitic elements. The objective function aims to maximize the array gain while considering the constraints on admittance to account for reactive loads. The study explores topologies with two and three electrically small dipole arrays, investigating the conditions for achieving supergain. Admittance constraints are formulated as linear or quadratic constraints, requiring an equivalent convex relaxation formulation. The paper also includes a design example for an electrically small superdirective rectenna, computing the upper bound on rectifier efficiency.