Programmable Antenna Design using Convex Optimization

This work presents an application of convex optimization and algebraic geometry in devising secure, powerefficient, beam-steerable, and on-chip transmission systems for wireless networks. First, we introduce a passively controllable smart (PCS) antenna system that can be programmed to generate different radiation patterns in far field by adjusting its variable passive controller at every signal transmission. To study the programming capability of a PCS antenna system, we consider a PCS antenna transmitting data in z directions, where some voltages v1, v2, ..., vz are induced in different directions in far field. The objective of this paper is to study the set of all feasible vectors (v1, v2, ..., vz) that can be generated by a passive control of the PCS antenna system. To this end, it is shown that all feasible vectors (v1, v2, ..., vz) form a convex semi-algebraic set parameterized by a linear matrix inequality (LMI). Later on, this LMI condition is further studied and it is proven that the geometry of the set of all feasible voltages (v1, v2, ..., vz) is simply an ellipsoid. This significant result makes it possible to compute the feasibility set online to decide how the PCS antenna must be programmed for either directional or simultaneous data transmission. Unlike the existing smart antennas whose programming leads to an NP-hard problem or are made of many active elements, the PCS antenna proposed in the present work has a low-complex programming capability and consists of only one active element.