Antenna Current Optimization using Semidefinite Relaxation

Far-field shaping of small antennas is a challenge and realization of non-dipole radiation of small to intermediate sized antennas are difficult but interesting in particular for IoT and WiFi applications. A reason for the interest is that tools like spatial filtering can mitigate package loss through a reduction of mutual interference, and hence increase the energy efficiency of the devices. We show that even a rather weak far-field shaping of smaller antennas is associated with a steep reduction in the best available bandwidth. We provide here Q-factor limitations tools to describe and determine the relation between the desired far-field and the available bandwidth for antennas of small to intermediate sized antennas. The technique is a extension and a further development of the recent successes of convex current optimization techniques. Current optimization has recently been used to predict reachable bandwidth limitations for small antennas. In this paper, we enlarge the class of current minimization problems to include a class of non-convex quadratic constraints using semi-definite relaxation. The technique is applied to different types of far-field requirement for small antennas, including a power front-to-back ratio type of bound and power pattern shaping for which the best Q-factor bound is determined.