Extremum Seeking Control for Beam Steering using Hypersurfaces

Hypersurface, a software defined metasurface (SDM) paradigm constitutes a revolutionary technology aiming at offering programmatic control over all aspects of a propagating wave, altering its direction, power, polarization and phase. In the absence of line of sight (LOS) between a transmitter and a receiver, HSF can provide seamless connectivity via programmatic reflection. However, such an application requires fine tuning of the metasurface reconfiguration parameters, which may not be effective when done in an open loop fashion due to model uncertainties. In this work, we consider a feedback-based formulation of the problem, which involves maximization of the received power and propose the use of Extremum Seeking Control (ESC) for the controller implementation due to fact that it is model-free and adheres to the maximization problem. Extensive simulations indicate that the proposed scheme is successful in guiding the impinging wave to the receiver within reasonable time even in the presence of time varying delays incurred by message propagation. In addition, a discrete time implementation is considered, investigating its limitations as we increase the sampling time while also characterizing the traffic within the controller network.