A Statistical Approach for Robust Metasurfaces and Metasurface-Based RIS Engineering

The design of metasurface-based devices (e.g. reflective intelligent surfaces - RIS) is inherently affected by unpredictable variations of the unit-cell response, due to undesired coupling effects among adjacent unit-cells, fabrication tolerances, physical discontinuities, the presence of bumps, etc. Such variations may dramatically affect the accuracy of the conventional design models. In this work, we present a statistical model resulting in a probability density function that allows defining a random local surface impedance (rLSI), that considers potential random variations derived from the von Mises distribution. To compensate for these variations, we propose a transformation kernel that matches the expected value to the design target value. By using an analytical formulation and a proper set of full-wave simulations, we demonstrate the effectiveness and robustness of the method against unpredictable variations caused by the mutual coupling among the unit-cells and fabrication tolerances/errors. The proposed method paves the way to foster advancements in realistic metasurface engineering.