A statistical approach for robust metasurfaces and metasurface-based RIS engineering

The design of metasurface-based devices [e.g., reflective intelligent surfaces (RISs)] 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, and so on. 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.