Phase-Space Representations for Smart Electronic Environments #

Martin Richter, Sergio Terranova, Gabriele Gradoni

15:10 Tuesday in 4Q07.

Part of the Industrial mathematics session.

Abstract #

We present a method to incorporate the anomalous reflection behaviour of so called Reconfigurable Intelligent Surfaces (RIS) into ray-based methods. This is an important step to create reliable algorithms for the configuration of next-generation mobile networks.

In these next generation mobile networks (6G), RIS form a corner stone. They consist of periodic sub-wavelength structures forming a meta-material for the electro-magnetic field. This gives them novel properties not known from other materials: They can be controlled such that the local boundary conditions change and impinging radiation can be reflected into a customisable direction. For this to work, the sub-wavelength pixels of the RIS have to be configured correctly. Finding the optimal configuration of these pixel arrays is far from trivial and current prototypes mainly use brute-force methods. A mathematical description is further complicated by the fact that the next generation networks will operate on shorter and shorter wavelengths. This means that modelling Maxwell’s Equations by means of, e.g., FEM or FDTD methods becomes more and more complicated.

In our work we will therefore focus on high-frequency / short-wavelength asymptotics in terms of ray-tracing. We will incorporate the influence of the RIS onto the ray dynamics by using methods known from Quantum Mechanics, most notably Wigner and Husimi functions. These are functions which allow us to combine the inherent wave picture of the problem with the underlying classical phase space of the ray-tracing approximation.