Spatially Selective Reconfigurable Intelligent Surfaces Through Element Permutation

A standard reconfigurable intelligent surface (RIS) can be configured to reflect signals from an arbitrary impinging direction to an arbitrary outgoing direction. However, if a signal impinges from any other direction, said signal is reflected, with full beamforming gain, to a specific direction, which is easily determined. The goal of this paper is to propose a RIS which \emph{only} reflects signals from the configured impinging direction. This can be accomplished by a RIS architecture that permutes the antenna elements in the sense that a signal is re-radiated from a different antenna than the one receiving the signal. We analytically prove this fact, and also discuss several variants and hardware implementations.