A Time-Domain Model of Reconfigurable Intelligent Surfaces Through the Fast Inversion of the Laplace Transform

The Reconfigurable Intelligent Surface (RIS) technology has gained a growing interest in both academia and industry given its capability to provide more flexible and controllable wireless propagation channels. RISs typically consist of inexpensive scattering elements (i.e., unit cells), which are spaced at sub-wavelength distances, and their characterization is mainly performed in the frequency domain. The aim of this work is to present a novel time-domain modeling approach for RISs, which is based on an inverse Laplace transform and allows to overcome some of the limitations of direct time domain analyses. In particular, since propagation delays between transmitters, RIS, and receivers are important and need to be accurately reproduced, a dedicated version of the Fast Inversion of the Laplace Transform (FILT) is presented and is found to guarantee accurate time-domain representation, while preserving the causality of the system response. In contrast to conventional time-stepping methods, the presented modeling technique is stable and allows to calculate the system response in a bounded time window within which the interaction takes place, thereby reducing the computational burden. Finally, the aforementioned claims are supported and validated by extensive numerical simulations and tests.