In this chapter, we investigate the mathematical foundation of the modeling and design of reconfigurable intelligent surfaces (RIS) in both the far- and near-field regimes. More specifically, we first present RIS-assisted wireless channel models for the far- and near-field regimes, discussing relevant phenomena, such as line-of-sight (LOS) and non-LOS links, rich and poor scattering, channel correlation, and array manifold. Subsequently, we introduce two general approaches for the RIS reflective beam design, namely optimization-based and analytical, which offer different degrees of design flexibility and computational complexity. Furthermore, we provide a comprehensive set of simulation results for the performance evaluation of the studied RIS beam designs and the investigation of the impact of the system parameters.
@article{arxiv.2401.08237,
title = {Far- versus Near-Field RIS Modeling and Beam Design},
author = {Mohamadreza Delbari and George C. Alexandropoulos and Robert Schober and Vahid Jamali},
journal= {arXiv preprint arXiv:2401.08237},
year = {2025}
}