We consider a reconfigurable intelligent surface (RIS) that can implement a phase rotation continuously over the whole surface rather than via a finite number of discrete elements. Such an RIS can be considered a design for future systems where advances in metamaterials make such an implementation feasible or as the limiting case where the number of elements in a traditional RIS increases in a given area. We derive the optimal RIS design for the single-user (SU) scenario assuming a line-of-sight (LoS) from the RIS to the base station (BS) and correlated Rayleigh fading for the other links. We also derive the associated optimal signal-to-noise ratio (SNR) and its mean, a bound on the mean spectral efficiency (SE), an approximation to the SNR outage probability and an approximation to the coefficient of variation for the investigation of channel hardening.
@article{arxiv.2506.14385,
title = {Performance Characterization of Continuous Reconfigurable Intelligent Surfaces},
author = {Amy S. Inwood and Peter J. Smith and Mahmoud AlaaEldin and Michail Matthaiou},
journal= {arXiv preprint arXiv:2506.14385},
year = {2025}
}