Optimal SNR Analysis for Single-user RIS Systems in Ricean and Rayleigh Environments

TL;DR

This paper analyzes the optimal uplink SNR in RIS-assisted wireless systems under Ricean and Rayleigh fading, deriving closed-form expressions and characterizing environmental effects on system performance.

Contribution

It provides exact and approximate analytical expressions for SNR distribution in RIS systems, revealing how correlation and K-factors influence performance.

Findings

Increasing K-factor and correlation in UE-BS channels can reduce mean SNR.

Higher K-factor and correlation in UE-RIS channels improve system performance.

SNR gain saturates to a constant as the number of RIS elements grows large.

Abstract

We present an analysis of the optimal uplink (UL) SNR of a SIMO Reconfigurable Intelligent Surface (RIS)-aided wireless link. We assume that the channel between base station (BS) and RIS is a rank-1 LOS channel while the user (UE)-RIS and UE-BS channels are correlated Ricean. For the optimal RIS matrix, we derive an exact closed form expression for the mean SNR and an approximation for the SNR variance leading to an accurate gamma approximation to the distribution of the UL SNR. Furthermore, we analytically characterise the effects of correlation and the Ricean K-factor on SNR, showing that increasing the K-factor and correlation in the UE-BS channel can have negative effects on the mean SNR, while increasing the K-factor and correlation in the UE-RIS channel improves system performance. We also present favourable and unfavourable channel scenarios which provide insight into the sort of environments that improve or degrade the mean SNR. We also show that the relative gain in the mean SNR when transitioning from an unfavourable to a favourable environment saturates to $(4-\pi)/\pi$ as $N \rightarrow \infty $