On the Performance of RIS-Assisted Communications With Direct Link Over <italic>&#x03BA;-&#x03BC;</italic> Shadowed Fading

Abstract

In reconfigurable intelligent surface (RIS)-assisted communications, the signal-to-noise ratio (SNR) is improved by optimizing the reflecting elements’ phases to make the reflected signals add coherently at the receiver. Nevertheless, the RIS cannot control the phase of the direct link if it exists. Although the RIS phase can still be controlled such that the direct and reflected signals add coherently, the SNR gain might be hindered. Therefore, this paper considers the performance analysis of such scenarios where a novel analytical framework is developed to evaluate the SNR, outage probability, and bit error rate (BER). To capture a broad range of fading conditions, the channels are modeled as independent but not identically distributed generalized $\kappa $ - $\mu $ shadowed fading channels. The Laplace transform is used to derive an accurate approximation of the probability density function (PDF) and cumulative distribution function (CDF) of the instantaneous fading, which are used to derive the PDF and CDF of the instantaneous SNR. The paper also considers deriving the asymptotic PDF, CDF, moment generating function (MGF) of the SNR, as well as the outage probability and BER. The obtained results show that a strong direct link may limit the gain obtained using the RIS.

Keywords

• κ-μ shadowed fading
• RIS
• intelligent surfaces
• diversity order
• outage probability
• MGF