On the Performance of RIS-Assisted Communications with Direct Link in κ-µ Shadowed Fading Channels

Reconfigurable intelligent surfaces (RISs) is a new technology that can be used to create a virtual line-of-sight (LOS) link when the direct link is blocked. The signal-to-noise ratio (SNR) can be significantly 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. In such scenarios, the RIS phase can still be controlled such that the direct and reflected signals add coherently, however, the gain obtained by using the RIS 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 κ-µ shadowed fading channels. The Laguerre expansion is used to derive the probability density function (PDF) and cumulative distribution function (CDF) of the instantaneous channel 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 derived expressions are used to evaluate the system performance in various fading environments such as Rayleigh, One-Sided Gaussian, Nakagami-m , Rician, and Rician-shadowed distributions since they are special cases of the κ-µ shadowed distribution. The obtained analytical results corroborated by Monte Carlo simulation show that a strong direct link can generally eliminate the gain obtained using the RIS. Therefore, the overhead required for the RIS operation becomes a burden on the network and may cause severe throughput degradation. In such scenarios, the RIS involvement should dynamically controlled to avoid unnecessary complexity and throughput reduction.