Performance Analysis of RIS-Assisted Communication With Direct Link: A New Copula Application

Abstract

Reconfigurable intelligent surfaces have received remarkable attention as promising solutions to enhance the capacity and coverage of wireless cellular networks. In this paper, we evaluate the performance of reconfigurable intelligent surfaces-assisted communication systems in the presence of phase noise, and consider a direct link in conjunction with cascade link between the transmitter and receiver by exploring different copulas. In particular, we first analyze the cumulative distribution function and the probability density function of the signal-to-noise-ratio distribution under phase noise in the presence of both direct and cascaded channel links. Moreover, we propose a copula-based solution to effectively model the non-linear dependencies among signal components induced by phase noise, and derive several exact closed-form expressions for outage probability in reconfigurable intelligent surfaces-assisted networks. In our method of analysis, we employ various copula families, including Archimedean copulas such as Farlie-Gumbel-Morgenstern, Frank, and Clayton, along with Elliptical copulas such as Gaussian and Student-T. Finally, numerical results are shown to confirm the validity of the closed-form expressions.INDEX TERMS copula theory, outage probability, reconfigurable intelligent surface (RIS), phase noise, 6G.