Level Crossing Rate and Average Fade Duration of RIS-Assisted RF Communication System

This paper investigates the second-order statistics of a reconfigurable intelligent surface (RIS)-assisted radio frequency (RF) communication system in terms of level crossing rate (LCR) and average outage duration (AOD) which is usually termed as average fade duration (AFD). We derive the closed-form expressions of LCR and AFD under non-identical Rician and Nakagami-m fading channels. We also derive the closed-form expressions for asymptotic LCR and AFD for high signal-to-noise ratio (SNR) conditions in order to get better insights. From these expressions, we have shown that these metrics are independent of the fade threshold for high SNR conditions. With the help of numerical results, it has been shown that the deployment of RIS provides significant gain in the LCR and AFD performances when compared with a system sans RIS. Further, the impact of various system and channel parameters on LCR and AFD performances of the system under consideration are presented.