Coverage Analysis of Reconfigurable Intelligent Surface Assisted THz Wireless Systems

This paper presents a connectivity analysis of reconfigurable intelligent surface (RIS) assisted terahertz (THz) wireless systems. Specifically, a system model that accommodates the particularities of THz band links as well as the characteristics of the RIS is reported, accompanied by a novel general end-to-end (e2e) channel attenuation formula. Based on this formula, we derive a closed-form expression that returns the optimal phase shifting of each reflection unit (RU) of the RIS. Moreover, we provide a tractable e2e channel coefficient approximation that is suitable for analyzing the RIS-assisted THz wireless system performance. Building upon the aforementioned approximation as well as the assumption that the user equipments are located in random positions within a circular cluster, we present the theoretical framework that quantifies the coverage performance of the system under investigation. In more detail, we deliver a novel closed-form expression for the coverage probability that reveals that there exists a minimum transmission power that guarantees 100% coverage probability. Both the derived channel model as well as the coverage probability are validated through extensive simulations and reveal the importance of taking into account both the THz channel particularities and the RIS characteristics, when assessing the system's performance and designing RIS-assisted THz wireless systems.