Ergodic capacity analysis of distributed RIS wireless communication system: How many RIS elements are required to beat direct LoS path?

Reconfigurable Intelligent Surface (RIS) can boost wireless communication systems’ capacity when direct Line-of-Sight (LoS) is blocked between the transceivers. This paper analyses the ergodic capacity of centralized RIS and distributed RIS setups. In the centralized setup, all the reflecting elements are consolidated into a single RIS entity. In stark contrast, the distributed approach evenly distributes the total number of reflecting elements among multiple RISs. The analysis begins by establishing upper bounds for ergodic capacity using Jensen’s inequality and explores the impact of RIS placement on system performance. Subsequently, we derive the expressions for the exact number of reflecting elements required by the RIS-generated virtual LoS to outperform the capacity of direct LoS, and the simulations conform to the exactness of the derived expressions. In addition, we analyze the impact of RISs location on the performance of all the systems under consideration.