Upper-Bound Ergodic Capacity Analysis of RIS-Aided Energy-Harvesting Relay Systems

In this paper, we consider a single-input single-output system consisting of a source, a destination, an energy harvesting (EH) decode-and-forward (DF) relay and two separate reconfigurable intelligent surfaces (RISs). A power-splitting ratio is employed at the EH DF relay to represent a tradeoff between the harvested energy partially for decoding the source signal received at the relay and the remaining energy for retransmitting the decode signal. By using Jensen Inequality, we derive a closed-form upper-bound expression of the ergodic capacity for the proposed RIS-aided EH relay transmission scheme with the optimal power-splitting ratio, which is shown to closely match Monte-Carlo simulations. We analyse the impact of the RIS and relay locations on the ergodic capacity performance. Additionally, our simulations show that the proposed transmission scheme achieves a better capacity than that without relay or just having a single RIS deployed between the source and relay.