Impact of Reconfigurable Intelligent Surface size on beamforming efficiency

Future wireless networks are expected to be highly assisted by reconfigurable intelligent surfaces (RIS) in non-line-of-sight links. The role of the RIS is to redirect the incident beam from the transmitter to the receiver and possibly modify its characteristics, in order to maximize the signal power at the receiver and optimize the beamforming efficiency. Therefore, it is crucial to understand what are the bounds imposed on the received power and how these bounds depend on the system design parameters. In this paper we show that there is an interplay between the transmitter beamwidth and the RIS size that leads to a maximum power at the receiver. We demonstrate our findings with numerical examples that provide insight on the effect of the RIS size on the received signal power.