On the Optimal Number of Reflecting Elements for Reconfigurable Intelligent Surfaces

This letter considers a point-to-point link where a reconfigurable intelligent surface assists the communication between a transmitter and a receiver. The system rate, energy efficiency, and their trade-off are optimized by tuning the number of reflecting elements to be activated and the phase shifts that they apply. Unlike most previous works, the considered resource allocation problem explicitly accounts, at the design stage, for the time and energy that are necessary for channel estimation and for reporting the optimal configuration of the phase shifts to the reconfigurable intelligent surface. Numerical results confirm the optimality of the proposed methods and show the potential gains of reconfigurable intelligent surfaces.