On The Optimal Number of Reflecting Elements for Reconfigurable Intelligent Surfaces

Abstract: This work considers a point-to-point link where a reconfigurable intelligent surface assists the communication between transmitter and receiver. The system rate, energy efficiency, and their trade-off are optimized with respect to the number of individually tunable elements of the intelligent surface. The resource allocation accounts for the communication phase and for the overhead due to channel estimation and to reporting the optimized resource allocation to the intelligent surface. Numerical results confirm the optimality of the proposed methods and show the potential gains of reconfigurable intelligent surfaces.