Asymptotic Optimality of Reconfigurable Intelligent Surfaces: Passive Beamforming and Achievable Rate

Reconfigurable intelligent surfaces (RISs) have recently emerged as a promising technology that can manipulate the properties of an incident wave, such as the frequency, amplitude, and phase, without the need for complex signal processing. In this paper, the asymptotic optimality of achievable rate in a downlink RIS system is analyzed under a practical RIS environment with its associated limitations. In particular, a passive beamformer that can achieve the asymptotic optimal performance by controlling the incident wave properties is designed, under practical reflection coefficients. In order to increase the achievable system sum-rate, a modulation scheme that can be used in an RIS without interfering with existing users is proposed and its average symbol error rate is asymptotically derived. Simulation results show that the proposed schemes are in close agreement with their upper bounds in presence of a large number of RIS reflecting elements thereby verifying that the achievable rate in practical RISs satisfies the asymptotic optimality.