Ergodic Secrecy Rate of RIS-Assisted Communication Systems in the Presence of Discrete Phase Shifts and Multiple Eavesdroppers

TL;DR

This paper analyzes the ergodic secrecy rate of RIS-assisted communication systems with discrete phase shifts and multiple eavesdroppers, deriving closed-form approximations and scaling laws for large RIS sizes.

Contribution

It provides the first closed-form approximation of the ESR in RIS systems with discrete phase shifts and multiple eavesdroppers, including asymptotic analysis and scaling laws.

Findings

ESR scales with log2 N for large N

Analytical results match numerical simulations

Impact of discrete phase shifts on secrecy rate

Abstract

This letter investigates the ergodic secrecy rate (ESR) of a reconfigurable intelligent surface (RIS)-assisted communication system in the presence of discrete phase shifts and multiple eavesdroppers (Eves). In particular, a closed-form approximation of the ESR is derived for both non-colluding and colluding Eves. The analytical results are shown to be accurate when the number of reflecting elements of the RIS $N$ is large. Asymptotic analysis is provided to investigate the impact of $N$ on the ESR, and it is proved that the ESR scales with $\log_2 N$ for both non-colluding and colluding Eves. Numerical results are provided to verify the analytical results and the obtained scaling laws.