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

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.

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