Secure Systems via Reconfigurable Intelligent Surfaces over Correlated Rayleigh Channels

In this paper, we explore the effect of practical channel conditions on the achievable secrecy of reconfigurable intelligent surface (RIS)-aided multiple-input single-output (MISO) wireless communications with the existence of both the legitimate (Bob) and the eavesdropper (Eve) nodes. Specifically, by considering beamforming at the source (Alice), we study the practical scenario where Alice has Bob's channel state information (CSI); however, she doesn't know Eve's CSI. (i.e., passive eavesdropping case). To this end, we first derive approximate expressions for modeling the RIS cascaded channel applying the Maximum Likelihood (ML) algorithm. This approach allows for incorporating relevant factors into RIS's channel modeling, including phase shift noise, correlation between RIS elements, and coexistence or not of the direct links at both the legitimate and eavesdropper nodes. Based on these findings, we obtain a closed-form solution of the outage secrecy probability for the underlying system. Finally, some valuable insights on how various channel features and the number of RIS elements affect the secrecy behavior are also presented.