Robust and Secure Transmission over Active Reconfigurable Intelligent Surface Aided Multi-User System

Active reconfigurable intelligent surface (RIS) draws great attentions recently due to its unique nature of 'changing' the wireless propagation channels via simultaneously adjusting the phase and amplifying the amplitude of signals, and is proved to effectively overcome the double fading effect when the signals are reflected by RIS compared with the widely investigated passive RIS with only adjusting the phase of the signals. Motivated by this great advantage, in this paper, we apply active RIS into a multi-user system and focus on enhancing the secure transmission performance in the presence of a malicious eavesdropper (Eve). Specifically, two types of imperfect channel state information (CSI) between RIS and Eve, namely imperfect CSI with bounded estimation error and with statistical distribution of estimation error, are considered, and we focus on enhancing the worst-case secrecy rate (SR) as well as weighted sum-SR of this system under each CSI condition. In particular, for the study of weighted sum-SR maximization, a more serious situation is assumed where Eve can filter out all the interference signals as well as the external noise generated by RIS when decoding each user's information. Given these settings, we propose a robust alternating optimization (AO)+line search combined algorithm to optimize the worst-case SR, and a dual-successive approximation algorithm to optimize the weighted sum-SR. Numerical examples demonstrate that compared with the benchmark scheme under passive RIS aided case, the proposed algorithms for the active RIS aided system greatly enhance both the worst-case and weighted-sum SR under these CSI conditions.