Maximization of Geometric Mean of Secrecy Rates in RIS-aided Communications Networks

In this paper, we study a secure communications network in which a multiple-antenna access point (AP) with the assistance of a reconfigurable intelligent surface (RIS) serves multiple single-antenna legitimate users (UEs) with the presence of an eavesdropper (EV). Specifically, the RIS, which can tune/control/alter the phase shift of reflected signals (onto it), is deployed to prevent potential information leaked (to the EV). To secure the downlinks from the AP to the UEs via the RIS, we consider the joint design of linear transmit beamformers at the AP and programmable reflecting coefficients of the RIS to maximize the geometric mean (GM) of all users' secrecy rates. Then, an efficient algorithm, called RIS-aided secure beamforming (RaSB) algorithm, which invokes a closed-form expression at each iteration, is proposed to solve this non-convex problem. Numerical results reveal that the performance of the proposed RaSB algorithm outperforms the one without phase optimization. Simulations are also performed to investigate the impact of the EV's position on the GM of secrecy rates.