Secure Outage Analysis for RIS-Aided MISO Systems with Randomly Located Eavesdroppers

In this paper, we consider the physical layer security of an RIS-assisted multiple-antenna communication system with randomly located eavesdroppers. The exact distributions of the received signal-to-noise-ratios (SNRs) at the legitimate user and the eavesdroppers located according to a Poisson point process (PPP) are derived, and a closed-form expression for the secrecy outage probability (SOP) is obtained. It is revealed that the secrecy performance is mainly affected by the number of RIS reflecting elements, and the impact of the transmit antennas and transmit power at the base station is marginal. In addition, when the locations of the randomly located eavesdroppers are unknown, deploying the RIS closer to the legitimate user rather than to the base station is shown to be more efficient. We also perform an analytical study demonstrating that the secrecy diversity order depends on the path loss exponent of the RIS-to-ground links. Finally, numerical simulations are conducted to verify the accuracy of these theoretical observations.