Secure Outage Analysis of RIS-Assisted Communications With Discrete Phase Control

This correspondence investigates a reconfigurable intelligent surface (RIS)-assisted wireless communication system with security threats. The RIS is deployed to enhance the secrecy outage probability (SOP) of the data sent to a legitimate user. By deriving the distributions of the received signal-to-noise-ratios (SNRs) at the legitimate user and the eavesdropper, we formulate, in a closed-form expression, a tight bound for the SOP under the constraint of discrete phase control at the RIS. The SOP is characterized as a function of the number of antenna elements,
$N$
, and the number of discrete phase choices,
$2^{b}$
. It is revealed that the performance loss in terms of SOP due to the discrete phase control is ignorable for large
$N$
when
$b \geq 3$
. In addition, we explicitly quantify the SOP loss when binary phase shifts, i.e.,
$b =1$
, are utilized. It is found that increasing the number of RIS elements by 1.6 times provides the same SOP as that of an RIS with continuous-valued phase shifts. Numerical simulations are conducted to verify the accuracy of these theoretical observations.