Covert Communications Assisted by Reconfigurable Intelligent Surfaces with Discrete Phase Shifts

This work examines the covert communication performance gain achieved by deploying a reconfigurable intelligent surface (RIS) with discrete phase shifts. To this end, we first analyze the average receive signal power at a legitimate receiver Bob and a warden Willie as a function of the number of RIS reflecting elements N and the number of bits d for its discrete phase shift levels. Our analysis reveals that Bob's average power is proportional to N-2 and highly depends on d, while Willie's average power is proportional to N-2 and does not depend on d. This leads to the potential of enhancing the system performance via increasing N or d in the considered covert communications scenario. Specifically, the performance gain is explicitly examined by tackling the transmission outage probability from a transmitter Alice to Bob subject to a covertness constraint based on Willie's detection performance. After analyzing the transmission outage probability and Willie's total detection error rate, we determine Alice's optimal transmit power. Our explicit examination confirms the performance enhancement achieved via increasing N or d. Furthermore, our analysis shows that the covert communication performance achieved with d = 3 is already sufficiently close to that achieved with d -> infinity. This shows that the major benefits of deploying RIS in covert communications can be achieved by an RIS with low-resolution phase shifts.