  In this paper, we investigate covert communication in an intelligent
reflecting surface (IRS)-assisted non-orthogonal multiple access (NOMA) system,
where a legitimate transmitter (Alice) applies NOMA for downlink and uplink
transmissions with a covert user (Bob) and a public user (Roy) aided by an IRS.
Specifically, we propose new IRS-assisted downlink and uplink NOMA schemes to
hide the existence of Bob's covert transmission from a warden (Willie), which
cost-effectively exploit the phase-shift uncertainty of the IRS and the
non-orthogonal signal transmission of Roy as the cover medium without requiring
additional uncertainty sources. Assuming the worst-case covert communication
scenario where Willie can optimally adjust the detection threshold for his
detector, we derive an analytical expression for the minimum average detection
error probability of Willie achieved by each of the proposed schemes. To
further enhance the covert communication performance, we propose to maximize
the covert rates of Bob by jointly optimizing the transmit power and the IRS
reflect beamforming, subject to given requirements on the covertness against
Willie and the quality-of-service (QoS) at Roy. Simulation results demonstrate
the covertness advantage of the proposed schemes and confirm the accuracy of
the derived analytical results. Interestingly, it is found that covert
communication is impossible without using IRS or NOMA for the considered setup
while the proposed schemes can always guarantee positive covert rates.
