  Covert transmission is studied for an intelligent reflecting surface (IRS)
aided communication system, where Alice aims to transmit messages to Bob
without being detected by the warden Willie. Specifically, an IRS is used to
increase the data rate at Bob under a covert constraint. For the considered
model, when Alice is equipped with a single antenna, the transmission power at
Alice and phase shifts at the IRS are jointly optimized to maximize the covert
transmission rate with either instantaneous or partial channel state
information (CSI) of Willie's link. In addition, when multiple antennas are
deployed at Alice, we formulate a joint transmit beamforming and IRS phase
shift optimization problem to maximize the covert transmission rate. One
optimal algorithm and two low-complexity suboptimal algorithms are proposed to
solve the problem. Furthermore, for the case of imperfect CSI of Willie's link,
the optimization problem is reformulated by using the triangle and the
Cauchy-Schwarz inequalities. The reformulated optimization problems are solved
using an alterative algorithm, semidefinite relaxation (SDR) and Gaussian
randomization techniques. Finally, simulations are performed to verify our
analysis. The simulation results show that an IRS can degrade the covert
transmission rate when Willie is closer to the IRS than Bob.
