  Intelligent reflecting surfaces (IRSs) have shown huge advantages in many
potential use cases and thus have been considered a promising candidate for
next-generation wireless systems. In this paper, we consider an IRS-assisted
multigroup multicast (IRS-MGMC) system in a multiple-input single-output (MISO)
scenario, for which the related existing literature is rather limited. In
particular, we aim to jointly design the transmit beamformers and IRS phase
shifts to maximize the sum rate of the system under consideration. In order to
obtain a numerically efficient solution to the formulated non-convex
optimization problem, we propose an alternating projected gradient (APG) method
where each iteration admits a closed-form and is shown to be superior to a
known solution that is derived from the majorization-minimization (MM) method
in terms of both achievable sum rate and required complexity, i.e., run time.
In particular, we show that the complexity of the proposed APG method grows
linearly with the number of IRS tiles, while that of the known solution in
comparison grows with the third power of the number of IRS tiles. The numerical
results reported in this paper extend our understanding on the achievable rates
of large-scale IRS-assisted multigroup multicast systems.
