  Intelligent reflecting surface (IRS) has recently been envisioned to offer
unprecedented massive multiple-input multiple-output (MIMO)-like gains by
deploying large-scale and low-cost passive reflection elements. By adjusting
the reflection coefficients, the IRS can change the phase shifts on the
impinging electromagnetic waves so that it can smartly reconfigure the signal
propagation environment and enhance the power of the desired received signal or
suppress the interference signal. In this paper, we consider downlink
multigroup multicast communication systems assisted by an IRS. We aim for
maximizing the sum rate of all the multicasting groups by the joint
optimization of the precoding matrix at the base station (BS) and the
reflection coefficients at the IRS under both the power and unit-modulus
constraint. To tackle this non-convex problem, we propose two efficient
algorithms under the majorization--minimization (MM) algorithm framework.
Specifically, a concave lower bound surrogate objective function of each user's
rate has been derived firstly, based on which two sets of variables can be
updated alternately by solving two corresponding second-order cone programming
(SOCP) problems. Then, in order to reduce the computational complexity, we
derive another concave lower bound function of each group's rate for each set
of variables at every iteration, and obtain the closed-form solutions under
these loose surrogate objective functions. Finally, the simulation results
demonstrate the benefits in terms of the spectral and energy efficiency of the
introduced IRS and the effectiveness in terms of the convergence and complexity
of our proposed algorithms.
