  Existing methods for robust multigroup multicast beamforming obtain feasible
points using semidefinite relaxation (SDR) and Gaussian randomization, and have
high computational complexity. In this letter, we consider the robust
multigroup multicast beamforming design to minimize the sum power (SP) or
per-antenna power (PAP) under the signal-to-interference-plus-noise ratio
(SINR) constraints and to maximize the worst-case SINR under the SP constraint
or PAP constraints, respectively. The resulting optimization problems are
challenging non-convex problems with infinitely many constraints. For each
problem, using the majorization-minimization (MM) approach, we propose an
iterative algorithm to obtain a feasible solution which is shown to be a
stationary point under certain conditions. We also show that the proposed
algorithms have much lower computational complexity than existing SDR-based
algorithms.
