  This paper considers the (NP-)hard problem of joint multicast beamforming and
antenna selection. Prior work has focused on using Semi-Definite relaxation
(SDR) techniques in an attempt to obtain a high quality sub-optimal solution.
However, SDR suffers from the drawback of having high computational complexity,
as SDR lifts the problem to higher dimensional space, effectively squaring the
number of variables. This paper proposes a high performance, low complexity
Successive Convex Approximation (SCA) algorithm for max-min SNR "fair" joint
multicast beamforming and antenna selection under a sum power constraint. The
proposed approach relies on iteratively approximating the non-convex objective
with a series of non-smooth convex subproblems, and then, a first order-based
method called Saddle Point Mirror-Prox (SP-MP) is used to compute optimal
solutions for each SCA subproblem. Simulations reveal that the SP-MP SCA
algorithm provides a higher quality and lower complexity solution compared to
the one obtained using SDR.
