  This paper studies the joint multicast beamforming and user scheduling
problem, with the objective of minimizing total transmitting power across
multiple channels by jointly assigning each user to appropriate channel and
designing multicast beamformer for each channel. The problem of interest is
formulated in two different optimization problems, a mixed binary quadratically
constrained quadratic program and a highly-structured nonsmooth program. Two
different algorithms, based on convex relaxation and convex restriction,
respectively, are proposed to solve the problem. The performance ratio between
the approximate solution provided by the convex-relaxation-based algorithm and
optimal solution is proved to be upper bounded by a constant independent of
problem data. The convex-restriction-based algorithm is guaranteed to converge
to a critical point to the nonsmooth formulation problem. Finally, extensive
simulation results verify the theoretical analysis and demonstrate the
advantage of the proposed co-design scheme over conventional fixed scheduling
and random scheduling in terms of power consumption.
