  This paper considers coordinated multicast beamforming in a multi-cell
multigroup multiple-input single-output system. Each base station (BS) serves
multiple groups of users by forming a single beam with common information per
group. We propose centralized and distributed beamforming algorithms for two
different optimization targets. The first objective is to minimize the total
transmission power of all the BSs while guaranteeing the user-specific minimum
quality-of-service targets. The semidefinite relaxation (SDR) method is used to
approximate the non-convex multicast problem as a semidefinite program (SDP),
which is solvable via centralized processing. Subsequently, two alternative
distributed methods are proposed. The first approach turns the SDP into a
two-level optimization via primal decomposition. At the higher level,
inter-cell interference powers are optimized for fixed beamformers while the
lower level locally optimizes the beamformers by minimizing BS-specific
transmit powers for the given inter-cell interference constraints. The second
distributed solution is enabled via an alternating direction method of
multipliers, where the inter-cell interference optimization is divided into a
local and a global optimization by forcing the equality via consistency
constraints. We further propose a centralized and a simple distributed
beamforming design for the signal-to-interference-plus-noise ratio (SINR)
balancing problem in which the minimum SINR among the users is maximized with
given per-BS power constraints. This problem is solved via the bisection method
as a series of SDP feasibility problems. The simulation results show the
superiority of the proposed coordinated beamforming algorithms over traditional
non-coordinated transmission schemes, and illustrate the fast convergence of
the distributed methods.
