  This paper studies energy-efficient coordinated beamforming in multi-cell
multi-user multigroup multicast multiple-input single-output systems. We aim at
maximizing the network energy efficiency by taking into account the fact that
some of the radio frequency chains can be switched off in order to save power.
We consider the antenna specific maximum power constraints to avoid non-linear
distortion in power amplifiers and user-specific quality of service (QoS)
constraints to guarantee a certain QoS levels. We first introduce binary
antenna selection variables and use the perspective formulation to model the
relation between them and the beamformers. Subsequently, we propose a new
formulation which reduces the feasible set of the continuous relaxation,
resulting in better performance compared to the original perspective
formulation based problem. However, the resulting optimization problem is a
mixed-Boolean non-convex fractional program, which is difficult to solve. We
follow the standard continuous relaxation of the binary antenna selection
variables, and then reformulate the problem such that it is amendable to
successive convex approximation. Thereby, solving the continuous relaxation
mostly results in near-binary solution. To recover the binary variables from
the continuous relaxation, we switch off all the antennas for which the
continuous values are smaller than a small threshold. Numerical results
illustrate the superior convergence result and significant achievable gains in
terms of energy efficiency with the proposed algorithm.
