  This paper proposes energy-efficient coordinated beamforming strategies for
multi-cell multi-user multiple-input single-output system. We consider a
practical power consumption model, where part of the consumed power depends on
the base station or user specific data rates due to coding, decoding and
backhaul. This is different from the existing approaches where the base station
power consumption has been assumed to be a convex or linear function of the
transmit powers. Two optimization criteria are considered, namely network
energy efficiency maximization and weighted sum energy efficiency maximization.
We develop successive convex approximation based algorithms to tackle these
difficult nonconvex problems. We further propose decentralized implementations
for the considered problems, in which base stations perform parallel and
distributed computation based on local channel state information and limited
backhaul information exchange. The decentralized approaches admit closed-form
solutions and can be implemented without invoking a generic external convex
solver. We also show an example of the pilot contamination effect on the energy
efficiency using a heuristic pilot allocation strategy. The numerical results
are provided to demonstrate that the rate dependent power consumption has a
large impact on the system energy efficiency, and, thus, has to be taken into
account when devising energy-efficient transmission strategies. The significant
gains of the proposed algorithms over the conventional low-complexity
beamforming algorithms are also illustrated.
