  In this paper, we investigate the optimal energy efficient coordinated
beamforming in multi-cell multiple-input single-output (MISO) systems with $K$
multiple-antenna base stations (BS) and $K$ single-antenna mobile stations
(MS), where each BS sends information to its own intended MS with cooperatively
designed transmit beamforming. We assume single user detection at the MS by
treating the interference as noise. By taking into account a realistic power
model at the BS, we characterize the Pareto boundary of the achievable energy
efficiency (EE) region of the $K$ links, where the EE of each link is defined
as the achievable data rate at the MS divided by the total power consumption at
the BS. Since the EE of each link is non-cancave (which is a non-concave
function over an affine function), characterizing this boundary is difficult.
To meet this challenge, we relate this multi-cell MISO system to cognitive
radio (CR) MISO channels by applying the concept of interference temperature
(IT), and accordingly transform the EE boundary characterization problem into a
set of fractional concave programming problems. Then, we apply the fractional
concave programming technique to solve these fractional concave problems, and
correspondingly give a parametrization for the EE boundary in terms of IT
levels. Based on this characterization, we further present a decentralized
algorithm to implement the multi-cell coordinated beamforming, which is shown
by simulations to achieve the EE Pareto boundary.
