  This paper considers base station (BS) cooperation in the form of coordinated
beamforming, focusing on min-max fairness in the power usage subject to target
SINR constraints. We show that the optimal beamforming strategies have an
interesting nested zero-forcing structure. In the asymptotic regime where the
number of antennas at each BS and the number of users in each cell both grow
large with their ratio tending to a finite constant, the dimensionality of the
optimization is greatly reduced, and only knowledge of statistics is required
to solve it. The optimal solution is characterized in general, and an algorithm
is proposed that converges to the optimal transmit parameters, for feasible
SINR targets. For the two cell case, a simple single parameter characterization
is obtained. These asymptotic results provide insights into the average
performance, as well as simple but efficient beamforming strategies for the
finite system case. In particular, the optimal beamforming strategy from the
large systems analysis only requires the base stations to have local
instantaneous channel state information; the remaining parameters of the
beamformer can be calculated using channel statistics which can easily be
shared amongst the base stations.
