  This paper considers maximizing the network-wide minimum supported rate in
the downlink of a two-cell system, where each base station (BS) is endowed with
multiple antennas. This is done for different levels of cell cooperation. At
one extreme, we consider single cell processing where the BS is oblivious to
the interference it is creating at the other cell. At the other extreme, we
consider full cooperative macroscopic beamforming. In between, we consider
coordinated beamforming, which takes account of inter-cell interference, but
does not require full cooperation between the BSs. We combine elements of
Lagrangian duality and large system analysis to obtain limiting SINRs and
bit-rates, allowing comparison between the considered schemes. The main
contributions of the paper are theorems which provide concise formulas for
optimal transmit power, beamforming vectors, and achieved signal to
interference and noise ratio (SINR) for the considered schemes. The formulas
obtained are valid for the limit in which the number of users per cell, K, and
the number of antennas per base station, N, tend to infinity, with fixed ratio.
These theorems also provide expressions for the effective bandwidths occupied
by users, and the effective interference caused in the adjacent cell, which
allow direct comparisons between the considered schemes.
