  We consider the problem of coordinated multi- cell downlink beamforming in
massive multiple input multiple output (MIMO) systems consisting of N cells, Nt
antennas per base station (BS) and K user terminals (UTs) per cell.
Specifically, we formulate a multi-cell beamforming algorithm for massive MIMO
systems which requires limited amount of information exchange between the BSs.
The design objective is to minimize the aggregate transmit power across all the
BSs subject to satisfying the user signal to interference noise ratio (SINR)
constraints. The algorithm requires the BSs to exchange parameters which can be
computed solely based on the channel statistics rather than the instantaneous
CSI. We make use of tools from random matrix theory to formulate the
decentralized algorithm. We also characterize a lower bound on the set of
target SINR values for which the decentralized multi-cell beamforming algorithm
is feasible. We further show that the performance of our algorithm
asymptotically matches the performance of the centralized algorithm with full
CSI sharing. While the original result focuses on minimizing the aggregate
transmit power across all the BSs, we formulate a heuristic extension of this
algorithm to incorporate a practical constraint in multi-cell systems, namely
the individual BS transmit power constraints. Finally, we investigate the
impact of imperfect CSI and pilot contamination effect on the performance of
the decentralized algorithm, and propose a heuristic extension of the algorithm
to accommodate these issues. Simulation results illustrate that our algorithm
closely satisfies the target SINR constraints and achieves minimum power in the
regime of massive MIMO systems. In addition, it also provides substantial power
savings as compared to zero-forcing beamforming when the number of antennas per
BS is of the same orders of magnitude as the number of UTs per cell.
