  We consider the coordinated downlink beamforming problem in a cellular
network with the base stations (BSs) equipped with multiple antennas, and with
each user equipped with a single antenna. The BSs cooperate in sharing their
local interference information, and they aim at maximizing the sum rate of the
users in the network. A set of new lower bounds (one bound for each BS) of the
non-convex sum rate is identified. These bounds facilitate the development of a
set of algorithms that allow the BSs to update their beams by optimizing their
respective lower bounds. We show that when there is a single user per-BS, the
lower bound maximization problem can be solved exactly with rank-1 solutions.
In this case, the overall sum rate maximization problem can be solved to a KKT
point. Numerical results show that the proposed algorithms achieve high system
throughput with reduced backhaul information exchange among the BSs.
