  In this paper, we consider a multi-cell network where every base station (BS)
serves multiple users with an antenna array. Each user is associated with only
one BS and has a single antenna. Assume that only long-term channel state
information (CSI) is available in the system. The objective is to minimize the
network downlink transmission power needed to meet the users'
signal-to-interference-plus-noise ratio (SINR) requirements. For this
objective, we propose an asynchronous distributed beamforming and power control
algorithm which provides the same optimal solution as given by centralized
algorithms. To design the algorithm, the power minimization problem is
formulated mathematically as a non-convex problem. For distributed
implementation, the non-convex problem is cast into the dual decomposition
framework. Resorting to the theory about matrix pencil, a novel asynchronous
iterative method is proposed for solving the dual of the non-convex problem.
The methods for beamforming and power control are obtained by investigating the
primal problem. At last, simulation results are provided to demonstrate the
convergence and performance of the algorithm.
