Asynchronous Distributed Downlink Beamforming and Power Control in Multi-cell Networks

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.