Distributed cooperative beamforming in multi-source multi-destination clustered systems

We consider the scenario of a multi-cluster network, in which each cluster contains multiple single-antenna source destination pairs that communicate simultaneously over the same channel. The communications are supported by cooperating amplify-and-forward relays, which perform beamforming. While the communications take place within the cluster, there is inter-cluster as well as intra-cluster interference. The beamforming weights are obtained so that the total relay transmit power is minimized, while a certain signal-to-interference-plus-noise-ratio (SINR) at the destinations is met. First, we show that a computationally efficient approximate solution is attainable by relaxing the original NP-hard nonconvex problem to a semidefinite optimization form. Then, we propose a decentralized method to solve the relaxed problem, based on the recently developed Accelerated Distributed Augmented Lagrangians (ADAL) algorithm, a distributed optimization technique that achieves fast convergence rates. Our decentralized solution allows for each cluster to compute its own beamforming weights, while coordinating with other clusters via appropriate message exchanges. Two different approaches are presented, differing in the message exchange patterns between clusters. The performance of the decentralized scheme is demonstrated via simulations.