Distributed beamforming for two-way relay networks with reciprocal channels

This paper studies the achievable rate region for a two-way relay network with collaborative beamforming under the assumption that the source-to-relay and relay-to-source channels are reciprocal. Specifically, we investigate the achievable rate regions for two cases where the relay cluster is subject to a sum-power constraint or to individual-power constraints. We can show that the optimal beamforming vectors obtained from solving the weighted sum inverse-SNR minimization (WSISMin) problems are sufficient to characterize the corresponding achievable rate region. Furthermore, we derive the closed forms for those optimal beamforming vectors and consequently propose the partially distributed algorithms to implement the optimal beamforming, where each relay node only needs the local channel information and one global parameter.