This paper studies the achievable rate region for an amplify-and-forward (AF)-based two-way relay network with collaborative beamforming. With different assumptions of channel reciprocity between the source-relay and relay-source channels, the achievable rate region is characterized under two setups. First, with reciprocal channels, we investigate the achievable rate regions when the relay cluster is subject to a sum-power constraint or individual-power constraints. We 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-form solutions 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. Second, with the nonreciprocal channels, the achievable rate regions are also characterized for both the sum-power constraint case and the individual-power constraint case. Although no closed-form solutions are available under this setup, we present efficient numerical algorithms by solving a sequence of semi-definite programming (SDP) problems after semi-definite relaxation(SDR), where the optimal beamformer can be obtained under the sum-power constraint and approximate optimal solutions can be obtained under the individual power constraints.
['Meng Zeng', 'Rui Zhang', 'Shuguang Cui']
On Design of Collaborative Beamforming for Two-Way Relay Networks