Achievable rate region and sum-rate maximization for network beamforming for bi-directional relay networks

We study the sum-rate maximization approach when applied to design a decentralized beamformer for two-way relay networks. Considering a constraint on the total transmit power consumed in the whole network, we prove that sum-rate maximization is equivalent to an SNR balancing approach where the smallest of the two receive SNRs is maximized subject to the same total power constraint.