Achievable Rate Region under Joint Distributed Beamforming and Power Allocation for Two-Way Relay Networks

We obtain the achievable beamforming rate region for a two-way cooperative network consisting of two transceivers and multiple relays, all single-antenna nodes. Assuming that the relay beamforming weights as well as the transceiver transmit powers are the design parameters, this region is characterized under a constraint on the total (network) transmit power consumption. Using the shape of the rate region, we then use a sum-rate maximization approach to obtain the jointly optimal relay beamforming weights and transceiver transmit powers. Interestingly, we show that the sum-rate maximization approach yields the same solution as the max-min fair design approach does. Using this relationship, we further present a semi-closed-form solution to the underlying distributed beamforming problem. We then prove that the transmit power of any of the two transceivers can be obtained as the solution to a one-dimensional optimization problem using a simple bisection method which enjoys a low computational complexity. Furthermore, we extend these results to obtain the relay beamforming weights and transceiver transmit powers corresponding to any point on the boundary of the rate region, through a weighted sum-rate maximization approach.