A semi-closed form solution to the SNR balancing problem of two-way relay network beamforming

In this paper, we present a semi-closed form solution to the SNR balancing problem, first considered in, in the context of network beamforming design for two-way relay networks. This solution relies on a simple bisection method to obtain the transmit power of one of the two transceivers. Given this transmit power, the relay beamforming weight vector is shown to have a closed-form solution. Simulation results show that the proposed solution has significantly lower computational complexity. We also present a suboptimal solution which does not use the aforementioned bisection algorithm while performs very closely to the optimal beamformer.