Optimal beamforming design for two-way relaying with simultaneous energy harvesting

We consider the beamforming design in nonregenerative multiuser two-way relaying (TWR) system where the multi-antenna relay performs simultaneous energy harvesting and information processing. Based on a power splitting receiver architecture at the relay, we develop the optimal beamforming scheme that maximizes the minimum of users' signal-to-interference-plus-noise-ratios (SINRs). Given the power splitting ratios, it is shown that the optimal max-min SINR value can be obtained by a semi-definite programming (SDP) based Dinkelbach-type algorithm with fast convergence. Specifically, when all the antennas at the relay use the same power splitting ratio, the jointly optimal power splitting and beamforming design reduces to a one-dimension search for the optimal max-min SINR value; while when the antennas at the relay are allowed to employ different power splitting ratios, a more complex search is required to find the solution. Numerical results demonstrate that simultaneous energy harvesting and information processing have the potential to significantly enhance the performance of multiuser TWR.