Max-min fair beamforming designs of SWIPT-aided full-duplex two-way relay systems

A full-duplex two-way relaying (FD-TWR) system with an energy-constrained relay is studied with simultaneous wireless information and power transfer (SWIPT). In this network, the sources have a reliable power supply, whereas the relay has to harvest energy from the source-emitted radio-frequency signal via time switching (TS) operation. Our aim is to maximize the minimum achievable rate of the two sources by jointly optimizing the relay beamforming vector and TS ratio under the energy-harvesting-then-transmitting mode, i.e., the relay harvested energy need to meet the consumed energy. Specifically, the max-min fairness beamforming design problems are formulated for both the perfect channel state information (CSI) model and imperfect CSI model. A one-dimensional search algorithm and the semidefinite relaxation technique are proposed to solve these complex non-convex problems. It is shown that the optimal beamforming vectors and the TS ratio can always be found under the two considered CSI model. Numerical results show that the proposed two FD schemes achieve significant performance improvement compared to the traditional half-duplex (HD) scheme. Moreover, the robust scheme can get most of the performance gain of the perfect scheme. Some tradeoffs are elucidated among the achievable rate and the TS ratio, the system performance and the self-interference cancellation (SIC) level under a max-min fairness criterion.