  This correspondence considers a full-duplex (FD) point-to-point system
consisting of one multi-antenna full-duplex access point (FD-AP) and one
two-antenna full-duplex mobile station (FD-MS). We adopt simultaneous wireless
information and power transfer (SWIPT) scheme and apply the self-energy
recycling at FD-MS. In order to minimize the weighted sum transmit power, we
jointly design the transmit beamforming vector of FD-AP, the receive power
splitting (PS) ratio of FD-MS, as well as the transmit power value of FD-MS.
Since the original problem is non-convex, we apply semidefinite relaxation
(SDR) and obtain a new convex problem. We further prove that both problems have
exactly the same solutions. Finally, simulations are provided to verify our
analysis, and the comparison with a half-duplex (HD) system demonstrates the
significant performance gain from self-energy recycling.
