  This paper investigates a multiuser multiple-input single-output (MISO)
full-duplex (FD) system for simultaneous wireless information and power
transfer (SWIPT), in which a multi-antenna base station (BS) simultaneously
sends wirelessly information and power to a set of single-antenna mobile
stations (MSs) using power splitters (PSs) in the downlink and receives
information in the uplink in FD mode. In particular, we address the joint
design of the receive PS ratio and the transmit power at the MSs, and the
beamforming matrix at the BS under signal-to-interference-plus-noise ratio
(SINR) and the harvested power constraints. Using semidefinite relaxation
(SDR), we obtain the solution to the problem with imperfect channel state
information (CSI) of the self-interfering channels. Furthermore, we propose
another suboptimal zero-forcing (ZF) based solution by separating the
optimization of the transmit beamforming vector and the PS ratio. Simulation
results are provided to evaluate the performance of the proposed beamforming
designs.
