  We consider a full-duplex (FD) decode-and-forward system in which the
time-switching protocol is employed by the multi-antenna relay to receive
energy from the source and transmit information to the destination. The
instantaneous throughput is maximized by optimizing receive and transmit
beamformers at the relay and the time-split parameter. We study both optimum
and suboptimum schemes. The reformulated problem in the optimum scheme achieves
closed-form solutions in terms of transmit beamformer for some scenarios. In
other scenarios, the optimization problem is formulated as a semi-definite
relaxation problem and a rank-one optimum solution is always guaranteed. In the
suboptimum schemes, the beamformers are obtained using maximum ratio combining,
zero-forcing, and maximum ratio transmission. When beamformers have closed-form
solutions, the achievable instantaneous and delay-constrained throughput are
analytically characterized. Our results reveal that, beamforming increases both
the energy harvesting and loop interference suppression capabilities at the FD
relay. Moreover, simulation results demonstrate that the choice of the linear
processing scheme as well as the time-split plays a critical role in
determining the FD gains.
