  We propose techniques for optimizing transmit beamforming in a full-duplex
multiple-input-multiple-output (MIMO) wireless-powered communication system,
which consists of two phases. In the first phase, the wireless-powered mobile
station (MS) harvests energy using signals from the base station (BS), whereas
in the second phase, both MS and BS communicate to each other in a full-duplex
mode. When complete instantaneous channel state information (CSI) is available,
the BS beamformer and the time-splitting (TS) parameter of energy harvesting
are jointly optimized in order to obtain the BS-MS rate region. The joint
optimization problem is non-convex, however, a computationally efficient
optimum technique, based upon semidefinite relaxation and line-search, is
proposed to solve the problem. A sub-optimum zero-forcing approach is also
proposed, in which a closed-form solution of TS parameter is obtained. When
only second-order statistics of transmit CSI is available, we propose to
maximize the ergodic information rate at the MS, while maintaining the outage
probability at the BS below a certain threshold. An upper bound for the outage
probability is also derived and an approximate convex optimization framework is
proposed for efficiently solving the underlying non-convex problem. Simulations
demonstrate the advantages of the proposed methods over the sub-optimum and
half-duplex ones.
