  This letter considers simultaneous wireless information and power transfer
(SWIPT) for a multiple-input multiple-output (MIMO) relay system. The relay is
powered by harvesting energy from the source via time switching (TS) and
utilizes the harvested energy to forward the information signal. Our aim is to
maximize the rate of the system subject to the power constraints at both the
source and relay nodes. In the first scenario in which the source covariance
matrix is an identity matrix, we present the joint-optimal solution for
relaying and the TS ratio in closed form. An iterative scheme is then proposed
for jointly optimizing the source and relaying matrices and the TS ratio.
