  This paper investigates a three-node amplify-and-forward (AF) multiple-input
multiple-output (MIMO) relay network, where an autonomous relay harvests power
from the source information flow and is further helped by an energy flow in the
form of a wireless power transfer (WPT) at the destination. An
energy-flow-assisted two-phase relaying scheme is proposed, where a source and
relay joint optimization is formulated to maximize the rate. By diagonalizing
the channel, the problem is simplified to a power optimization, where a relay
channel pairing problem is solved by an ordering operation. The proposed
algorithm, which iteratively optimizes the relay and source power, is shown to
converge. Closed-form solutions can be obtained for the separate relay and
source optimizations. Besides, a two-phase relaying without energy flow is also
studied. Simulation results show that the energy-flow-assisted scheme is
beneficial to the rate enhancement, if the transmit power of the energy flow is
adequately larger than that of the information flow. Otherwise, the scheme
without energy flow would be preferable.
