  This paper investigates wireless information and power transfer in a
full-duplex MIMO relay channel where the self-sustained relay harvests energy
from both source transmit signal and self-interference signal to decode and
forward source information to a destination. We present a novel technique to
jointly optimize power splitting at the relay and precoding design (power
allocation) for both the source and relay transmissions. We formulate a new
convex optimization problem, establish the dual problem via closed-form optimal
primal solutions, and design an efficient primal-dual algorithm to maximize the
achievable throughput. Numerical results demonstrate the benefits of using
multiple transmit and receive antennas in both information decoding and energy
harvesting. We also extend our analysis to the case when channel state
information is only available at receiving nodes and show how our algorithm can
optimize the power splitting at the relay for it to remain self-sustained.
Through analysis and simulation, we show how an optimal combination of
non-uniform power splitting, variable power allocation, and self-interference
power harvesting effectively exploits a full-duplex MIMO system to achieve
significant performance gains over existing uniform power splitting and
half-duplex transmission techniques.
