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 formulate a new problem to jointly optimize power splitting at the relay and precoding design for both the source and relay transmissions. Using duality theory, we establish closed-form optimal primal solutions in terms of the dual variables, based on which we then design a customized and efficient primal-dual algorithm to maximize the achievable throughput. Numerical results demonstrate the rate gains from using multiple transmit and receive antennas in both information decoding and energy harvesting, and the significant benefit of harvesting energy from self-interference signals. 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 demonstrate that an optimal combination of non-uniform power splitting, variable power allocation, and self-interference power harvesting can effectively exploit a full-duplex MIMO system to achieve significant performance gains over existing uniform power splitting and half-duplex transmissions.
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