  This paper focuses on energy recycling in full-duplex (FD) relaying
multiple-input-multiple-output orthogonal frequency division multiplexing
(OFDM) communication. The loop self-interference (SI) due to full-duplexing is
seen as an opportunity for the energy-constrained relay node to replenish its
energy requirement through wireless power transfer. In forwarding the source
information to the destination, the FD relay can simultaneously harvest energy
from the source wireless transmission and also through energy recycling from
its own transmission. The objective is to maximize the overall spectral
efficiency by designing the optimal power allocation over OFDM sub-carriers and
transmit antennas. Due to a large number of sub-carriers, this design problem
poses a large-scale nonconvex optimization problem involving a few thousand
variables of power allocation, which is very computationally challenging. A new
path-following algorithm is proposed, which converges to an optimal solution.
This algorithm is very efficient since it is based on \textit{closed-form}
calculations. Numerical results for a practical simulation setting show
promising results by achieving high spectral efficiency.
