  In this paper we explore the use of full-duplex radio to improve the spectrum
efficiency in a two-way relay channel where two sources exchange information
through an multi-antenna relay, and all nodes work in the full-duplex mode. The
full-duplex operation can reduce the overall communication to only one phase
but suffers from the self-interference. Instead of purely suppressing the
self-interference, we aim to maximize the end-to-end performance by jointly
optimizing the beamforming matrix at the relay which uses the
amplify-and-forward protocol as well as the power control at the sources. To be
specific, we propose iterative algorithms and 1-D search to solve two problems:
finding the achievable rate region and maximizing the sum rate. At each
iteration, either the analytical solution or convex formulation is obtained. We
compare the proposed full-duplex two-way relaying with the conventional
half-duplex two-way relaying, a full-duplex one-way relaying and a performance
upper bound. Numerical results show that the proposed full-duplex scheme
significantly improves the achievable data rates over the conventional scheme.
