  This letter studies bi-directional secure information exchange in a
simultaneous wireless information and power transfer (SWIPT) system enabled by
a full-duplex (FD) multiple-input multiple-output (MIMO) amplify-and-forward
(AF) relay. The AF relay injects artificial noise (AN) in order to confuse the
eavesdropper. Specifically, we assume a zeroforcing (ZF) solution constraint to
eliminate the residual self-interference (RSI). As a consequence, we address
the optimal joint design of the ZF matrix and the AN covariance matrix at the
relay node as well as the transmit power at the sources. We propose an
alternating algorithm utilizing semi-definite programming (SDP) technique and
one-dimensional searching to achieve the optimal solution. Simulation results
are provided to demonstrate the effectiveness of the proposed algorithm.
