  In this paper, we investigate the physical layer security of a full-duplex
base station (BS) aided system in the worst case, where an uplink transmitter
(UT) and a downlink receiver (DR) are both equipped with a single antenna,
while a powerful eavesdropper is equipped with multiple antennas. For securing
the confidentiality of signals transmitted from the BS and UT, an artificial
noise (AN) aided secrecy beamforming scheme is proposed, which is robust to the
realistic imperfect state information of both the eavesdropping channel and the
residual self-interference channel. Our objective function is that of
maximizing the worst-case sum secrecy rate achieved by the BS and UT, through
jointly optimizing the beamforming vector of the confidential signals and the
transmit covariance matrix of the AN. However, the resultant optimization
problem is non-convex and non-linear. In order to efficiently obtain the
solution, we transform the non-convex problem into a sequence of convex
problems by adopting the block coordinate descent algorithm. We invoke a linear
matrix inequality for finding its Karush-Kuhn-Tucker (KKT) solution. In order
to evaluate the achievable performance, the worst-case secrecy rate is derived
analytically. Furthermore, we construct another secrecy transmission scheme
using the projection matrix theory for performance comparison. Our simulation
results show that the proposed robust secrecy transmission scheme achieves
substantial secrecy performance gains, which verifies the efficiency of the
proposed method.
