  In this paper, we study resource allocation for a full-duplex (FD) radio base
station serving multiple half-duplex (HD) downlink and uplink users
simultaneously. The considered resource allocation algorithm design is
formulated as a non-convex optimization problem taking into account minimum
required receive signal-to-interference-plus-noise ratios (SINRs) for downlink
and uplink communication and maximum tolerable SINRs at potential
eavesdroppers. The proposed optimization framework enables secure downlink and
uplink communication via artificial noise generation in the downlink for
interfering the potential eavesdroppers. We minimize the weighted sum of the
total downlink and uplink transmit power by jointly optimizing the downlink
beamformer, the artificial noise covariance matrix, and the uplink transmit
power. We adopt a semidefinite programming (SDP) relaxation approach to obtain
a tractable solution for the considered problem. The tightness of the SDP
relaxation is revealed by examining a sufficient condition for the global
optimality of the solution. Simulation results demonstrate the excellent
performance achieved by the proposed scheme and the significant transmit power
savings enabled optimization of the artificial noise covariance matrix.
