  This paper considers full-duplex (FD) device-to-device (D2D) communications
in a downlink MISO cellular system in the presence of multiple eavesdroppers.
The D2D pair communicate sharing the same frequency band allocated to the
cellular users (CUs). Since the D2D users share the same frequency as the CUs,
both the base station (BS) and D2D transmissions interfere each other. In
addition, due to limited processing capability, D2D users are susceptible to
external attacks. Our aim is to design optimal beamforming and power control
mechanism to guarantee secure communication while delivering the required
quality-of-service (QoS) for the D2D link. In order to improve security,
artificial noise (AN) is transmitted by the BS. We design robust beamforming
for secure message as well as the AN in the worst-case sense for minimizing
total transmit power with imperfect channel state information (CSI) of all
links available at the BS. The problem is strictly non-convex with infinitely
many constraints. By discovering the hidden convexity of the problem, we derive
a rank-one optimal solution for the power minimization problem.
