  This paper proposes a robust beamforming scheme to enhance the physical layer
security (PLS) of multicast transmission in a cognitive satellite and aerial
network (CSAN) operating in the millimeter wave frequency band. Based on
imperfect channel state information (CSI) of both eavesdroppers (Eves) and
primary users (PUs), we maximize the minimum achievable secrecy rate (ASR) of
the secondary users (SUs) in the aerial network under the constraints of the
interference to the PUs in the satellite network, the quality of service (QoS)
requirements of the SUs and per-antenna power budget of the aerial platform. To
tackle this mathematically intractable problem, we first introduce an auxiliary
variable and outage constraints to simplify the complex objective function. We
then convert the non-convex outage constraints into deterministic forms and
adopt penalty function approach to obtain a semi-definite problem such that it
can be solved in an iterative fashion. Finally, simulation results show that
with the transmit power increase, the minimal ASR of SUs obtained from the
proposed BF scheme well approximate the optimal value.
