Secure Transmission in MISOME Wiretap Channels with Half and Full-Duplex Active Eavesdroppers

In this paper, the security issue in a multi- input-single-output (MISO) system in the presence of multiple randomly distributed eavesdroppers (Eves) is investigated. The Eves are distributed according to a Poisson Point Process (PPP) and each of them can operate in either a half-duplex (HD) or full-duplex (FD) mode. For a FD-mode Eve, it can overhear the secret information transmission and send some jamming signals simultaneously to degrade the reception of Bob. Based on the stochastic geometry method, we first derive the cumulative distribution function (cdf) expressions of the signal-to-interference-plus- noise ratio (SINR) for Bob and Eves. Following that, a lower bound of the intercept probability is obtained. Some important properties are derived, which provide very useful insights. Finally, the optimal power allocation of Alice and the optimal fraction of FD-mode Eves are solved by using a game-theoretical approach. Simulation results are shown to validate the theoretical analysis.