Proactive Eavesdropping via Jamming in Full-Duplex Multi-Antenna Systems: Beamforming Design and Antenna Selection

This paper investigates the application of full-duplex (FD) multi-antenna transceivers in proactive eavesdropping systems. To this end, we jointly optimize the transmit and receive beamformers at the legitimate FD monitor to maximize the eavesdropping non-outage probability of the system. The resulting non-convex problem is solved using two-layer decomposition technique. The inner layer problem is formulated as a semidefinite relaxation problem, and the outer problem is solved by one-dimensional line search. We further propose sub-optimum beamforming designs, where the beamformers are obtained using zero-forcing, and maximum ratio transmission. To archive a low-complexity implementation, we study the antenna selection problem as an alternative for performance optimization. Particularly, based on the system's eavesdropping non-outage probability, several antenna selection schemes are proposed to choose single transmit and single receive antenna at the FD monitor. For each scheme, we derive closed-form expressions of the eavesdropping non-outage probability. Our findings reveal that proposed antenna selection schemes can achieve the performance close to that of the proposed optimum/sub-optimum beamforming design, but with much lower implementation complexity.