To improve national security, government agencies have long been committed to enforcing powerful surveillance measures on suspicious individuals or communications. In this paper, we consider a wireless legitimate surveillance system, where a full-duplex multi-antenna legitimate monitor aims to eavesdrop on a dubious communication link between a suspicious pair via proactive jamming. Assuming that the legitimate monitor can successfully overhear the suspicious information only when its achievable data rate is no smaller than that of the suspicious receiver, the key objective is to maximize the eavesdropping non-outage probability by joint design of the jamming power, receive and transmit beamformers at the legitimate monitor. Depending on the number of receive/transmit antennas implemented, i.e., single-input single-output, single-input multiple-output, multiple-input single-output and multiple-input multiple-output (MIMO), four different scenarios are investigated. For each scenario, the optimal jamming power is derived in closed-form and efficient algorithms are obtained for the optimal transmit/receive beamforming vectors. Moreover, low-complexity suboptimal beamforming schemes are proposed for the MIMO case. Our analytical findings demonstrate that by exploiting multiple antennas at the legitimate monitor, the eavesdropping non-outage probability can be significantly improved compared to the single antenna case. In addition, the proposed suboptimal transmit zero-forcing scheme yields similar performance as the optimal scheme.
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