Proactive eavesdropping with full-duplex relay and cooperative jamming

In this paper, we consider a proactive eavesdropping scenario, where a central monitor tries to intercept the information exchanged between a pair of suspicious entities through amplify-and-forward full-duplex relays and a cooperative jammer. Specifically, the eavesdropping relays simultaneously listen to the suspicious transmitter and forward the eavesdropped information to the central monitor. At the same time, the jammer broadcasts jamming signals to maintain the data rate of the suspicious users below the channel capacity of the central monitor so that the eavesdropped information can be successfully decoded by the central monitor. In this system, we jointly design the receive combining vector at the central monitor, the relay precoders at the eavesdropping relays and the transmit covariance matrix at the jammer to maximize the eavesdropping rate. First, we examine the case of a single eavesdropping relay equipped with a single antenna and provide some useful insights. Also, an effective two-layer optimization method is proposed to obtain the globally optimal solution. Then, we study a general case of multiple eavesdropping relays with multiple antennas, and solve a semi-definite relaxation problem. Numerical results verify the efficiency of our proposed solutions for both single and multiple relay cases and show considerable performance gains over conventional schemes.