Two Birds With One Stone: Beamforming Design for Target Sensing and Proactive Eavesdropping

This work studies the beamforming design in the joint proactive eavesdropping (PE) and target sensing (TS) systems. The base station (BS) wiretaps the information transmitted by the illegal transmitter and sends the waveform for TS. The shared waveform also serves as artificial noise to interfere with the illegal receiver, thereby achieving successful PE.We firstly optimize the transmitting beampattern of the BS only to maximize the eavesdropping rate or only to minimize the Cram{\'{e}}r-Rao bound, respectively. Then, the joint design of PE and TS is investigated by formulating the PE-centric, the TS-centric, and the normalized weighted optimization problems. The formulated problems are solved by the semi-definite relaxation technique and the sequential rank-one constraint relaxation method to address the complexity of the original problem. Furthermore, the scenario in which the quality of the eavesdropping channel is stronger than that of the illegal channel is considered. Numerical results demonstrate that the proposed algorithm can effectively realize PE and TS simultaneously.