Beamforming Design for Joint Target Sensing and Proactive Eavesdropping

This work studies the beamforming design in the joint target sensing and proactive eavesdropping (JTSAPE) system. The JTSAPE base station (BS) receives the information transmitted by the illegal transmitter and transmits the waveform for target sensing. The shared waveform also serves as artificial noise to interfere with the illegal receiver, thereby achieving proactive eavesdropping. We firstly optimize the transmitting beam of the BS to maximize the eavesdropping signal-to-interference-plus-noise ratio or minimize the target estimation parameter Cram{\'{e}}r-Rao bound, respectively. Then, the joint optimization of proactive eavesdropping and target sensing is investigated, and the normalized weighted optimization problem is formulated. To address the complexity of the original problem, the formulated problem is decomposed into two subproblems: proactive eavesdropping and target sensing, which are solved by the semi-definite relaxation technique. Furthermore, the scenario in which the quality of the eavesdropping channel is stronger than that of the illegal channel is considered. We utilize the sequential rank-one constraint relaxation method and iteration technique to obtain the high-quality suboptimal solution of the beam transmit covariance matrix. Numerical simulation shows the effectiveness of our proposed algorithm.