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.

翻译：本文研究了联合目标感知与主动窃听系统中的波束成形设计问题。在该系统中，基站接收非法发射机传输的信息，同时发射用于目标感知的波形。该共享波形也作为人工噪声干扰非法接收机，从而实现主动窃听。我们首先分别优化基站的发射波束，以最大化窃听信号与干扰加噪声比或最小化目标估计参数的克拉美-罗下界。随后，研究了主动窃听与目标感知的联合优化，并建立了归一化加权优化问题。为应对原问题的复杂性，将所提问题分解为主动窃听和目标感知两个子问题，并采用半定松弛技术进行求解。此外，考虑了窃听信道质量优于非法信道质量的场景。我们利用序列秩一约束松弛方法与迭代技术，获得了波束发射协方差矩阵的高质量次优解。数值仿真验证了所提算法的有效性。