Joint Beamforming for Simultaneous Proactive Eavesdropping and Communication With a Cooperative Base Station

In this paper, we investigate a simultaneous proactive eavesdropping and communication system, where a cooperative multi-antenna base station (BS) works with a legitimate eavesdropper (E) to serve multiple communication users (CUs), while simultaneously interfering with a pair of suspicious users (SUs). Specifically, we propose a joint information and jamming beamforming design to minimize the transmit power of BS, subject to the quality-of-service (QoS) requirements of CUs and the condition for successful eavesdropping by E. The resulting optimization problem is non-convex and challenging to solve directly. To overcome this, the semi-definite relaxation (SDR) technique is employed to reformulate the initial non-convex problem into a convex semi-definite programming (SDP). Then, we rigorously prove the optimality of SDR by demonstrating the existence of optimal rank-one transmit covariance matrices. However, solving the SDP for large-scale antenna systems incurs prohibitively high computational complexity. Therefore, we develop two sub-optimal algorithms based on minimum mean square error (MMSE) and zero-forcing (ZF) criteria, respectively. Simulation results demonstrate that the proposed schemes achieve a favorable trade-off between power consumption and computational complexity, while exhibiting strong robustness against imperfect channel state information (CSI).