In this paper, we study a secure integrated sensing and communication (ISAC) system where one multi-antenna base station (BS) simultaneously serves a downlink communication user and senses the location of a target that may potentially serve as an eavesdropper via its reflected echo signals. Specifically, the location information of the target is unknown and random, while its a priori distribution is available for exploitation. First, to characterize the sensing performance, we derive the posterior Cram\'er-Rao bound (PCRB) which is a lower bound of the mean squared error (MSE) for target sensing exploiting prior distribution. Due to the intractability of the PCRB expression, we further derive a novel approximate upper bound of it which has a closed-form expression. Next, under an artificial noise (AN) based beamforming structure at the BS to alleviate information eavesdropping and enhance the target's reflected signal power for sensing, we formulate a transmit beamforming optimization problem to maximize the worst-case secrecy rate among all possible target (eavesdropper) locations, under a sensing accuracy threshold characterized by an upper bound on the PCRB. Despite the non-convexity of the formulated problem, we propose a two-stage approach to obtain its optimal solution by leveraging the semi-definite relaxation (SDR) technique. Numerical results validate the effectiveness of our proposed transmit beamforming design and demonstrate the non-trivial trade-off between secrecy performance and sensing performance in secure ISAC systems.

翻译：本文研究了一种安全感知通信一体化（ISAC）系统，其中多天线基站（BS）同时服务于下行通信用户，并通过目标反射的回波信号感知其位置（该目标可能充当窃听者）。具体而言，目标的位置信息未知且随机，但可利用其先验分布。首先，为刻画感知性能，我们推导了利用先验分布的目标感知均方误差（MSE）下界——后验克拉美-罗界（PCRB）。由于PCRB表达式难以处理，我们进一步推导了其具有闭式表达式的新型近似上界。其次，在基站采用基于人工噪声（AN）的波束赋形结构以减轻信息窃听并增强目标反射信号感知功率的背景下，我们构建了一个发射波束赋形优化问题，在由PCRB上界表征的感知精度阈值约束下，最大化所有可能目标（窃听者）位置中的最差情况保密速率。尽管该优化问题具有非凸性，我们提出了一种两阶段方法，利用半定松弛（SDR）技术获得其最优解。数值结果验证了所提发射波束赋形设计方案的有效性，并揭示了安全ISAC系统中保密性能与感知性能之间的非平凡权衡关系。