This paper studies an integrated sensing and communication (ISAC) system where a multi-antenna base station (BS) communicates with multiple single-antenna users in the downlink and senses the unknown and random angle information of a target based on its prior distribution information and the received echo signals. We focus on a challenging scenario with heterogeneous unknown parameters where the target's reflection coefficient is also unknown with no prior information. We consider a general transmit beamforming structure with both communication beams and dedicated sensing beams, where the communication users can cancel the interference caused by the pre-determined sensing signals. By adopting the periodic posterior Cramer-Rao bound (PCRB) to quantify a lower bound of the mean-cyclic error (MCE) for sensing the periodic angle parameter, we optimize the transmit beamforming to minimize the periodic PCRB, subject to individual communication user rate constraints, which is a non-convex problem. By leveraging the semi-definite relaxation (SDR) technique and Lagrange duality theory, we derive the optimal solution and prove that at most one dedicated sensing beam is needed. Numerical results validate our analysis and effectiveness of the proposed beamforming design.

翻译：本文研究了一种集成感知与通信（ISAC）系统，其中多天线基站（BS）在下行链路中与多个单天线用户通信，并基于目标的先验分布信息和接收到的回波信号，感知目标的未知随机角度信息。我们关注一个具有挑战性的场景：目标的反射系数也是未知的且无先验信息，即存在异构未知参数。我们考虑一种通用的发射波束成形结构，包含通信波束和专用感知波束，其中通信用户能够消除由预定感知信号引起的干扰。通过采用周期后验克拉美罗界（PCRB）来量化感知周期角度参数的平均循环误差（MCE）下界，我们优化发射波束成形以最小化周期PCRB，同时满足各个通信用户的速率约束。这是一个非凸问题。利用半正定松弛（SDR）技术和拉格朗日对偶理论，我们推导出最优解，并证明最多只需要一个专用感知波束。数值结果验证了我们的分析以及所提出的波束成形设计的有效性。