This paper studies an integrated sensing and communication (ISAC) system where a multi-antenna base station (BS) aims to communicate with a single-antenna user in the downlink and sense the unknown and random angle parameter of a target via exploiting its prior distribution information. We consider a general transmit beamforming structure where the BS sends one communication beam and potentially one or multiple dedicated sensing beam(s). Firstly, motivated by the periodic feature of the angle parameter, we derive the periodic posterior Cram\'{e}r-Rao bound (PCRB) for quantifying a lower bound of the mean-cyclic error (MCE), which is more accurate than the conventional PCRB for bounding the mean-squared error (MSE). Then, note that more sensing beams enable higher flexibility in enhancing the sensing performance, while also generating extra interference to the communication user. To resolve this trade-off, we formulate the transmit beamforming optimization problem to minimize the periodic PCRB subject to a communication rate requirement for the user. Despite the non-convexity of this problem, we derive the optimal solution by leveraging the semi-definite relaxation (SDR) technique and Lagrange duality theory. Moreover, we analytically prove that at most one dedicated sensing beam is needed. Numerical results validate our analysis and the advantage of having a dedicated sensing beam.

翻译：本文研究一种集成感知与通信（ISAC）系统，其中多天线基站（BS）在下行链路中与单天线用户通信，并利用目标的先验分布信息感知其未知且随机的角度参数。我们考虑一种通用的发射波束赋形结构，其中基站发送一个通信波束以及可能的一个或多个专用感知波束。首先，基于角度参数的周期性特征，我们推导了用于量化均循环误差（MCE）下界的周期后验克拉美-罗界（PCRB），该界比传统PCRB在约束均方误差（MSE）方面更为精确。其次，注意到更多的感知波束能够提供更高的灵活性以增强感知性能，但同时也会对通信用户产生额外干扰。为解决这一权衡问题，我们构建了发射波束赋形优化问题，目标是在满足用户通信速率要求的前提下最小化周期PCRB。尽管该问题具有非凸性，我们通过利用半定松弛（SDR）技术和拉格朗日对偶理论推导出了最优解。此外，我们通过分析证明至多需要一个专用感知波束。数值结果验证了我们的分析以及配置专用感知波束的优势。