In this paper, we investigate the hybrid beamforming design for a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) with hybrid analog-digital transmit antenna arrays sends dual-functional signals to communicate with a multi-antenna user and simultaneously sense the location information of a point target based on the reflected echo signals. Specifically, we aim to sense the target's unknown and random angle information by exploiting its prior distribution information, with posterior Cram\'{e}r-Rao bound (PCRB) employed as the sensing performance metric. First, we consider a sensing-only case and study the hybrid beamforming optimization to minimize the sensing PCRB. We analytically prove that hybrid beamforming can achieve the same performance as the optimized digital beamforming as long as the number of radio frequency (RF) chains is larger than 1. Then, we propose a convex relaxation based algorithm for the hybrid beamforming design with a single RF chain. Next, we study the hybrid beamforming optimization to minimize the PCRB subject to a communication rate target. Due to the intractability of the exact PCRB expression, we replace it with a tight upper bound. Although this problem is still non-convex and challenging to solve, we propose an alternating optimization (AO) algorithm for finding a high-quality suboptimal solution based on the feasible point pursuit successive convex approximation (FPP-SCA) method. Numerical results validate the effectiveness of our proposed hybrid beamforming design.

翻译：本文研究多输入多输出集成感知与通信系统中的混合波束成形设计。该系统采用具有混合模数发射天线阵列的多天线基站，通过发送双功能信号与多天线用户进行通信，同时基于反射回波信号感知点目标的定位信息。具体而言，我们旨在利用目标角度的先验分布信息感知其未知随机角度信息，并采用后验克拉美-罗界作为感知性能度量指标。首先，考虑纯感知场景，研究以最小化感知PCRB为目标的混合波束成形优化问题。通过理论证明，只要射频链数量大于1，混合波束成形即可达到与优化数字波束成形相同的性能。随后，针对单射频链场景提出基于凸松弛的混合波束成形设计算法。接着，研究在满足通信速率目标约束下最小化PCRB的混合波束成形优化问题。由于精确PCRB表达式难以处理，我们采用其紧致上界进行替代。尽管该问题仍为非凸且求解困难，我们基于可行点追踪连续凸逼近方法提出交替优化算法以获得高质量次优解。数值结果验证了所提混合波束成形设计方案的有效性。