This paper considers a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) with transceiver hybrid analog-digital arrays transmits dual-functional signals to communicate with a multi-antenna user and simultaneously sense the unknown and random location information of a target based on the reflected echo signals and the prior distribution information on the target's location. Under transceiver hybrid arrays, we characterize the sensing performance by deriving the posterior Cramér-Rao bound (PCRB) of the mean-squared error which is a function of the transmit hybrid beamforming and receive analog beamforming. We study joint transmit hybrid beamforming and receive analog beamforming optimization to minimize the PCRB subject to a communication rate requirement. We first consider a sensing-only system and derive the optimal solution to each element in the transmit/receive analog beamforming matrices that minimizes the PCRB in closed form. Then, we develop an alternating optimization (AO) based algorithm. Next, we study a narrowband MIMO ISAC system and devise an efficient AO-based hybrid beamforming algorithm by leveraging weighted minimum mean-squared error and feasible point pursuit successive convex approximation methods. Furthermore, we extend the results for narrowband systems to a MIMO orthogonal frequency-division multiplexing (OFDM) ISAC system. Numerical results validate the effectiveness of our proposed hybrid beamforming designs. It is revealed that the number of receive RF chains has more significant impact on the sensing performance than its transmit counterpart. Under a given budget on the total number of transmit/receive RF chains at the BS, the optimal number of transmit RF chains increases as the communication rate target increases due to the non-trivial PCRB-rate trade-off.

翻译：本文研究一种多输入多输出（MIMO）集成感知与通信（ISAC）系统，其中配备收发混合模拟-数字阵列的多天线基站（BS）发射双功能信号，以与多天线用户进行通信，并同时基于反射回波信号以及目标位置的先验分布信息，感知目标未知且随机的方位信息。在收发混合阵列架构下，我们通过推导均方误差的后验克拉美-罗下界（PCRB）来刻画感知性能，该下界是发射混合波束成形与接收模拟波束成形的函数。我们研究联合发射混合波束成形与接收模拟波束成形优化，以在满足通信速率要求的条件下最小化PCRB。首先考虑一个纯感知系统，以闭式解形式推导出最小化PCRB的发射/接收模拟波束成形矩阵中各元素的最优解。随后，提出一种基于交替优化（AO）的算法。接着，研究一个窄带MIMO ISAC系统，通过利用加权最小均方误差及可行点追踪逐次凸逼近方法，设计了一种高效的基于AO的混合波束成形算法。此外，将窄带系统的结果推广至MIMO正交频分复用（OFDM）ISAC系统。数值结果验证了所提混合波束成形设计的有效性。结果表明，接收射频链路的数量对感知性能的影响比发射射频链路更为显著。在给定基站收发射频链路总数预算的条件下，由于PCRB与速率之间存在非平凡的权衡关系，最优发射射频链路数量随通信速率目标的提高而增加。