In this paper, we study a multi-input multi-output (MIMO) beamforming design in an integrated sensing and communication (ISAC) system, in which an ISAC base station (BS) is used to communicate with multiple downlink users and simultaneously the communication signals are reused for sensing multiple targets. Our interested sensing parameters are the angle and delay information of the targets, which can be used to locate these targets. Under this consideration, we first derive the Cram\'{e}r-Rao bound (CRB) for joint angle and delay estimation. Then, we optimize the transmit beamforming at the BS to minimize the CRB, subject to the communication rate requirement and the maximum transmit power constraint. In particular, we obtain the closed-form optimal solution in the case of single-target and single-user, and in the case of multi-target and multi-user scenario, the sparsity of the optimal solution is proven, leading to a reduction in computational complexity during optimization. The numerical results demonstrate that the optimized beamforming yields excellent positioning performance and effectively reduces the requirement for a large number of antennas at the BS.

翻译：本文研究集成感知与通信系统中多输入多输出波束成形设计问题，其中集成感知与通信基站需同时服务多个下行用户，并将通信信号复用至多个目标感知任务。本文关注的感知参数为目标的角度与延迟信息，该信息可用于目标定位。基于此，我们首先推导了联合角度与延迟估计的克拉美-罗下界。随后，在满足通信速率需求与最大发射功率约束条件下，通过优化基站发射波束成形以最小化该下界。特别地，我们在单目标单用户场景中获得了闭式最优解；在多目标多用户场景中，证明了最优解具有稀疏性，从而显著降低了优化过程中的计算复杂度。数值结果表明，优化后的波束成形方案能够实现优异的定位性能，并有效降低了基站对大规模天线阵列的需求。