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 angle and delay estimation. Then, we optimize the transmit beamforming at the BS to minimize the CRB, subject to communication rate and power constraints. In particular, we obtain the optimal solution in closed-form 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：本文研究通感一体化（ISAC）系统中多输入多输出（MIMO）波束赋形设计，其中ISAC基站（BS）用于与多个下行用户通信，同时通信信号被复用感知多个目标。我们所关心的感知参数为目标的角度和时延信息，这些参数可用于定位目标。基于此考虑，我们首先推导了角度和时延估计的克拉美-罗界（CRB）。随后，在通信速率和功率约束条件下，优化基站的发射波束赋形以最小化CRB。特别地，在单目标和单用户情形下，我们给出了最优解的闭式表达式；在多目标和多用户场景中，证明了最优解的稀疏性，从而降低了优化过程中的计算复杂度。数值结果表明，优化后的波束赋形展现了优异的定位性能，并有效减少了基站所需的天线数量。