Joint Angle and Delay Cram\'{e}r-Rao Bound Optimization for ISAC

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.