This paper studies an integrated sensing and communication (ISAC) system, where a multi-antenna base station transmits beamformed signals for joint downlink multi-user communication and radar sensing of an extended target (ET). By considering echo signals as reflections from valid elements on the ET contour, a set of novel Cram\'er-Rao bounds (CRBs) is derived for parameter estimation of the ET, including central range, direction, and orientation. The ISAC transmit beamforming design is then formulated as an optimization problem, aiming to minimize the CRB associated with radar sensing, while satisfying a minimum signal-to-interference-pulse-noise ratio requirement for each communication user, along with a 3-dB beam coverage constraint tailored for the ET. To solve this non-convex problem, we utilize semidefinite relaxation (SDR) and propose a rank-one solution extraction scheme for non-tight relaxation circumstances. To reduce the computation complexity, we further employ an efficient zero-forcing (ZF) based beamforming design, where the sensing task is performed in the null space of communication channels. Numerical results validate the effectiveness of the obtained CRB, revealing the diverse features of CRB for differently shaped ETs. The proposed SDR beamforming design outperforms benchmark designs with lower estimation error and CRB, while the ZF beamforming design greatly improves computation efficiency with minor sensing performance loss.

翻译：本文研究一种集成感知与通信系统，其中多天线基站发射波束成形信号，以同时实现下行多用户通信与对扩展目标的雷达感知。通过将回波信号视为扩展目标轮廓上有效单元的反射，本文推导出一组用于估计扩展目标参数（包括中心距离、方向与朝向）的新颖克拉美-罗界。随后，将集成感知与通信的发射波束成形设计表述为一个优化问题，其目标是在满足各通信用户最低信号-干扰-脉冲噪声比要求以及为扩展目标定制的3分贝波束覆盖约束的同时，最小化与雷达感知相关的克拉美-罗界。为解决这一非凸问题，我们采用半定松弛技术，并针对松弛非紧致的情况提出了一种秩一解提取方案。为降低计算复杂度，我们进一步采用一种基于迫零的高效波束成形设计，其中感知任务在通信信道的零空间内执行。数值结果验证了所得克拉美-罗界的有效性，揭示了不同形状扩展目标的克拉美-罗界多样性特征。所提出的半定松弛波束成形设计在估计误差与克拉美-罗界方面均优于基准设计，而迫零波束成形设计则以微小的感知性能损失显著提升了计算效率。