This paper considers an integrated sensing and communication (ISAC) system where a multi-antenna base station transmits a common signal for joint multi-user communication and extended target (ET) sensing. We first propose a second-order truncated Fourier series surface model for an arbitrarily-shaped three-dimensional ET. Utilizing this model, we derive novel closed-form Cram{\'e}r-Rao bounds (CRBs) for the ET kinematic parameter estimation, such as the center range, azimuth angle, elevation angle, and orientation. Further, we formulate and solve two transmit beamforming design problems with optimization algorithms. The first one, named the CRB minimization problem, minimizes the CRB under constraints of communication signal-to-interference-plus-noise ratio (SINR) requirement, transmit power, and ET-specific beam coverage requirement, which is solved using the semidefinite relaxation technique. The second one, named the weighted-ISAC-metric problem, targets an weighted objective function combining the communication sum rate and sensing CRB, and is solved using the successive convex approximation technique. Additionally, by exploiting the penalty method, we introduce an unsupervised learning-based approach and propose a unique ISAC graph neural network (ISACGNN), composed of separate communication, sensing, and integration modules, to address both problems. Numerical results reveal the diverse CRB characteristics for different radar targets. The proposed beamforming designs are superior to existing baselines with better trade-off between communication and sensing performance, and a more appropriate beampattern for sensing the 3D ET. Besides, our proposed ISACGNN can effectively mimic the dynamic structures of the SINR, sum rate, and CRB, demonstrating remarkable scalability.

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公共信号以同时实现多用户通信与扩展目标感知。首先，针对任意形状的三维扩展目标，提出一种二阶截断傅里叶级数表面模型。基于该模型，推导出扩展目标运动参数估计的闭式克拉美罗界，包括中心距离、方位角、俯仰角及朝向角。进一步，通过优化算法构建并求解两类发射波束成形设计问题。第一类称为CRB最小化问题，在通信信干噪比需求、发射功率及扩展目标特定波束覆盖约束下最小化CRB，采用半定松弛技术求解。第二类称为加权ISAC指标问题，以通信总速率与感知CRB构成的加权函数为目标，通过逐次凸逼近技术求解。此外，利用罚函数法提出基于无监督学习的方法，构建由独立通信模块、感知模块与融合模块组成的ISAC图神经网络，以同时处理两类问题。数值结果表明不同雷达目标的CRB特性存在显著差异。所提波束成形设计在通信与感知性能间取得更优权衡，其波束方向图更适用于三维扩展目标感知，性能优于现有基线方案。同时，所提ISACGNN能有效模拟信干噪比、总速率与CRB的动态结构，展现出卓越的可扩展性。