This paper investigates an integrated sensing and communication (ISAC) system where the sensing target is a three-dimensional (3D) extended target, for which multiple scatterers from the target surface can be resolved. We first introduce a second-order truncated Fourier series surface model for an arbitrarily-shaped 3D ET. Utilizing this model, we derive tractable Cramer-Rao bounds (CRBs) for estimating the ET kinematic parameters, including the center range, azimuth, elevation, and orientation. These CRBs depend explicitly on the transmit covariance matrix and ET shape. Then we formulate two transmit beamforming optimization problems for the base station (BS) to simultaneously support communication with multiple users and sensing of the 3D ET. The first minimizes the sensing CRB while ensuring a minimum signal-to-interference-plus-noise ratio (SINR) for each user, and it is solved using semidefinite relaxation. The second balances minimizing the CRB and maximizing communication rates through a weight factor, and is solved via successive convex approximation. To reduce the computational complexity, we further propose ISACBeam-GNN, a novel graph neural network-based beamforming method that employs a separate-then-integrate structure, learning communication and sensing (C&S) objectives independently before integrating them to balance C&S trade-offs. Simulation results show that the proposed beamforming designs that account for ET shapes significantly outperform existing baselines, offering better communication-sensing performance trade-offs as well as an improved beampattern for sensing. Results also demonstrate that ISACBeam-GNN is an efficient alternative to the optimization-based methods, with remarkable adaptability and scalability.

翻译：本文研究一种集成感知与通信系统，其中感知目标为三维扩展目标，其表面多个散射点可被分辨。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，推导了估计扩展目标运动学参数（包括中心距离、方位角、俯仰角与朝向角）的易处理克拉美-罗界。这些克拉美-罗界显式依赖于发射协方差矩阵与扩展目标形状。随后，为基站构建了两个发射波束成形优化问题，以同时支持多用户通信与三维扩展目标感知。第一个问题在保证各用户最低信干噪比的前提下最小化感知克拉美-罗界，并通过半定松弛求解；第二个问题通过权重因子平衡克拉美-罗界最小化与通信速率最大化，并采用逐次凸逼近求解。为降低计算复杂度，进一步提出ISACBeam-GNN——一种基于图神经网络的新型波束成形方法，采用“分离-集成”结构，先独立学习通信与感知目标，再整合二者以权衡其性能折衷。仿真结果表明，所提出的考虑扩展目标形状的波束成形设计显著优于现有基线方法，在通信-感知性能权衡与感知波束模式方面均表现更优。结果同时验证了ISACBeam-GNN可作为基于优化方法的有效替代方案，具有出色的适应性与可扩展性。