This paper investigates an extremely large-scale reconfigurable intelligent surface (XL-RIS) assisted near-field integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) simultaneously sends unicast data to multiple single-antenna communication users (CUs) and senses multiple targets (TGTs). The BS, CUs and TGTs are \emph{all} assumed to be located in the near-field region of the XL-RIS. We aim to maximize the weighted sum rate (WSR) of all CUs, subject to the sensing beampattern gain constraint for each TGT, the transmit power constraint for the BS, and the unit modulus constraints on the XL-RIS phase shift. First, we develop a fractional programming (FP) based block coordinate descent (BCD) algorithm to obtain a locally optimal solution for such a non-convex joint design problem. Secondly, to address the high-dimensional spatial correlations and scalability of the XL-RIS near-field channels, we propose a customized graph neural network (GNN) scheme to generate the BS transmit beamforming variables and the XL-RIS reflecting coefficient vector for ISAC, where the near-field ISAC system is modeled as a heterogeneous graph comprising XL-RIS/CU/TGT nodes. The proposed GNN scheme can effectively learn the near-field channel state information (CSI) features, in which the message passing mechanism is employed to exchange CSI among these directly connected nodes in the graph. Furthermore, each XL-RIS/CU/TGT node maintains a feature vector for mapping to the BS transmit beamforming variables or the XL-RIS reflecting coefficient vector. Numerical results show that the proposed GNN-based beamforming design scheme achieves a better performance than the existing baselines, in terms of computational efficiency, feasibility, robustness, and the ability of generalization.

翻译：本文研究了一种超大规模可重构智能反射面辅助的近场通感一体化系统，其中配备多天线的基站同时向多个单天线通信用户发送单播数据并感知多个目标。假设基站、通信用户和目标均位于超大规模智能反射面的近场区域内。我们的目标是在满足每个目标的感知波束方向图增益约束、基站发射功率约束以及超大规模智能反射面相移的单位模值约束下，最大化所有通信用户的加权和速率。首先，我们提出了一种基于分式规划的块坐标下降算法，以获取该非凸联合设计问题的局部最优解。其次，为应对超大规模智能反射面近场信道的高维空间相关性和可扩展性问题，我们提出了一种定制化的图神经网络方案来生成通感一体化所需的基站发射波束成形变量和超大规模智能反射面反射系数向量。该方案将近场通感一体化系统建模为由超大规模智能反射面/通信用户/目标节点构成的异构图。所提出的图神经网络方案能有效学习近场信道状态信息的特征，其中采用消息传递机制在图中的直接连接节点间交换信道状态信息。此外，每个超大规模智能反射面/通信用户/目标节点维护一个特征向量，用于映射到基站发射波束成形变量或超大规模智能反射面反射系数向量。数值结果表明，所提出的基于图神经网络的波束成形设计方案在计算效率、可行性、鲁棒性和泛化能力方面均优于现有基线方法。