This paper investigates a joint active and passive beamforming design for distributed simultaneous transmitting and reflecting (STAR) reconfigurable intelligent surface (RIS) assisted multi-user (MU)- mutiple input single output (MISO) systems, where the energy splitting (ES) mode is considered for the STAR-RIS. We aim to design the active beamforming vectors at the base station (BS) and the passive beamforming at the STAR-RIS to maximize the user sum rate under transmitting power constraints. The formulated problem is non-convex and nontrivial to obtain the global optimum due to the coupling between active beamforming vectors and STAR-RIS phase shifts. To efficiently solve the problem, we propose a novel graph neural network (GNN)-based framework. Specifically, we first model the interactions among users and network entities are using a heterogeneous graph representation. A heterogeneous graph neural network (HGNN) implementation is then introduced to directly optimizes beamforming vectors and STAR-RIS coefficients with the system objective. Numerical results show that the proposed approach yields efficient performance compared to the previous benchmarks. Furthermore, the proposed GNN is scalable with various system configurations.

翻译：本文研究了分布式同时透射与反射可重构智能表面辅助的多用户多输入单输出系统中联合主动与被动波束成形设计问题，其中STAR-RIS采用能量分割模式。我们的目标是在发射功率约束下，通过设计基站处的主动波束成形向量与STAR-RIS的被动波束成形配置，最大化用户和速率。由于主动波束成形向量与STAR-RIS相位偏移之间的耦合关系，该问题具有非凸性且难以获得全局最优解。为有效求解此问题，我们提出了一种新颖的基于图神经网络的框架。具体而言，我们首先使用异质图表示对用户与网络实体间的交互关系进行建模，随后引入异质图神经网络实现方案，直接以系统目标优化波束成形向量与STAR-RIS参数。数值结果表明，与现有基准方法相比，所提方案能实现高效性能。此外，所提出的图神经网络框架在不同系统配置下均具有良好的可扩展性。