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：本文研究了一种面向分布式同时透射与反射（STAR）可重构智能表面（RIS）辅助多用户（MU）多输入单输出（MISO）系统的联合主动与被动波束赋形设计，其中STAR-RIS采用能量分裂（ES）模式。我们旨在基站（BS）发射功率约束下，设计基站处的主动波束赋形向量与STAR-RIS处的被动波束赋形，以最大化用户和速率。所构建的问题为非凸问题，且因主动波束赋形向量与STAR-RIS相移之间存在耦合，难以获得全局最优解。为高效求解该问题，我们提出了一种新颖的基于图神经网络（GNN）的框架。具体而言，我们首先利用异构图表示对用户与网络实体间的交互关系进行建模。随后引入异构图表征网络（HGNN）实现，以系统目标为导向直接优化波束赋形向量与STAR-RIS系数。数值结果表明，与现有基准相比，所提方法能够实现高效性能。此外，该GNN方法在多种系统配置下均具有良好的可扩展性。