Space-air-ground integrated networks (SAGINs) will play a pivotal role in 6G communication systems. They are considered a promising technology for enhancing network capacity in densely populated urban areas and extending connectivity to rural regions. However, the complex, multi-layered, and heterogeneous nature of SAGINs demands an innovative approach to designing their multi-tier associations. In this context, we propose a modeling of the SAGINs association problem using multi-sided matching theory. Our objective is to devise a reliable, asynchronous, and fully distributed approach that associates nodes across the layers to maximize the total end-to-end rate of the assigned agents. To achieve this, our problem is formulated as a multi-sided many-to-one matching game. We introduce a randomized matching algorithm with minimal information exchange. The algorithm is shown to reach an efficient and stable association between nodes in adjacent layers. Simulation results show that our proposed approach yields significant gains compared to both greedy and distance-based algorithms.

翻译：空间-天空-地面一体化网络（SAGINs）将在6G通信系统中发挥关键作用。该技术被视为提升人口密集城区网络容量、并将连接延伸至农村地区的前沿方案。然而，SAGINs复杂、多层且异构的特性，要求对其多层关联机制进行创新性设计。在此背景下，我们基于多边匹配理论对SAGINs的关联问题建立数学模型。我们的目标是设计一种可靠、异步且完全分布式的关联方法，通过跨层节点匹配实现被分配智能体的端到端总速率最大化。为此，我们将该问题构建为多边多对一匹配博弈，并提出一种仅需最小信息交换的随机匹配算法。理论证明该算法能在相邻网络层节点间达成高效且稳定的关联。仿真结果表明，与贪婪算法及基于距离的算法相比，本文所提方法能带来显著的性能增益。