Low-Earth orbit (LEO) mega-constellations are emerging as high-capacity backbones for next-generation Internet. Deployment of laser terminals enables high-bandwidth, low-latency inter-satellite links (ISLs); however, their limited number, slow acquisition, and instability make forming a stable satellite topology difficult. Existing patterns like +Grid and Motif ignore regional traffic, ground station placement, and constellation geometry. Given sparse population distribution on Earth and the isolation of rural areas, traffic patterns are inherently non-uniform, providing an opportunity to orient inter-satellite links (ISLs) according to these traffic patterns. In this paper, we propose Starfield, a novel demand-aware satellite topology design heuristic algorithm supported by mathematical analysis. We first formulate a vector field on the constellation's shell according to traffic flows and define a corresponding Riemannian metric on the spherical manifold of the shell. The metric, combined with the spatial geometry, is used to assign a distance to each potential ISL, which we then aggregate over all demand flows to generate a heuristic for each satellite's link selection. Inspired by +Grid, each satellite selects the link with the minimum Riemannian heuristic along with its corresponding angular links. To evaluate Starfield, we developed a custom, link-aware, and link-configurable packet-level simulator, comparing it against +Grid and Random topologies. For the Phase 1 Starlink, simulation results show up to a 30% reduction in hop count and a 15% improvement in stretch factor across multiple traffic distributions. Moreover, static Starfield, an inter-orbital link matching modification of Starfield, achieves a 20% improvement in stretch factor under realistic traffic patterns compared to +Grid. Experiments further demonstrate Starfield's robustness under traffic demand perturbations.

翻译：低地球轨道（LEO）巨型星座正成为下一代互联网的高容量骨干网络。激光终端的部署实现了高带宽、低延迟的星间链路（ISL）；然而，其数量有限、捕获速度慢且不稳定的特性使得构建稳定的卫星拓扑变得困难。现有模式如+Grid和Motif忽略了区域流量、地面站布局及星座几何结构。考虑到地球人口分布稀疏且偏远地区孤立，流量模式本质上是非均匀的，这为根据这些流量模式定向星间链路（ISL）提供了机会。本文提出星域（Starfield），一种由数学分析支持的新型需求感知卫星拓扑设计启发式算法。我们首先根据流量在星座壳层上构建一个向量场，并在壳层的球面流形上定义相应的黎曼度量。该度量结合空间几何结构，用于为每条潜在的ISL分配一个距离值，随后我们聚合所有需求流以生成每颗卫星链路选择的启发式准则。受+Grid启发，每颗卫星选择具有最小黎曼启发式值的链路及其对应的角向链路。为评估星域，我们开发了一个定制化的、链路感知且链路可配置的分组级仿真器，将其与+Grid和随机拓扑进行比较。针对第一阶段星链（Starlink）的仿真结果表明，在多种流量分布下，跳数最多可减少30%，拉伸因子改善达15%。此外，星域的改进版本——静态星域（通过星间轨道链路匹配优化）在实际流量模式下，其拉伸因子相比+Grid提升了20%。实验进一步证明了星域在流量需求扰动下的鲁棒性。