发表机构
School of Electrical Engineering, KAIST; Telecom Paris and Inria Paris（KAIST电气工程学院; 巴黎电信学院和巴黎Inria）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Walker星座路由表的周期性，发现其取决于地球自转与卫星角速度之比，有理数时周期，无理数时非周期但可遍历平均，并用于与地面光纤的往返时间比较。
AI 中文摘要
在随地球旋转的参考系中，Delta Walker星座中卫星构型的动力学可以被分析为一个动力系统，其行为表现为环面上的平移。本文将此类分析扩展到基于固定地面中继的Walker星座路由问题。它考虑了在此类卫星和中继集合上的任意确定性、时不变路由规则。主要研究对象是与该规则相关联的路由表，该表为所有源-目的对指定一条由卫星和中继组成的路径，例如最短路径，并包含路径每一步下一跳的角度信息，这对于该场景下的波束成形至关重要。主要结果是：对于每条此类路由规则，路由表继承了环面流的二分性：当地球自转速度与卫星角速度之比为有理数时，路由表过程是周期性的，且周期与星座周期相同。当该比值为无理数时，路由表是非周期性的，但允许遍历长期平均值，这些平均值可以相对于一个显式不变测度作为系综平均值来计算。混合卫星-网关贪心路由的仿真从Walker路由表时间序列的时间和频谱特性两方面说明了这些发现。本文还讨论了如何定义能够应对此类非周期波动（当存在时）的度量。这通过比较两个遥远城市之间的往返时间来说明，该往返时间分别由使用贪心路由的Walker星座和当前可用的地面光纤提供。文中展示了如何利用遍历性，使星座的时变瞬时往返时间与光纤网络的恒定往返时间之间的比较变得有意义。
英文摘要
In a referential that rotates with Earth, the dynamics of the configurations of satellites in a Delta Walker constellation can be analyzed as a dynamical system as a function of a translation on the torus. This paper extends this type of analysis to routing over a Walker constellation, leveraging fixed ground relays. It considers any deterministic, time-invariant routing rule on such a collection of satellites and relays. The main object of interest is the routing table associated with this rule, which specifies, for all source-destination pairs, a route made of satellites and relays between them, for instance the shortest, together with angular information on next hop at each step of the route, which is essential for beamforming in this context. The main result is that, for each such routing rule, the routing table inherits the dichotomy of the torus flow: when the ratio of the Earth-spin and satellite angular speeds is rational, the routing table process is periodic with the same period as the constellation. When it is irrational, the table is non periodic but admits ergodic long-run averages which can be computed as ensemble averages w.r.t. an explicit invariant measure. Simulations with mixed satellite--gateway greedy routing illustrate these findings in terms of both temporal and spectral properties of the Walker routing table time series. The paper also discusses how to define metrics that cope with such non periodic fluctuations when present. This is illustrated by a comparison of the round-trip times between two far away cities as offered by a Walker constellation using greedy routing on one side, and by the currently available terrestrial fiber on the other side. It is shown how ergodicity can be used to make this comparison between the time varying instantaneous round trip times of the constellation and the constant round trip time of the fiber network meaningful.
Commentssubmitted to IEEE Journal
