STARLINK

In Starlink’s initial phase, 1,600 satellites in 1,150 km altitude orbits will provide connectivity to all except far north and south regions of the world. A second phase adds another 2,825 satellites in orbits ranging from 1,100 km altitude to 1325 km, increasing density of coverage at lower latitudes and providing coverage at least as far as 70 degrees North. Finally, in an additional FCC filing SpaceX proposes launching an additional 7,518 satellites in approximately 340 km VLEO orbits. In this paper, we examine only the LEO constellation.

在Starlink的初始阶段，将通过部署1,600颗运行于1,150公里高轨道的卫星，为全球范围内提供连接服务，但远北和远南地区除外。第二阶段将新增2,825颗卫星，其轨道高度从1,100公里到1,325公里不等，以增加低纬度地区的覆盖密度，并至少覆盖至北纬70度。最后，根据SpaceX的一份额外FCC申请，其计划再发射7,518颗轨道高度约为340公里的超低轨道（VLEO）卫星。然而，本文仅研究低地轨道（LEO）星座的特性。

SpaceX’s FCC filings necessarily concentrate on the properties of phased-array beam steering and spectrum allocations, so as to demonstrate they will not interfere with other spectrum users. In contrast, we are mostly concerned with satelliteto-satellite communication, and primarily consider the RF up and down links from the point of view of which satellites can be reached from which ground location at any time. The main restriction is that satellites are considered reachable if, from the ground, they are within 40 degrees from the vertical.

SpaceX的FCC申请文件主要关注相控阵波束控制和频谱分配的特性，目的是证明其系统不会对其他频谱用户造成干扰。相比之下，我们主要研究卫星间的通信，并从地面位置能在任意时刻接入哪些卫星的角度出发，分析射频（RF）上下行链路的覆盖范围。其主要限制在于，若某颗卫星从地面看在垂直方向40度以内，则认为其可达。

The FCC filings also discuss debris risks when the Starlink satellites are finally de-orbited. We see that each satellite will have five 1.5 kg silicon carbide “communication components” that may survive reentry due to silicon carbide’s melting point of 2,730C. This material is used in mirrors for laser communication links. A good working assumption is that each satellite will have five free-space laser links to connect to other Starlink satellites. In fact, as we shall explore, five laser links per satellite is also effectively the minimum number needed to build a low-latency dense LEO network.

FCC文件还讨论了Starlink卫星最终脱轨时的碎片风险。据悉，每颗卫星将包含五个1.5公斤的碳化硅通信组件，由于碳化硅的熔点高达2,730℃，这些组件可能在再入大气层时幸存。碳化硅用于激光通信链路的反射镜。一个合理的工作假设是，每颗卫星将配备五个自由空间激光链路，用于与其他Starlink卫星通信。事实上，正如我们将探讨的，五个激光链路也是构建低延迟高密度LEO网络的最低需求。

While free-space optical communications have been tested in orbit, no high-bitrate system exists that operates over the moderate distances Starlink will use, except for SpaceX’s own pair of test satellites launched in Feb 2018. In 2014, the European Data Relay System (EDRS) achieved 1.8 Gb/s from LEO to geostationary earth orbit (GEO), across a distance of 45,000 km[13]. ESA claims that the design is capable of 7.2Gb/s. In contrast, the distances in Starlink are much lower - most links are likely to be 1000 km or less. At EDRS distances, lasers will spread due to diffraction. If Starlink uses similar power lasers, the inverse square law suggests that received power on Starlink could be as much as 2000 times greater than on EDRS. It seems probable that free-space laser link speeds of 100 Gb/s or higher will be possible. However, in this paper we will refrain from modelling network capacity, as this is too speculative, and focus instead on latency, which is constrained only by topology and the speed of light.

尽管自由空间光通信已在轨道上进行过测试，但尚不存在能以Starlink所需的中等距离运行的高比特率系统，唯一的例外是SpaceX于2018年2月发射的两颗测试卫星。在2014年，欧洲数据中继系统（EDRS）在从LEO到地球同步轨道（GEO）45,000公里的距离上实现了1.8 Gb/s的通信速率[13]。欧洲航天局（ESA）声称该系统设计的最高能力为7.2 Gb/s。相比之下，Starlink的通信距离要短得多 —— 大多数链路距离可能在1,000公里以内。注意到，在EDRS这样的距离上，由于衍射效应，激光束会扩散，而LEO的相邻卫星间隔距离很短，因此：若Starlink采用类似功率的激光器，根据平方反比定律，其接收到的功率可能是EDRS的2,000倍。这使得100 Gb/s或更高的自由空间激光链路速率极有可能实现！然而，本文将不对网络容量进行建模，因为这具有很大的不确定性，而是 专注于延迟问题，该问题仅受限于网络拓扑和光速 。

sum

这一部分只是在介绍Starlink计划，物理性质之类的一概掠过，我们只需要关心UCL他们做的事情！

1. 主要研究卫星之间的通信（激光通信）
2. 地面位置任意时刻接入哪些卫星（卫星在法线40度以内，则认为可达）
3. 地空连接（上下行链路射频的覆盖范围）
4. 时延问题（拓扑通信 / 不同环境下的光速）

The orbital data[12] for the LEO constellation（星座/星宿） are:

低地球轨道（LEO）星座的轨道数据[12]如下：

	Initial	Final Deployment
Satellites	1,600 sats	2,825 satellites
Orbital Planes	32	32, 8, 5, 6
Sats per plane	50	50, 50, 75, 75
Altitude (km)	1,150	1,110, 1,130, 1,275, 1,325
Inclination	53°	53.8°, 74°, 81°, 70°

Orbital Phase Offset. Let us first consider the initial phase of deployment: 1,600 satellites in 53 ◦ inclination orbits. To provide continuous coverage density, the 50 satellites in each orbital plane need to be evenly spaced around the orbit. In addition, the 32 orbital planes will need to be oriented so they cross the equator at evenly spaced longitudes. For us to calculate the satellites relative positions, we also need to know the phase offset between satellites in consecutive orbital planes. This information is not in the SpaceX filings.

我们首先考虑部署的初始阶段：1,600颗卫星运行在倾角为53°的轨道上。为了提供连续的覆盖密度，每个轨道面上的50颗卫星需要均匀分布在轨道上。此外，32个轨道面需要以均匀间隔的经度穿过赤道。为了计算卫星的相对位置，我们还需要知道连续轨道面之间的相位偏移。然而，这一信息未包含在SpaceX的申请文件中。

The phase offset between orbital planes is a number between zero and one indicating when satellites in consecutive orbits cross the equator. If it is zero, satellite n in orbital plane p crosses the equator at the same time as satellite n in orbital plane p +1. If it is one, satellite n in orbital plane p crosses the equator at the same time as satellite n + 1 in plane p + 1. To achieve a uniform constellation with 32 orbital planes, phase offset must be a multiple of 1/32.

轨道面的相位偏移是一个介于0到1之间的数值，用于指示连续轨道面上的卫星何时穿越赤道。如果相位偏移为0，则轨道面 \(p\) 的第 \(n\) 颗卫星与轨道面 \(p+1\) 的第 \(n\) 颗卫星同时穿越赤道。如果相位偏移为1，则轨道面 \(p\) 的第 \(n\) 颗卫星与轨道面 \(p+1\) 的第 \(n+1\) 颗卫星同时穿越赤道。为了实现包含32个轨道面的均匀星座设计，相位偏移必须是1/32的整数倍。

why multiple of 1/32

没有理解为什么相位偏移必须是1/32的整数倍

The initial 1,600 satellites are all in 1,150 km altitude orbits with an inclination of 53°. The other key constraint, then, is that the satellites in different orbital places do not collide as the orbital planes cross. We simulated the 32 different possible phase offsets for orbits of this inclination. With all even multiples of 1 /32 as phase offset, satellites collide. The simulated minimum distances between satellites for the odd phase offsets are shown in the top graph in Figure 1. To minimize the probability of collision if station-keeping is not perfect, we conclude that the phase offset should be 5/32.

初始阶段的1,600颗卫星全部运行在高度为1,150公里、倾角为53°的轨道上。另一个关键约束是，不同轨道面上的卫星在轨道面交叉时不能发生碰撞。我们对该倾角的轨道进行了32种不同相位偏移的模拟。结果表明，当相位偏移为1/32的偶数倍时，卫星会发生碰撞。对于奇数倍的相位偏移，其最小卫星间距如图1的顶部图表所示。为了在轨道保持不完全精准的情况下最小化碰撞概率，我们得出结论：最佳相位偏移应为5/32。

Figure 2 shows the orbital planes and positions of the 1,600 satellites positions at one instant in time. A video of our simulations[8] shows their motion, and other results from this paper. It should be immediately clear that coverage provided is not uniform - the constellation is much denser at latitudes approaching 53 ◦ North and South. For example, London is located at 51.5 ◦ N, and will have approximately 30 satellites overhead within the 40 ◦ RF coverage angle.

图2展示了在某一时刻1,600颗卫星在轨道平面中的分布位置。视频模拟[8]显示了卫星的运动以及本文中的其他结果。可以明显看出，星座提供的覆盖并不均匀——在接近北纬和南纬53°的区域覆盖密度更高。例如，伦敦位于北纬51.5°，其40°射频覆盖角内大约会有30颗卫星。

For the second deployment phase, there are an additional 1,600 satellites in 53.8°inclination orbits. These are 40 km lower than the first phase satellites, so they orbit slightly faster. A 53°and a 53.8°satellite that start close together in the sky will slowly drift apart. To provide spatial diversity for the RF beams, it makes most sense to stagger their orbital planes so that the 53.8°orbital planes are equidistant between the 53°orbital planes at the equator. The bottom graph in Figure 1 shows minimum crossing distances vs orbital phase offsets for this constellation. We conclude that17 /32 is the best phase offset, though a few other values also appear to be viable.

在第二阶段部署中，额外的1,600颗卫星运行在倾角为53.8°的轨道上。这些卫星的轨道高度比第一阶段低40公里，因此轨道速度稍快。一颗53°轨道卫星与一颗53.8°轨道卫星如果在天空中起初相距较近，它们会逐渐分离开。为了为射频波束提供空间分集，将53.8°轨道面均匀插入53°轨道面的赤道交点之间是最合理的设计。图1底部图表展示了该星座中不同相位偏移下的最小交叉距离。我们得出结论：最佳相位偏移为17/32，但其他一些值也可能可行。

Performing a similar analysis for the satellites in higher inclination orbits, and arranging them to maximize minimum distance between their orbital planes, we end up with the 4,425 satellite constellation, as shown in Figure 3. Coverage over extreme latitudes is still sparse, but appears to be sufficient to satisfy FCC requirements to cover Alaska, and also provide some polar routes for long distance communication.

对于更高倾角轨道的卫星，我们进行了类似的分析，并调整它们的轨道面以最大化轨道面之间的最小距离。最终形成的4,425颗卫星星座如图3所示。尽管极高纬度地区的覆盖仍然稀疏，但这一覆盖已足以满足FCC要求，包括覆盖阿拉斯加，并提供一些用于长距离通信的极地航线。