# NGSO Constellation Design for Global Connectivity

Israel Leyva-Mayorga1, Beatriz Soret12, Bho Matthiesen34, Maik Röper3,
Dirk Wübben3, Armin Dekorsy3, and Petar Popovski14  1Department of Electronic
Systems, Aalborg University, Aalborg, Denmark  1Telecommunications Research
Institute (TELMA), University of Malaga, Malaga, Spain  3Gauss-Olbers Center,
c/o University of Bremen, Dept. of Communications Engineering, Germany
4University of Bremen, U Bremen Excellence Chair, Dept. of Communications
Engineering, Germany  Email: {ilm, bsa<EMAIL_ADDRESS>{matthiesen,
roeper,wuebben<EMAIL_ADDRESS>
## Acronyms

3GPP

    3rd Generation Partnership Project
AI

    artificial intelligence
AIaaS

     artificial intelligence (AI) as-a-service
AoI

    age of information
AP

    access point
AWGN

    additive white Gaussian noise
BS

    base station
CDF

    Cumulative Distribution Function
DTN

    Delay and Disruption Tolerant Networking
E2E

    end-to-end
EDRS

    European Data Relay System
FCC

    Federal Communications Commission
FSO

    free-space optical
GEO

    geostationary orbit
GS

    ground station
GSL

    ground-to-satellite link
HAP

    high-altitude platform
IoT

    Internet of Things
IRS

    intelligent reflecting surfaces
ISL

    inter-satellite link
KPI

    key performance indicator
LEO

    low Earth orbit
LoS

    line-of-sight
LPWAN

    low-power wide-area network
MCS

    modulation and coding scheme
MEO

    medium Earth orbit
MIMO

    multiple-input multiple-output
NB-IoT

    Narrowband Internet of Things (IoT)
NGSO

    non-geostationary orbit
NR

    New Radio
OFDM

    orthogonal frequency division multiplexing
PAA

    point-ahead-angle
RF

    radio frequency
RTT

    round-trip time
SNR

    signal-to-noise ratio
UAV

    unmanned aerial vehicle

##  1 Introduction

Providing global connectivity is not possible with terrestrial infrastructure
alone. This is due to a multitude of factors, the most important of which are
geographical conditions and economic reasons. So far, it seems that every new
mobile wireless generation has ambitions to connect sparsely populated areas,
but terrestrial options have not proven to be cost-effective. While providing
radio access merely necessitates the deployment of a base station (BS) or
access point (AP) in the area of interest, connecting this infrastructure to
the core network and, hence, to the Internet through _backhaul_ and, possibly,
_fronthaul_ links is much more challenging. A clear use case is providing
global connectivity to vessels in open ocean, where deploying BSs and the
necessary backhaul links (i.e., sea cables) to the many possible routes is not
feasible.

In contrast, geostationary orbit (GEO) satellites have been used to provide
global communication coverage for several decades, for instance, for TV
broadcasting or maritime connectivity. In addition, GPS is an example of a
widespread medium Earth orbit (MEO) service. Even though GEO satellites are
able to provide global service availability in underserved and disconnected
areas [1], they are not efficient on their own as a competitive global
connectivity solution. Due to the high altitude of the orbit, GEO satellites
suffer from a long propagation delay and a high signal attenuation. The latter
aspect is specially problematic when devices with energy and size restrictions
attempt to communicate in the uplink, which are some of the defining
characteristics of IoT devices [2, 3].

Non-geostationary orbit (NGSO) satellite constellations represent a
cornerstone in the NewSpace paradigm and thus have become one of the hottest
topics for the industry, academia, but also for national space agencies and
regulators. For instance, numerous companies worldwide, including Starlink,
OneWeb, Kepler, SPUTNIX, and Amazon have started or will soon start to deploy
their own NGSO constellations [4], which aim to provide either broadband [5,
6] or IoT services [2]. One of the major drivers for such a high interest on
NGSO constellations is that, with an appropriate design, they are capable of
providing global coverage and connectivity. While global connectivity can also
be provided by a small set of GEO satellites, NGSO constellations present
three main advantages over terrestrial and GEO satellite communications:

  1. 1.

Short propagation delay: Electromagnetic waves propagate faster in the vacuum
than in optic fiber, which has typical refraction index of $1.44$ to $1.5$
[7]. Moreover, NGSO satellites are deployed at much lower altitudes than GEO
satellites, which reduces the one-way ground-to-satellite propagation delays
to a few milliseconds. As a consequence, the end-to-end (E2E) latency with
NGSO satellites over long distances may be competitive and even lower than
that of terrestrial networks [7].

  2. 2.

Global connectivity: NGSO satellites can provide coverage in remote areas
where terrestrial infrastructure is not available. Furthermore, if appropriate
functionalities are implemented, the data could be routed E2E by the
satellites themselves.

  3. 3.

Feasible uplink communication from small devices: Due to the relatively low
altitude of deployment and the signals propagating mainly through free-space,
it is feasible for small devices to communicate directly with low Earth orbit
(LEO) satellites. This has lead to companies and organisations to aim for
integrated space and terrestrial infrastructures using low-power wide-area
network (LPWAN) technologies such as LoRaWAN and Narrowband IoT (NB-IoT) [8,
9].

Based on these advantages, some of the main use cases for NGSO constellations
include:

  1. 1.

Backhauling: Inter-satellite communication can be used to transmit the data
towards the Earth, even when the source and destination are not within the
coverage of the same satellite [10].

  2. 2.

Offloading: NGSO constellations can serve as additional infrastructure in
urban hot-spots where the capacity of the terrestrial network is temporarily
exceeded, for example, during sport and cultural events.

  3. 3.

Resilience: Satellites in NGSO can serve as failback backhaul network for
terrestrial BSs in case the primary backhaul fails, e.g., due to natural
disasters.

  4. 4.

Edge computing and AI as-a-service (AIaaS): IoT devices have limited
processing capabilities and limited energy supply (i.e., batteries).
Therefore, NGSO satellites can be used as edge computing nodes [11] to reduce
the computational load at the IoT devices. Furthermore, the satellites can
gather data from several devices and locations along their orbit and use it,
along with their computational capabilities, to provide AIaaS to devices where
the data and/or processing capabilities are insufficient for AI [12].

  5. 5.

Earth observation: NGSO satellites can be used as moving sensing devices that
capture data, e.g., in the form of images or video, of physical phenomena at
the Earth’s surface or within its atmosphere. To obtain a sufficient
resolution, LEOs are the preferred choice in most Earth observation satellite
missions. Furthermore, sun-synchronous orbits, i.e., an orbit where the
satellite maintains a constant angle towards the sun when viewed from Earth,
often have favorable properties for Earth observation tasks.

For the use cases mentioned above, and many more, _global connectivity_ is
essential, as it allows to fully exploit the benefits of NGSO constellations.
Specifically, it would allow the constellation to deliver the data generated
on the ground, by aerial vehicles, or by the satellites themselves to the
destination without heavily relying in additional (e.g., terrestrial)
infrastructure.

Nevertheless, there are several key performance indicators (KPIs) that should
be considered to determine whether an NGSO constellation design is appropriate
for the target application. These include, but are not restricted to

  * •

Service availability: The fraction of the time in which the ground terminal is
able to communicate with the constellation [8]. Through this chapter, we will
assess this KPI based on the coverage of the constellation in different
locations, including remote (e.g., polar) regions.

  * •

Transport capacity: The maximum amount of data that can be transmitted by the
constellation, E2E, per time unit.

  * •

Throughput: Data rate experienced by the users.

  * •

Scalability: Maximum number of devices supported by the constellation per unit
area.

  * •

Inter-satellite connectivity: The ability to achieve inter-satellite
communication. Oftentimes it is assessed by the number of satellites with
active connections [13] or by the number of satellites within communication
range [14].

  * •

Latency and reliability: Probability that the data can be transmitted to the
destination within a given time $t$.

  * •

Energy efficiency: Since IoT devices and satellites are usually powered by
batteries, minimizing the energy required for communication is essential.

Several of these KPIs were considered by Del Portillo [6] to compare the
OneWeb, Starlink (outdated configuration with $h>1000$ km), and Telesat
constellations.

Other KPIs have been defined for satellite constellations. For example, Soret
et al. [10] emphasised the relevance of timing metrics beyond the packet
delay, such as the age of information (AoI) and its by-products, for some
satellite tracking or remote sensing applications.

##  2 NGSO constellation design

Satellite constellations are groups of satellites organized in orbital planes.
The $N_{\text{op}}$ satellites in one orbital plane follow the same orbital
trajectory, one after the other, and are usually uniformly spaced around the
orbit. Furthermore, an orbital shell is a group of $P$ orbital planes in a
constellation that are deployed at approximately the same altitude; some
orbital shells may implement minor variations of a few kilometers called
orbital separation. To maximize the coverage for communications, the
organisation of satellites in one orbital shell usually belongs to one of two
basic types: Walker star and Walker delta (also called Rosette) [5, 2, 15,
16]. Satellite constellation design may include one or more orbital shells.

Walker star orbital shells consist of nearly-polar orbits, with typical
inclinations of $\delta\approx 90^{\circ}$, which are evenly spaced within
$180^{\circ}$. As such, the angle between neighbouring orbital planes is
$180/P$.

Walker delta orbital shells, on the other hand, typically consist of inclined
orbits, with typical inclinations of $\delta<60^{\circ}$, which are evenly
spaced within $360^{\circ}$. As such, the angle between neighbouring orbital
planes is $360/P$.

Due to the use of inclined orbits, Walker delta orbital shells do not provide
coverage in polar regions nor in the northernmost countries such as Greenland.
However, this allows to keep the satellites within the areas where most of the
population resides and, hence, where data traffic is generated and consumed.

Since both Walker star and delta geometries provide distinct advantages and
disadvantages, some companies such as SpaceX have considered a mixed design
consisting of multiple orbital shells. Specifically, the design of the
Starlink constellation considered a Walker delta orbital shell at around $550$
km and at around $1100$ km. However, the Federal Communications Commission
(FCC) granted permission to SpaceX to modify the constellation geometry and to
lower the $2814$ satellites in the $1100$ km orbital shell to an altitude
between $540$ and $570$ km [17]. Table I shows the design parameters of some
relevant NGSO constellations. The values in this table were obtained from the
companies web pages, related papers [6, 14], and FCC filings and some of them
have not yet been approved.111Updates on ongoing launches can be found at the
New Space webpage https://www.newspace.im/

Beyond the technical aspects, the dramatic increase in the number of objects
put into orbit around the Earth due to the deployment of NGSO constellations
has raised concerns on their long-term sustainability. Naturally, the more
satellites orbit the Earth, the higher the risk of collision. Hence, measures
to minimize the collision risk have been explored and should be adopted in
commercial constellations [18]. In particular, deploying the orbital planes at
slightly different altitudes, with differences of less than $4$ km, greatly
reduces the collisions caused by failed satellites: a scenario that cannot be
avoided. However, this introduces slight asymmetries in the constellations
that complicate several technical aspects; these will be further described in
Section 4-B. Another example of slight asymmetries in the constellations is
that the satellites between neighbouring orbital planes may be shifted across
the orbit, so that the satellites in one orbital plane are rotated by a
relatively small angle w.r.t. those in the neighbouring planes.

Figure 2.1: Diagram of Walker star, Walker delta (Rosette), and mixed constellation geometries. TABLE I: Parameters for some commercial NGSO satellite constellations Parameter | Constellation
---|---
| Starlink | OneWeb | Kepler
Type | Mixed | Walker star | Walker star
Number of satellites $N$ | $1584$ | $1584$ | $720$ | $348$ | $172$ | $648$ | $140$
Number of orbital planes $P$ | $72$ | $72$ | $36$ | $6$ | $4$ | $18$ | $7$
Altitude $h$ (km) | $550$ | $540$ | $570$ | $560$ | $560$ | $1200$ | $575$
Inclination $\delta$ (∘) | $53$ | $53.2$ | $70$ | $97.6$ | $97.6$ | $86.4$ | $98.6$
Intended service | Broadband | Broadband | IoT

##  3 Communication links

The endpoints for communication in an NGSO constellation can be either the
ground or at satellite level. Therefore, the paths that the data can take in
the constellation can be classified into the following four _logical links_
[19].

  * •

Ground to ground [G2G]: With both, source and destination, being ground and/or
aerial terminals. This is the typical use of the constellation for terrestrial
backhauling.

  * •

Ground to satellite [G2S]: With the source being a ground or aerial terminal
and the destination being a satellite. This link is mainly used for operations
initiated by dedicated ground stations such as constellation, route, and link
establishment and maintenance, tele-control and tele-command, and content
caching.

  * •

Satellite to Ground [S2G]: With the source being a satellite and the
destination being a ground or aerial terminal. This link is mainly used when
the satellites themselves generate application data that must be transmitted
to a ground station for storage and/or processing. For example, in Earth and
space observation, but also for telemetry, handover, link maintenance and
adaptation, and fault reporting.

  * •

Satellite to Satellite [S2S]: With the source and destination being
satellites, possibly deployed at different altitudes and/or orbits. This link
is used for localised network maintenance, updating routing tables, neighbour
discovery, or other applications such as distributed processing, sensing and
inference.

These links must be realised with a moving infrastructure. NGSO satellites
move rapidly with respect to each other in higher and lower orbits and in
different orbital planes.They also move with respect to the Earth due to the
satellite orbital velocity and to the Earth’s rotation [20]. Specifically, the
orbital velocity of the satellites $v_{o}$ is determined by the altitude of
deployment $h$ as

$v_{o}(h)\approx\sqrt{\frac{\text{G}M_{E}}{R_{E}+h}},$ (1)

where G is the universal gravitational constant; $M_{E}$ and $R_{E}$ are the
mass and radius of the Earth, respectively. Then, according to Kepler’s third
law of planetary motion, the orbital period of a satellite can be closely
approximated as

$T_{o}(h)\approx\frac{2\pi(R_{E}+h)}{v_{o}(h)}=\sqrt{\left(\frac{4\pi^{2}}{\text{G}M_{E}}\right)\left(R_{E}+h\right)^{3}}.$
(2)

From here, and assuming traditional LEO altitudes, for example, with $h=600$
km, it is easy to observe that the orbital velocity of NGSO satellites may
exceed $7.6$ km/s and that their orbital period is usually around $90$
minutes.

Furthermore, satellites in different locations of the constellation may move
rapidly w.r.t. to each other. Finally, the whole satellite constellation is
moving w.r.t. the Earth due to its rotation [20, 2]. Hence, an important
aspect to select the altitude of deployment of a constellation is whether it
is desired that the orbit is _recursive_. That is, whether the satellites
should pass over the same point in the Earth at a specific time of the day
after a given number of days $m$. For this, we require to find an altitude
$h_{\text{rec}}$ for which $nT_{o}=mT_{E}$, where $T_{E}=86164$ s is the
equinoctial day [2]. To find the required altitude for the recursive orbit,
let us first rewrite the right-hand side of 2 as

$T_{o}^{2}=\left(\frac{4\pi^{2}}{\text{G}M_{E}}\right)\left(R_{E}+h\right)^{3},$
(3)

which allows us to define $h$ as a function of $T_{o}$ as

$h=\left(\frac{T_{o}^{2}\text{G}M_{E}}{4(\pi)^{2}}\right)^{1/3}-R_{E}.$ (4)

Finally, we substitute the period $T_{o}=mT_{E}/n$ in (4) to find the altitude
for a recursive satellite orbit as

$h_{\text{rec}}(n,m,T_{E})=\left(\frac{(mT_{E})^{2}\text{G}M_{E}}{(2n\pi)^{2}}\right)^{1/3}-R_{E}$
(5)

From (5) we obtain that NGSO satellites at $h=554$ km, close to Starlink’s
altitude of deployment, have recursive orbits for $n=15$ and $m=1$. That is,
these will orbit the Earth exactly $15$ times each day. Moreover, those at
$h=1248$ km, close to OneWeb’s altitude of deployment, have recursive orbits
for $n=13$ and $m=1$.

An essential aspect to observe about NGSO satellite constellations is that,
even though the relative positions and velocities of satellites w.r.t. other
satellites and to the ground terminals are dynamic, the dynamics of the
constellation are fully dictated by the physics of the system and, hence,
completely predictable. Therefore, the topology of the network (space and
terrestrial) at a point in time $t$ can be perfectly predicted with a high
level of certainty. Because of this, approaches from ad-hoc networks [21] as
well as from fully structured networks have been applied in the context of
NGSO satellite constellations.

Furthermore, the different time scales of the various ongoing processes offer
opportunities for simplification via time-scale separation. For instance, the
orbital period of a satellite is extremely long when compared to most of the
communication tasks within the constellation. Therefore, the satellite
constellation can be assumed to be static during short periods to simplify the
analysis. In the following, we exemplify this later aspect by calculating one-
hop latency of the different links.

Depending on whether we consider a ground-to-satellite link (GSL) or an inter-
satellite link (ISL), the one-hop latency is determined by different factors.
Naturally, it depends on the position of the transmitter $u$ and the receiver
$v$ at time $t$, when the packet is ready to be transmitted and also on the
packet length $p$. In the following, we calculate the three main components of
the one-hop latency by considering the relative position of $u$ w.r.t. $v$ to
be fixed during a period $[t,\Delta t]$.

First, the waiting time at the transmission queue $q_{t}(u,v)$ is the time
elapsed since the packet is ready to be transmitted until the beginning of its
transmission. Note that, depending on the communication protocols, for
example, signaling, and frame structure, it may occur that $q_{t}(u,v)>0$ for
all $u,v$ even when there are no more packets in the queue. Second, the
transmission time, which is the time it takes to transmit $p$ bits at the
selected rate $R_{t}(u,v)$ bps. Third, the propagation time, which is the time
it takes for the electromagnetic radiation to travel the distance $d_{t}(u,v)$
from $u$ to $v$. Hence, the latency to transmit a packet of size $p$ from $u$
to $v$ at time $t$ is given by

$L_{t}(u,v)=\\!\underbrace{q_{t}(u,v)}_{\text{Waiting
time}}+\\!\underbrace{\dfrac{p}{R_{t}(u,v)}}_{\text{Transmission
time}}+\underbrace{\dfrac{d_{t}(u,v)}{c}}_{\text{Propagation time}}.$ (6)

Note that all the factors that contribute to the one-hop packet latency depend
on the time the packet is generated. Furthermore, due to the movement of the
satellites, the set of established links and communication paths (routes)
change depending on $t$. This creates a greatly dynamic network topology that
introduces distinctive challenges in the design and implementation of the
distinct physical links. In the following, we elaborate on the main
technologies for satellite communications: radio frequency (RF) and free-space
optical (FSO) links.

_RF links_ occur in frequencies either in the S-band, the Ka-band or the Ku-
band. These links are mainly affected by free-space path loss and thermal
noise, so additive white Gaussian noise (AWGN) channels are oftentimes
considered. The free-space path loss between two terminals $u$ and $v$ at time
$t$ is determined by the distance $d_{t}(u,v)$ between them and the carrier
frequency $f$ as

$\mathcal{L}_{t}(u,v)=\left(\frac{4\pi d_{t}(u,v)f}{c}\right)^{2},$ (7)

where $c$ is the speed of light.

Next, let $P^{(u)}$ be the transmission power of transmitter $u$ – assumed to
be constant for simplicity – and $\sigma^{2}_{v}$ be the noise power at
receiver $v$. Further, let $G_{t}^{(u,v)}$ and $G_{t}^{(v,u)}$ be the antenna
gain of transmitter $u$ towards receiver $v$ and vice versa. Based on this,
the maximum data rate for reliable communication between two satellites and/or
a satellite and a ground terminal at time $t$ can be calculated as a function
of the signal-to-noise ratio (SNR)

$R_{t}(u,v)=B\log_{2}\Big{(}1+\text{SNR}_{t}\left(u,v\right)\Big{)}=B\log_{2}\left(1+\frac{P^{(u)}G_{t}^{(u,v)}G_{t}^{(v,u)}}{\mathcal{L}_{t}(u,v)\sigma^{2}_{v}}\right).$
(8)

Naturally, the achievable data rate in the presence of interference will be
lower than (8). Nevertheless, the use of directional antennas and/or
orthogonal resource allocation [13] greatly reduces interference within
constellations. Building on this, the achievable rate mainly depends on the
transmission power, the large-scale fading (path loss), and noise power, but
also on the gain of the communicating antennas in the direction of the
receiver/transmitter. Since the constellation is a moving infrastructure,
antenna pointing technology is an essential aspect of constellation design.

Throughout this chapter, we evaluate the performance of the RF physical links
by assuming the parameters listed in Table II unless stated otherwise. These
parameters were selected to focus on comparing the constellation design and
not the implemented (envisioned) communication technologies.

TABLE II: Parameter configuration for the physical links: GSL and ISL. Parameter | Symbol | NGEO to GS | ISL
---|---|---|---
Carrier frequency (GHz) | $f$ | $20$ | $26$
Bandwidth (MHz) | $B$ | $500$ | $500$
Transmission power (W) | $P_{t}$ | $10$ | $10$
Noise temperature (K) | $T_{N}$ | $150$ | $290$
Noise figure (dB) | $N_{f}$ | $1.2$ | $2$
Noise power (dBW) | $\sigma^{2}$ | $-117.77$ | $-114.99$
Parabolic antennas |  |  |
Antenna diameter (Tx – Rx) (m) | $D$ |  ($0.26$ – $0.33$) |  ($0.26$ – $0.26$)
Antenna gain (Tx – Rx) (dBi) | $G_{\text{max}}$ |  ($32.13$ – $34.20$) |  ($34.41$ – $34.41$)
Pointing loss (dB) | $L_{p}$ | $0.3$ | $0.3$
Antenna efficiency (–) | $\eta$ | $0.55$ | $0.55$

_FSO links_, on the other hand, face different challenges depending on where
they are implemented: GSL or ISL [22]. Hence, these challenges will be briefly
described in the following sections.

###  3-A Ground-to-satellite links (GSLs)

Communication between devices deployed at ground level and the satellites
takes place through GSLs. This can occur either by communicating the user
devices (e.g., IoT devices) directly or through gateways. The gateways can be
deployed at ground level, but also in the air, such as unmanned aerial
vehicles (UAVs) or high-altitude platforms (HAPs). For simplicity, we use the
term ground terminal to refer to any device deployed at ground level. The area
where ground-to-satellite communication is possible is called the _coverage
area_ and the time the satellite and a terrestrial terminal can communicate is
called the duration of the _satellite pass_.

In the following, we provide the expressions to calculate the coverage area
and, hence, to determine whether a ground terminal is able to communicate with
a specific satellite at a given time $t$.

The distance between an NGSO satellite and a device located on the Earth’s
surface within line-of-sight at time $t$ is determined by the altitude $h$ and
the elevation angle of the satellite w.r.t. the device $\varepsilon_{t}$.
Specifically, the distance of the GSL can be calculated from these parameters
using the Pythagorean theorem in a triangle with sides of length: a)
$R_{E}+h$; b) $R_{E}+d_{\text{GSL}}(h,\varepsilon_{t})\sin\varepsilon_{t}$;
and c) $d_{\text{GSL}}(h,\varepsilon_{t})\cos\varepsilon_{t}$ and then
applying the quadratic formula to obtain:

$d_{\text{GSL}}(h,\varepsilon_{t})=\sqrt{R_{E}^{2}\sin^{2}(\varepsilon_{t})+2R_{E}h+h^{2}}-R_{E}\sin(\varepsilon_{t}).$
(9)

A similar procedure can be applied to the case of devices above the Earth’s
surface (e.g., UAVs, HAPs, etc.), by simply substituting the length of side b)
of the triangle to be
$R_{E}+h_{u}+d_{\text{GSL}}(h,\varepsilon_{t})\sin\varepsilon_{t}$, where
$h_{u}$ is the altitude of the user above the sea level $R_{E}$. For notation
simplicity, the rest of the equations presented are for satellites deployed at
the Earth’s surface only. However, a the substitution described above can be
used to adapt the following equations to devices deployed above the Earth’s
surface.

Once $d_{\text{GSL}}(h,\varepsilon_{t})$ has been found, we calculate the
Earth central angle [14] $\alpha(h,\varepsilon_{t})$ as

$\alpha(h,\varepsilon_{t})=\arccos\left(\frac{(R_{E}+h)^{2}+R_{E}^{2}-d_{\text{GSL}}(h,\varepsilon_{t})^{2}}{2(R_{E}^{2}+hR_{E})}\right),$
(10)

which determines the shift in the position of the device w.r.t. the
satellite’s nadir point.

The coverage of an NGSO satellite is usually defined by a minimum elevation
angle $\varepsilon_{\text{min}}$. Hence, a device located at an elevation
angle $\varepsilon_{t}\geq\varepsilon_{\text{min}}$ is considered to be within
coverage of the satellite at time $t$. Consequently, the coverage area of a
satellite is a function of the altitude of deployment $h$ and of
$\varepsilon_{\text{min}}$. By using $h$ and $\varepsilon_{\text{min}}$ we
find the angle $\alpha(h,\varepsilon_{\text{min}})$, which allows us to
calculate the coverage area as

$A(h,\varepsilon_{\text{min}})=2\pi
R_{E}^{2}(1-\cos(\alpha(h,\varepsilon_{\text{min}})).$ (11)

Furthermore, by assuming a spherical model of the Earth, we can easily
determine whether a ground terminal $u$ is within coverage of a satellite $v$
at a given time $t$; this occurs when the distance $d_{t}(u,v)$ between them
is shorter than $d_{\text{GSL}}(h,\varepsilon_{\text{min}})$.

Next, we calculate the maximum duration of a satellite pass as a function of
$\alpha(h,\varepsilon_{\text{min}})$ and $T_{o}(h)$. For this, let $t=0$ be
the time when the ground terminal enters the coverage area of the satellite.
The satellite pass has maximum duration in the case where, at exactly at the
middle of the pass, the satellite is exactly located at the zenith point of
the ground terminal and, hence, there is an angle $\epsilon_{t}=90^{\circ}$
between the terminal and the satellite w.r.t. the Earth’s center. In such
case, the satellite travels $\alpha(h,\varepsilon_{\text{min}})/180$ degrees
of its orbit and hence, the satellite pass has a duration

$T_{\text{pass}}(h,\varepsilon_{\text{min}})\leq\frac{T_{o}(h)\alpha(h,\varepsilon_{\text{min}})}{\pi}.$
(12)

For any other cases where the ground terminal and the satellite are not
perfectly aligned, we define the angle

$\alpha_{\text{min}}=\min_{t}\alpha(h,\varepsilon_{t})\quad\text{s.t.
}t\in\left[0,T_{\text{pass}}(h,\varepsilon_{\text{min}})\right],$ (13)

which determines the misalignment of the ground station w.r.t. the orbital
plane of the satellite. Naturally, $\alpha_{\text{min}}=0$ for the perfect
alignment case.

The ground coverage of a NGSO satellite is illustrated in Fig. 3.1 and the
evolution of the achievable data rate along the pass for the altitudes of
deployment for Kepler and OneWeb. We considered a typical value for the
minimum elevation angle of $\varepsilon_{\text{min}}=30^{\circ}$. For devices
deployed above the Earth’s surface, this angle may be larger as their line-of-
sight (LoS) is less affected by obstacles. From these, it is easy to observe
that lower altitudes of deployment result in shorter propagation delays but
also in faster orbital velocities, shorter satellite passes, and smaller
coverage areas.

(a)

(b)

Figure 3.1: (a) Ground coverage of an NGSO satellite at altitude $h$ and (b)
the evolution of the achievable data rate along the pass.

Note that the coverage area simply defines the area where communication is
possible. However, the beams oftentimes present a beamwidth that is much
narrower than the coverage area. Therefore, these must be pointed in the
desired direction of communication [8]. Because of this, having more than one
satellite within communication range can be beneficial as the access load can
be shared among the satellites covering the same areas. Hence, it provides an
indicator of the scalability and capacity of the network.

Based on the coverage area and the geometry of a specific constellation, the
service availability and the average number of satellites within range can be
obtained. Fig. 3.2 shows the service availability and the mean number of
satellites within coverage for the Kepler and OneWeb constellations, along
with the Starlink orbital shell at $h=550$ km considering the requested
modification in the latest FCC filing, where
$\varepsilon_{\text{min}}=25^{\circ}$.

As it can be seen, the density of the Kepler constellation and the considered
$\varepsilon_{\text{min}}=30^{\circ}$ are insufficient to provide full service
availability near the Equator and it increases in near-polar areas. In
contrast, the service availability of the Starlink orbital shell is guaranteed
between latitudes $[-60^{\circ},60^{\circ}]$ and the OneWeb constellation
provides full service availability across the globe. Furthermore, it can be
seen in Fig. 3.2b that there is a significant number of OneWeb satellites
within coverage in the polar regions and a considerably lower number in
Equatorial regions. This is a distinctive characteristic of Walker star
constellations, as the distances between satellites is maximal near the
Equator. In contrast, the coverage of the Starlink orbital shell between the
latitudes $[-60^{\circ},60^{\circ}]$ is relatively balanced. To solve the
problem of lack of coverage in the polar regions, the Starlink constellation
is planned to incorporate satellites in polar orbits, as listed in Table I.

(a)

(b)

Figure 3.2: (a) Service availability: probability of being within the coverage
area of a satellite as a function of the latitude and (b) average number of
satellites within communication range at GSL.

There are many benefits of using RF over FSO for the GSL. For instance, RF
links present a wider beamwidth and, hence, a broader coverage. This
simplifies the beam switching and allows to provide coverage to several ground
terminals simultaneously. Additionally, the use of RF links allows to use the
same physical layer technologies as in terrestrial networks, which simplifies
the hardware design and enables the integration of satellites and terrestrial
networks through mature terrestrial technologies. For instance, the 3rd
Generation Partnership Project (3GPP) is aiming to integrate satellites and
cellular networks using NB-IoT and 5G New Radio (NR) cellular technologies [8,
1, 3].

In contrast, FSO GSL are mainly affected by the atmosphere. In particular, the
atmosphere absorbs and scatters the beam. These effects depend on different
factors such as temperature, humidity, and the concentration of aerosol
particles. Furthermore, the effects vary widely between uplink and downlink
communication, with the uplink signals being affected most due to the presence
of the atmosphere around the transmitter [22].

Yet another factor that impacts the GSL is the Doppler shift. The latter
varies significantly during a satellite pass as a result of the high orbital
velocity in combination with the varying relative position and speed with
respect to time. That is, the Doppler shift is different between the edge and
the center of the coverage, so this must be taken into account to select an
appropriate frequency band and during waveform and antenna design. If
information from the Global Navigation Satellite System (GNSS) is available,
the Doppler shift can be first pre-compensated at the satellite w.r.t. to a
reference point, by exploiting the predictable movement of the satellites.
Then, the residual frequency offsets are compensated at the ground terminals
using traditional Doppler compensation techniques as in terrestrial networks
[8].

###  3-B Inter-satellite links (ISLs)

Inter-satellite communication takes place in 1) the same orbital plane, 2)
different orbital planes of the same orbital shell, and 3) different orbital
altitudes. The dynamics in each of these are significantly different. However,
it is essential to establish these links in an efficient manner to maximize
the connectivity within the constellation.

Intra-plane ISLs connect satellites in the same orbital plane, usually, at
both sides of the roll axis, which is aligned with the velocity vector. In
particular, the relative distances between neighbouring satellites within the
orbital plane – the intra-plane distance – at an altitude can be considered a
constant

$d_{\text{intra}}(N_{\text{op}},h)=2(R_{E}+h)\sin\left(\frac{\pi}{N_{\text{op}}}\right).$
(14)

Hence, intra-plane ISLs are rather stable. Still, the orbital velocity of the
satellites must be considered. But this is easily, compensated by selecting an
appropriate point-ahead-angle (PAA): instead of pointing the antennas directly
towards the instantaneous position of the receiver at the same time instant
$t$, they are pointed to its position after considering the propagation time
$t+d_{\text{intra}}(h)/c$. Because of this, the antennas used for intra-plane
communication can be highly directive and the beams can be fixed to the
appropriate direction. Due to the use of narrow beams, FSO links present an
interesting option for intra-plane communication, as their power efficiency
may be greater than that of RF links [22]. Nevertheless, RF links with either
parabolic or patch antenna arrays are also an efficient candidate that
combines relatively high gains, cheap components, and low power requirements
when compared to FSO.

Inter-plane ISLs, on the other hand, connect satellites within the same
orbital shell but in different orbital planes. Usually, satellites will
possess either one or two transceivers for inter-plane communication, with
antennas pointing towards both sides of the pitch axis. Depending on the
constellation geometry, the distances and the velocity vectors between
satellites in different orbital planes may be either very similar or vary
widely. For instance, in Walker star geometries, the orbital planes are
separated by the angle $\pi/P$ and the shortest inter-plane distances occur at
the crossing points of the orbits near the poles. In contrast, the longest
inter-plane distances to the nearest neighbour occur for satellites near the
Equator.

Let $u$ and $v$ be a pair of satellites located in neighbouring orbital
planes, where $v$ is the closest inter-plane neighbour of $u$ at time $t$. For
simplicity, we assume the same altitude of deployment for both orbital planes
to be $h$. We denote the polar angle of satellites $u$ and $v$ as
$\theta^{(u)}_{t}$ and $\theta^{(v)}_{t}$, respectively. First, we recall that
the distance between two points $u$ and $v$ on a sphere of radius $R_{E}+h$
with azimuth angles $\phi_{u}$ and $\phi_{v}$ is given as

$\displaystyle
d_{uv}(t)=\sqrt{2\left(\mathrm{R_{E}}+h\right)^{2}\left(1-\cos\theta_{t}^{(u)}\cos\theta_{t}^{(v)}-\cos\left(\phi_{u}-\phi_{v}\right)\sin\theta_{t}^{(u)}\sin\theta_{t}^{(v)}\right)}.$
(15)

The latter can be used to approximate the distance between two satellites
adjacent orbital planes in a Walker star constellation assuming perfectly
polar orbits. For this, recall that orbital planes in Walker star
constellations are separated by $\pi/P$, hence, this is also the azimuth angle
between satellites in adjacent orbital planes.

If $u$ and $v$ are exactly at the Equator we have
$\theta^{(u)}_{t}=\theta^{(v)}_{t}=\pi/2$, and the maximum intra-plane
distance for the case where the satellites are perfectly aligned at all times
only depends on $P$ and $h$ as

$d_{\text{inter,
aligned}}^{*}(P)=\sqrt{2(R_{E}+h)^{2}\left(1-\cos\left(\frac{\pi}{P}\right)\right)}=2(R_{E}+h)\sin\left(\frac{\pi}{2P}\right).$
(16)

However, in a general case where the satellites $u$ and $v$ are not perfectly
aligned, we have that, if $v$ is the closest inter-plane neighbour to $u$,
then it follows that
$|\theta^{(v)}_{t}-\theta^{(u)}_{t}|\in\left[0,\pi/N_{\text{op}}\right]$.
Therefore, the maximum inter-plane distance occurs when
$\theta^{(u)}_{t}=\pi/2$ and $\theta^{(v)}_{t}=\pi/2\pm\pi/N_{\text{op}}$,
which can be approximated as

$\displaystyle d_{\text{inter}}^{*}(N_{\text{op}},P)$ $\displaystyle=$
$\displaystyle\max_{t}~{}d_{uv}(t)\quad\text{s.t.
}\theta^{(v)}_{t}\in\left[-\pi/N_{\text{op}},\pi/N_{\text{op}}\right]$
$\displaystyle\approx$
$\displaystyle\left(\mathrm{R_{E}}+h\right)\sqrt{2-2\cos\left(\frac{\pi}{P}\right)\sin\left(\frac{\pi}{2}\pm\frac{\pi}{N_{\text{op}}}\right)}.$
(17)

Hence, to ensure that satellites at the Equator can communicate with at least
one of their inter-plane neighbours, it is necessary to ensure that a non-zero
data rate can be achieved at this location. To illustrate this aspect in a
general case where the satellites are not perfectly aligned, let $\mathcal{R}$
be the set of available rates for communication, which depend on the available
modulation and coding schemes (MCSs) and where $0\notin\mathcal{R}$. Then, to
guarantee global ISL connectivity, it is required that any given satellite $u$
can select a rate $R\in\mathcal{R}$ that allows it to achieve reliable
communication with the nearest inter-plane neighbour $v$ at all times. Hence,
global ISL connectivity is achieved if

$\exists
R\in\mathcal{R}:0<R<B\log_{2}\left(1+\frac{P^{(u)}G^{(u,v)}_{t}G^{(v,u)}_{t}c^{2}}{\left(2\pi\,\sigma_{v}\,d^{*}_{\text{inter}}(N,P)f\right)^{2}}\right).$
(18)

As it can be seen, for a fixed set of rates $\mathcal{R}$, global ISL
connectivity can be achieved by either increasing the power and/or gains of
the antennas or by decreasing the maximum inter-plane distances. The latter is
usually achieved by either increasing the number of orbital planes $P$, but
also the number of satellites per orbital plane $N_{\text{op}}$. The
interested reader is referred to our previous work for a general formulation
that considers orbital separation and where the effect of increasing the
number of orbital planes $P$ is illustrated [13].

Yet another characteristic of Walker star constellations is that the velocity
vectors of the satellites in neighbouring orbital planes usually point in a
similar direction. As a result of this, the relative velocities between these
satellites are relatively low. However, there are specific pairs of orbital
planes where the velocity vectors point in a nearly opposite direction: the
so-called cross-seam ISLs. In the latter, the relative velocity of the
satellites increases to nearly $2v_{o}$ and varies along with time.

As a consequence of these great differences, the Doppler shift and the
_contact times_ in the inter-plane ISL— the period where two satellites can
communicate — also vary widely. Therefore, it is essential to consider the
movement of the satellites to select the inter-plane ISL that must be
established and to point the beams in the desired directions [13, 23]. Fig.
3.3 shows the Cumulative Distribution Function (CDF) of the achievable rate in
the inter-plane ISL with a specific link establishment mechanism. While the
mechanisms for ISL establishment and beam pointing are described in Section
4-B, Fig. 3.3 shows that the data rate achieved by inter-plane ISL in the
Starlink orbital shell is considerably larger than in the OneWeb and Kepler
constellations. The main reason for this is the higher density of satellites
caused by the low altitude of deployment, the use of Walker delta geometry,
and, naturally, the large number of satellites.

Figure 3.3: CDF of the achievable data rate per inter-plane ISL with parabolic
antennas.

Finally, inter-orbit ISLs connect satellites between different orbital
altitudes [22]. For example, they can connect LEO satellites in different
orbital shells or LEO satellites with MEO or even GEO satellites. A clear
example are the FSO links in the European Data Relay System (EDRS) and those
envisioned to connect the different orbital shells in the Starlink
constellation.

##  4 Functionalities and challenges

###  4-A Physical Layer

Pure LoS connections, high velocities, and large transmission distances
between satellites and ground terminals introduce some unique characteristics
to the physical layer design for NGSO constellations, both in the GSL and the
ISL.

In the GSL, it is particularly appealing to maintain the waveforms used in
terrestrial systems, for example, orthogonal frequency division multiplexing
(OFDM) in 5G NR and NB-IoT [24, 9]. This would allow full compatibility of
terrestrial devices and direct IoT-to-satellite access which, in turn, grants
maximum flexibility of deployment following the place-and-play vision.
However, the subcarrier spacing in terrestrial OFDM systems is narrow –
between $3.75$ kHz for NB-IoT and from $15$ to $240$ kHz for 5G NR [25]. Such
narrow subcarrier spacings make OFDM highly sensitive to Doppler shifts and
thus, accurate Doppler compensation is required to achieve reliable
communication. To overcome these limitations, several alternatives have been
studied intensively in the literature over the past few years, such as
Universal Filtered Multi-Carrier (UFMC), Generalised Frequency Division
Multiplexing (GFDM) and Filter Bank Multi-Carrier (FBMC) [26]. These waveforms
allow for higher robustness against Doppler shifts and flexible time-frequency
resource allocation in exchange for a higher equalisation complexity. However,
in case of severe Doppler shifts, Factor Graph based equalisation for FBMC
transmissions outperforms the OFDM system in terms of complexity and
performance [27].

Another challenge for keeping reliable GSL and also ISL is the implementation
of adaptive modulation and coding. In 3GPP networks, the users exchange
information about the channel quality with the BS [9], which adapts the MCS
based on the error rate. Due to the altitude of deployment, the round trip
time between the ground terminals and a satellite is usually greater than $4$
ms. Hence, such a feedback link would introduce a significant delay. Instead,
the fully predictable movement of the satellite along the pass, in combination
with free-space propagation and the minor impact of atmospheric conditions in
RF links, can be exploited to achieve efficient adaptive modulation and coding
with minimal signaling.

Furthermore, while multiple-input multiple-output (MIMO) techniques have
experienced a dramatic surge of advancements in terrestrial networks,
achieving efficient MIMO communication with NGSO satellites is more
complicated. In particular, due to the long distances between transmitter and
receiver, exploiting the full MIMO gain requires a large array aperture, that
is, large distances between transmit and/or receive antennas, that are not
feasible in individual satellites [28]. Nevertheless, this separation can be
realised by using a group of satellites flying in close formation, usually
called a _satellite swarm_. Specifically, by placing an antenna at each of the
satellites in the swarm, these can operate as distributed MIMO arrays. Doing
so allows to form extremely narrow beams for GSL, which leads to better
spatial separation via coordinated beamforming and, eventually, to higher
spectral efficiency when serving different ground terminals located
geographically close to each other [29]. An example of the achievable gain of
distributed MIMO in a satellite swarm, with $N_{S}$ satellites, is shown in
Fig. 4.1 for $N_{r}=1$ and $N_{r}=6$ receiving antennas. The overall transmit
power as well as the antenna gains are normalised such that they are the same
in all scenarios, i.e., the transmit power and antenna gain per satellite are
$10/N_{S}$ W and $32.13\,\text{dBi}-10\log_{10}(N_{S})$, respectively, and the
receive antenna gain is $34.20\,\text{dBi}-10\log_{10}(N_{r})$. Fig. 4.1 shows
that, despite maintaining the total transmitted power in all cases, the use of
distributed MIMO increases the data rate by around $33$% with multiple
receiving antennas. However, with a single receiving antenna, no MIMO gains
can be achieved and resulting in even lower rates because the transmitted
signals superimpose constructively or destructively with same probability,
reducing the overall received signal energy.

(a)

(b)

Figure 4.1: Data rate for satellite swarms as a function of the inter-
satellite distance for (a) one and (b) six receiving antennas.

Beam pointing/steering is another essential functionality in NGSO
constellations due to the constant and rapid movement of the satellites.
Mechanical steering of RF antennas becomes problematic as beams become
narrower, which is essential to attain a high SNR. In addition, the ultra-
narrow beams present in FSO require high pointing precision and fast
repointing to maintain adequate link quality.

A different approach made possible by recent advances in antenna technology is
the use of phased antenna arrays, even in small satellites. In these, the
antenna elements are separated by a small distance $d_{e}$, which is
proportional to the wavelength $\lambda$, and can be used to produce highly
directed beams. This enables efficient interference management due to
beamforming, which exploits the spatial domain via Spatial Division Multiple
Access (SDMA) or Rate-Splitting Multiple Access (RSMA), and thus, allow for an
efficient use of the bandwidth. Furthermore, these beams can be steered
electronically by manipulating the input signals to the antenna elements
through variable phase shifters.

Let us consider a satellite $u$ equipped with a $K\times K$ antenna array that
attempts to steer the beam towards satellite $v$ at a given time $t$. To do
so, it first needs to calculate the $K$-dimensional steering vectors for the
azimuth angle $\phi_{t}^{(u,v)}$ as

$\displaystyle\mathbf{a}^{(u,v)}_{t,\text{az}}=\left[1,e^{\frac{-j2\pi
d_{e}}{\lambda}\sin\left(\phi_{t}^{(u,v)}\right)},\dotsc,e^{\frac{-j2\pi
d_{e}(K-1)}{\lambda}\sin\left(\phi_{t}^{(u,v)}\right)}\right]^{\intercal}$
(19)

and for the polar angle $\Theta_{t}^{(u,v)}$ as

$\displaystyle\mathbf{a}^{(u,v)}_{t,\text{pol}}\\!=\\!\left[1,e^{\frac{-j2\pi
d_{e}}{\lambda}\cos\left(\Theta_{t}^{(u,v)}\right)}\\!,\dotsc,e^{\frac{-j2\pi
d_{e}(K-1)}{\lambda}\cos\left(\Theta_{t}^{(u,v)}\right)}\right]^{\intercal}\\!\\!.$
(20)

Then, it calculates the overall steering vector
$\mathbf{a}_{t}^{(u,v)}=\mathbf{a}^{(u,v)}_{t,\text{pol}}\otimes\mathbf{a}^{(u,v)}_{t,\text{az}}\,.$
This approach is often called digital beam steering and it is attractive to
combat the fast orbital velocities of the NGSO satellites due to its precision
and switching velocity [5]. Nevertheless, it has the main downside that the
implementation of the variable phase shifters adds a considerable amount of
complexity to the hardware, which might be restrictive for nano-satellites and
CubeSats.

Butler matrix beamforming networks offer a simpler mechanism to point the
beams and, hence, have gained relevance in terrestrial communications [30,
31]. These are cost-efficient and low-complexity beam switching networks that
produce a series of beams in pre-defined directions [32, 33]. In contrast to
digital beam steering, the beams in a Butler matrix are switched by simply
feeding one or more of the fixed phase shifters (input ports), which offers an
interesting trade-off between performance, cost, and complexity of operation
and implementation that is especially attractive for CubeSats, which
oftentimes rely on small and simple dipole antennas with low directivity.

In particular, the steering vector in the polar angle of a Butler matrix is
fixed to a specific direction $\theta$

$\mathbf{b}_{\text{pol}}=\frac{1}{\sqrt{K}}\left[1,e^{\frac{-j2\pi
d_{e}}{\lambda}\cos\left(\theta\right)},\dotsc,e^{\frac{-j2\pi
d_{e}(K-1)}{\lambda}\cos\left(\theta\right)}\right]^{\intercal},$ (21)

whereas the steering vector of the $k$-th beam in the azimuth angle is set to

$\mathbf{b}_{k,\text{az}}=\frac{1}{\sqrt{K}}\left[1,e^{\frac{-j\pi(2k-1)}{K}},\dotsc,e^{-j\frac{\pi(2k-1)(K-1)}{K}}\right]^{\intercal}\,.$
(22)

The overall steering vector for beam $k$ is
$\mathbf{b}_{k}=\mathbf{b}_{\text{pol}}\otimes\mathbf{b}_{k,\text{az}}$. Fig.
4.2 illustrates the gain of $K=4$ beams in a Butler matrix with $4\times 4$
antenna elements.

Figure 4.2: Gains for the beams in a $4\times 4$ antenna array with Butler
matrix.

Finally, while achieving direct IoT communication with NGSO is feasible with
LPWAN technologies, the use of gateways is often beneficial. These gateways
may incorporate traditional dish antennas or phased antenna arrays that gather
the transmissions from IoT devices with non-directive antennas and, then,
transmit to the satellites with highly directive antennas. However, another
option made possible by the predictable movement of the satellites is to
deploy intelligent reflecting surfacess (IRSs). These low-complexity elements
that modify the characteristics of the incident signals and, hence, can help
direct the signals towards the satellites [34].

###  4-B Frequent link establishment and adaptation

Due to the movement of the satellites, the physical links must be frequently
re-established and adapted. This includes selecting the pairs of satellites to
establish the ISLs, beam pointing/steering or switching for the Butler matrix
case, and rate adaptation. Since the movement of the constellation is fully
predictable, these problems can be solved in advance with a specific
optimisation objective in mind. These objectives depend on the target
service(s) and can be, as listed in Section 1, to maximize the _transport
capacity_ [35, 36] of the constellation or to minimize the E2E latency for a
set of specific paths.

Some constellations designs are fully symmetric, with each and every one the
orbital planes containing the same number of satellites and these being
deployed at the exact same altitude. In these cases, the orbital period
$T_{o}$ of all the satellites is exactly the same and, hence, these will all
be periodically at the exact same position. In these cases, the optimal
configuration of the links can be obtained for several instants within the
period $T_{o}$ and applied periodically.

However, asymmetries in the constellation are usually present, either 1) to
enhance the sustainability of the constellation by considering orbital
separation as in OneWeb [18], 2) to fulfill certain coverage and service
availability targets by incorporating several orbital shells as in Starlink,
or 3) to provide service during the initial phases of deployment of the
constellation. In these cases, fixed solutions cannot be used and the links
must be established on the fly.

An essential aspect for link establishment and maintenance is to implement an
adequate beam steering technology as discussed in the previous section.
Furthermore, the MCS and transmit power may be adapted to maximize throughput
and reliability while minimizing potential interference. Naturally, the
characteristics of the antennas and beams must be considered during link
establishment [23].

An option to re-establish the links is to treat the link establishment as a
one-to-one matching problem in a dynamic weighted graph
$\mathcal{G}_{t}=\left(\mathcal{V},\mathcal{E}_{t}\right)$, where the
satellite antennas, transceivers, or even beams (for the case of beam
selection) form a multi-partite vertex set $\mathcal{V}$ and the weighted edge
set at time $t$, denoted as $\mathcal{E}_{t}$ are the feasible ISLs with non-
zero rates. Then, the matching at a time $\mathcal{M}_{t}$ is the set of pairs
of antennas/transceivers/beams and the rates for communication. In this case,
the matching $\mathcal{M}_{t}$ can be calculated periodically, once every
$\Delta t$ seconds, in a centralised entity with full knowledge of the
constellation parameters and dynamics. Then, the solution for the matching for
the satellite positions at time $t$ must be propagated through the
constellation before this time. With the full predictability of the movement
of the constellation, the solution can be calculated sufficiently in advance
and, hence, the latency of communicating it to the satellites is irrelevant.
Hence, this approach can lead to near-optimal or optimal solutions at the
expense of injecting periodic traffic into the network to communicate the
solution to all the satellites. An important aspect of the inter-plane ISL
link establishment is that the graph $\mathcal{G}$ that represents a single
orbital shell is multi-partite, with each subset representing an orbital plane
and, hence, traditional algorithms such as the Hungarian algorithm cannot be
used and other solutions are needed.

On the other hand, localised decisions may be implemented, for example using
distributed algorithms for the matching. An example of these is the Deferred
Acceptance algorithm [37], where the individual agents maintain and inform
their preferences to the neighbourhood and the matching is solved in parallel,
after a few iterations. While more research is needed to determine the
performance of distributed vs. centralised matching solutions, distributed
algorithms are required 1) to establish the links during the deployment phase
before the constellation is fully operative, and 2) in case the connection
with the centralised entity is lost.

To solve the inter-plane ISL establishment problem, we have explored the use
of greedy matching algorithms with 2) ideal beam pointing (i.e., at each time
$t$) and resource allocation and 2) with periodic repointing via digital
beamforming and beam switching via Butler matrix beamforming networks with
period $\Delta t$ [13], [23]. Algorithm 1 illustrates the steps of a general
greedy matching algorithm for link establishment. The latter can be extended
to include orthogonal resource allocation (e.g., frequency sub-bands) to
minimize interference [19].

Algorithm 1 Greedy satellite matching with multiple beams.

0: Set of feasible weighted edges $\mathcal{E}_{t}$ and $\mathcal{E}_{t+\Delta
t}$ and the initial state of the matching $\mathcal{M}_{t}$

0: Antenna configuration

1: Initialise indicator variables

2: while More edges can be matched do

3: Select the edge with maximum weight

4: if the selected vertices are not in $\mathcal{M}_{t}$ then

5: Add the vertices to the matching $\mathcal{M}_{t}$

6: Update the indicator variables

7: Remove all adjacent edges to the selected vertices from $\mathcal{E}_{t}$
and $\mathcal{E}_{t+\Delta t}$

8: Update the interference and weights to all edges in $\mathcal{M}_{t}$,
$\mathcal{E}_{t}$ and $\mathcal{E}_{t+\Delta t}$

9: end if

10: end while

Note that Algorithm 1 attempts to maximize the sum of weights in the matching.
Throughout our previous work, we have defined the weights to be the achievable
rate for communication at the ISLs in $\mathcal{E}_{t}$. Following this
approach, Fig. 4.3a illustrates the increase of the rates per ISL as a
function of the number of elements $K$ in a Butler matrix beamforming network
for the Kepler constellation. As it can be seen in Fig. 4.3a increasing the
number of elements $K$ greatly improves the data rates, however, this also
increases the number of beams that must be considered by the matching
algorithm and, hence, increases the running time of the algorithm.

Furthermore, Fig 4.3b shows the effect of the re-establishment period $\Delta
t$ on the average data rate per inter-plane ISL with digital beamforming; the
data rate achieved with ideal pointing (i.e., with $\Delta t=0$ and parabolic
antennas is included as a reference. It can be seen that increasing the
frequency of link re-establishment and adaptation increases the data rates and
phased antenna arrays of $K=64$ can be used to achieve similar rates as with
greatly directional parabolic antennas, even with ideal pointing. However, the
re-establishment period cannot be reduced arbitrarily as this can cause
problems, for example, for routing algorithms, due to the frequent changes of
the network topology.

Throughout our analyses, we have observed that Butler matrix networks with
relatively low dimensions $K$ are an attractive option for the inter-plane
link establishment in resource-constrained satellites (i.e., CubeSats and
small-sats). However, if large antenna arrays and variable phase shifters can
be implemented on the satellites, beamforming offer gains in the data rates
that are greater than $200$% and, hence, these should be preferred.

(a)

(b)

Figure 4.3: (a) CDF of the rates per inter-plane ISL with Butler matrix arrays
and (b) average rates per inter-plane ISL with parabolic antennas with ideal
pointing and for digital beam forming for different link re-establishment
periods $\Delta t$.

It is important to mention that rate maximisation does not directly increases
the _transport capacity_ f the network, which is a difficult measure to
define. Usually, specific source-destination pairs are defined and the
transport capacity is the maximum amount of data (i.e., flow) that can be
transmitted between them [38]. In these cases, calculating the transport
capacity usually involves assigning flow to all possible paths from the source
to the destination, as in the Edmons-Karp algorithm, which has been used to
calculate the capacity of constellations with multiple orbital shells [36].
However, this is complicated in dynamic and large networks, so upper bounds
based on selecting cuts from the network graph have been used [35]. Yet
another hindrance of using the Edmonds-Karp algorithm is that is assumes that
ideal mechanisms to redistribute the traffic flows are in place. Instead, in a
network with multiple source-destination pairs, the capacity of some links is
likely to be shared among them and the number of alternate paths may be
limited depending due to the implemented routing, load balancing, and
congestion control mechanisms. Furthermore, the distribution of the traffic
among the different paths will usually be imbalanced. Therefore, defining the
transport capacity of a satellite constellation is complicated.

A simple scenario where it is possible to calculate the maximum [G2G] traffic
that can be generated from each ground stations (GSs) is where these have
equal traffic characteristics and where unipath source routing is used [39].
In this scenario, we can define $\mathcal{P}_{t}$ as the set of possible paths
at time $t$. A path $\mathbf{p}\in\mathcal{P}_{t}$ is an ordered set of edges,
denoted as $\mathcal{E}(\mathbf{p})=\left(e_{1},e_{2},e_{3},\dotsc\right)$.
Here, the load $\lambda$ of each of the $N_{\text{GS}}$ GSs is distributed
evenly to the rest of the $N_{\text{GS}}-1$ GSs, using the paths in
$\mathcal{P}_{t}$. Hence, the load assigned to each path
$\mathbf{p}\in\mathcal{P}_{t}$ is

$\lambda_{\mathbf{p}}=\frac{2\lambda}{N_{\text{GS}}-1}.$ (23)

The max-flow min-cut theorem states that the maximum flow that can be
transmitted through a path is determined by the link (i.e., edge) with minimum
capacity (i.e., throughput) [38]. Hence, at a time $t$ we have

$\sum_{\mathbf{p}\in\mathcal{P}_{t}}~{}\sum_{uv\in\mathcal{E}_{t}(\mathbf{p})}\lambda_{\mathbf{p}}=N_{\mathbf{p}}(uv)\lambda_{\mathbf{p}}\leq
R_{t}(u,v),\quad\forall u,v\in\mathcal{V},$ (24)

where $N_{\mathbf{p}}(uv)$ is the number of paths in $\mathcal{P}_{t}$ that
contain the edge $uv$. Naturally, $N_{\mathbf{p}}(uv)$ depends on the routing
metric. Building on this, it is possible to calculate the maximum load per GS
at time $t$ as

$\lambda_{t}^{*}=\min_{uv\in\mathcal{E}_{t}}\frac{R_{t}(u,v)\left(N_{\text{GS}}-1\right)}{N_{\mathbf{p}}(uv)}.$
(25)

###  4-C Routing, load balancing and congestion control

A general goal to achieve in the design of higher layer algorithms is to
account for both the traffic characteristics (load, queues, and QoS/QoE
requirements) and the instantaneous state of the links/paths. However, the
time-variations of the traffic and the channel are different in terrestrial
and satellite networks and, e.g., the conventional TCP/IP stack is ineffective
against the long delays, packet losses and intermittent connectivity that
characterizes NGSO communications. Therefore, specific networking solutions
are required.

A routing algorithm is a collaborative process for deciding, in every
intermediate node, the directions to reach the destination as soon as
possible.222In NGSO constellations and other satellite systems, a second
option for delay-tolerant applications is the store-carry-forward strategy
where nodes can temporarily store and carry in-transit data until a suitable
link becomes available, e.g., until the next pass with a ground station. This
routing problem presents the following unique characteristics in NGSO
constellations:

  * •

The topology is highly dynamic, with frequent handovers in the links between
ground and NGSO, and between NGSOs in different orbital planes (inter-plane
ISL).

  * •

The load from the ground terminals (ground stations and users) is imbalanced,
with 1) some satellites serving, e.g., deserted/ocean areas while other nodes
pass above densely populated regions and 2) some source-destination pairs
experiencing more intense data flows than others.

  * •

The need to have a reliable and resilient routing solution, which implies that
the satellite segment must possess a sufficient degree of autonomy to cope
with, e.g., queueing delays or local link or satellite failures and find
alternative routes at each time instant. However, this must be achieved while
exchanging minimal feedback and routing information to limit the signaling
overhead.

A good overview of routing protocols for satellite can be found in [40]. Most
previous works have oversimplified the ground/space segments geometry and the
ISL connectivity to focus on other challenges like the QoS. One prominent
exception is [7], although the study is for a specific commercial
constellations. [39] takes a more general approach and focuses on two
distinctive elements to the routing problem in a NGSO constellation. First,
the propagation time has a great impact on the overall latency, contrary to
terrestrial mesh networks. Second, the location of the ground stations greatly
impacts the traffic load injected to the constellation and the geographic
locations where the traffic is injected. As in Section 4-B, the space and
ground infrastructure at a given time $t$ is modeled as a dynamic weighted
undirected graph $\mathcal{G}_{t}=\left(\mathcal{V},\mathcal{E}_{t}\right)$.
However, by adding the GSs, the vertex set is now defined as
$\mathcal{V}=\mathcal{U}\bigcup_{a\in\mathcal{P}}\mathcal{V}_{a}$, where
$\mathcal{U}$ is the set of ground stations and $\mathcal{V}_{a}$ is the set
of satellites deployed in orbital plane $a$, and
$\mathcal{P}=\\{1,2,\dotsc,P\\}$ is the set of orbital planes. The edge set
$\mathcal{E}_{t}$ represents the wireless links available for communication.
For instance, the satellites might deploy four ISLs at all times: two intra-
plane ISLs and two inter-plane ISLs. In this case, the intra-plane ISLs within
an orbital plane $a$ constitute the fixed set of edges
$\mathcal{E}^{(a)}=\left\\{uv:u,v\in\mathcal{V}_{a}\right\\}\subset\mathcal{E}_{t}$.
On the other hand, the inter-plane ISLs between orbital plane $a$ and orbital
plane $b$ constitute the set of edges
$\mathcal{E}^{\text{inter}}_{t}=\left\\{uv:u\in\mathcal{V}_{a},v\in\mathcal{V}_{b},a\neq
b\right\\}\subset\mathcal{E}_{t}$; as mentioned in Section 4-B, these must be
frequently re-established due to the movement of the satellites. Furthermore,
the ground stations maintain one GSL with their closest satellite at all
times. These GSLs constitute the set of edges

$\mathcal{E}^{G}_{t}=\left\\{uv:u\in\mathcal{U},v\in\mathcal{V}_{a},a\in\mathcal{P}\right\\}.$

Finally, we define the edge set as

$\mathcal{E}_{t}=\mathcal{E}^{G}_{t}\cup\mathcal{E}^{\text{inter}}_{t}\bigcup_{a\in\mathcal{P}}\mathcal{E}^{a}_{t}.$

The route of a single packet transmitted at time $t$ is then a weighted path
$\mathbf{p}$ in $\mathcal{G}_{t}=(\mathcal{V},\mathcal{E}_{t})$ with edge set
$\mathcal{E}(\mathbf{p})$. The weights $w(e)$ for all $e\in\mathcal{E}_{t}$
are defined by the routing metric to account to, e.g., the path loss and/or
the communication latency. Specifically, capturing the non-linearity of the
path loss in the ISL will favour paths with high-data rates and consequently
reduce the waiting times in the buffers. Rather than complex feedback
mechanisms to collect up-to-date network status information, this simpler
approach has proven to provide a good trade-off between complexity and
performance.

The degree of integration of the NGSO constellation with the terrestrial
infrastructure has also an effect on the traffic load. Not in vain, a
prominent application of 5G satellite communications is to offload the
terrestrial networks in congested urban areas, either with direct satellite
access or through a gateway [10]. In both cases, it will further exacerbate
the load imbalance. A subsidiary case is the use of the constellation as a
backhaul that transparently carries the payload between the two communication
extremes. This is typically used to connect isolated base stations to the core
network.

Regarding resilience, the classical approach to space routing is to centrally
compute all the paths in a location register, and then broadcast the
information to all the satellites. Satellites forward the packets according to
the on-board routing tables, which are configured based on the central
computations. In the case of NGSO, the central location register can be a
terrestrial station or a GEO satellite. In any case, this approach scales
poorly due to the highly dynamic topology, with frequent handover events
between nodes and terminals causing significant signaling overhead. Moreover,
the current status of the satellites (load, buffers, batteries) should be
included in the decision, but this requires an enormous amount of feedback
from each node in the graph to the central location register. The alternative
is to move towards more distributed solutions. From semi-distributed to fully
autonomous algorithms, the idea is that each satellite decides the next hop
for each received packet, taking into consideration all the available
information, including the prior knowledge (past) and the predicted paths
(future).

As in terrestrial networks, the space network might be shared by several
services with heterogeneous requirements. For example, some broadband users
require high rates, as provided by the GEO segment, whereas IoT devices are
sensitive to delays or freshness of the information [10], better provided by
the NGSO segment, or some services demand extra satellite computation. In
general, there are multiple paths for most source-destination pairs, and this
diversity should be exploited to meet the heterogeneity of requirements.

The example in Figure 4.4 illustrates the performance of different routing
metrics, taking the latency as the KPI of interest. Three different
configurations are considered: (a) the Kepler constellation with the
communication parameters listed in Table II; (b) the Kepler constellation with
transmission power $P_{t}=1$ W; and (c) a Walker-star constellation with $P=5$
orbital planes at height $h=600$ km and $N_{\text{op}}=40$ satellites per
orbital plane and $P_{t}=1$ W. The time-varying data rate follows the channel
variations. The ground segment consists of $N_{\text{GS}}=23$ GSs placed
accordingly to the KSAT ground station
service333https://www.ksat.no/services/ground-station-services/. The details
of the simulations can be found in [39].

The compared metrics are: (1) a classical hop-count approach that merely
minimizes the number of hops to reach the destination; (2) a path loss metric
that considers the non-linearity of the ISL; (3) a latency metric that takes
into account the propagation and transmission times but skips the need for a
feedback channel by having a statistical model of the queueing times. As
expected, the latency metric effectively selects the routes with the shortest
propagation and transmission times in all three cases. However, the waiting
times are shorter with the pathloss metric. This is because the pathloss
metric emphasises the selection of high data rate links over short routes,
which support greatest traffic load. As a consequence, the pathloss metric
leads to the lowest overall latency with configuration (c) and to a closely
similar latency to the latency metric in the other two cases. The reason for
this is that the configuration with $P=5$ and $N_{\text{op}}=40$ has a greater
density of satellites along the orbital planes, which leads to a much greater
data rate at the intra-plane when compared to the inter-plane ISLs. These
links are prioritized by the pathloss metric. Furthermore, it can be observed
that, while the propagation delay changes slightly, the choice of
communication and constellation parameters greatly affects the transmission
and waiting times. Finally, Figure 4.4 illustrates the need for an advanced
routing metric: even when the number of satellites with configuration (c) is
greater than that with the other two configurations, the latency achieved by
the hop-count metric is greater for this case.

(a)

(b)

(c)

Figure 4.4: Average routing latency per packet due to propagation,
transmission, and waiting times for three topology-aware metrics with: (a)
Kepler constellation; (b) Kepler constellation with $P_{t}=1$ W; and (c)
constellation with $P=5$, $N_{\text{op}}=40$, and $P_{t}=1$ W.

A complementary function to routing is congestion control, which aims at
ensuring high bandwidth utilisation while avoiding network congestion. This is
done at the transport layer by regulating the rate at which traffic sources
inject packets into the network. However, the standard TCP assumes that the
bottleneck link will stay the same over time and that changes in its capacity
are erratic. This is not true in the satellite network case, in which the
capacity of a link is predictable and therefore a location-aware congestion
control mechanism can improve the throughput and latency. In this direction,
several works have proposed variations of TCP for space networks. Although the
topic is definitely not new [41], the initial works were targeting space
networks very different from NGSO constellations, where delay- and disruption-
tolerant satellite applications and large distances Earth-GSO were the norm.
For example, the Space Communications Protocol Specification-Transport
Protocol (SCPS-TP), mainly developed by NASA and the US Department of Defence,
has a selective negative acknowledgement to accommodate asymmetric channels
and explicit congestion notification [41]. Another option that does not modify
the underlying protocol is the Delay and Disruption Tolerant Networking (DTN)
architecture, which provides long-term information storage on intermediate
nodes to cope with disrupted or intermittent links [42]. A more recent
alternative is the use of QUIC (Quick UDP Internet Connections), the general
purpose transport protocol defined by Google [43] to combine the advantages of
connected-oriented TCP and low-latency UDP. NGSO networks can benefit from
QUIC [44] when there is a high round-trip time (RTT) and a poor bandwidth.
Moreover, QUIC introduces a connection ID instead of IP addresses as
identification which inherently avoids re-connections with frequently
changeable topological space networks.

##  5 Conclusions

In this chapter, we described relevant aspects of NGSO constellation design to
achieve global connectivity. That is, to provide global service availability
to ground terminals but also to ensure inter-satellite connectivity can be
achieved along the constellation. We emphasized that the constellation
geometry, the altitude of deployment, and the density of satellites have a
major impact on these and other relevant KPIs and compared the performance of
three commercial designs: Kepler, OneWeb, and the Starlink orbital shell at
$550$ km. We observed that, while the Starlink orbital shell has a greater
number of satellites than the other two constellations, it still requires an
additional orbital shell with nearly-polar orbital planes to provide
connectivity near polar regions. On the other hand, around $45$ satellites
from the OneWeb constellation are simultaneously within communication range in
the near-polar regions, which may lead to waste of communication resources.
Finally, the Kepler constellation may suffer from coverage holes near the
Equator where, on average, less than one satellite is within communication
range from the Earth’s surface. To provide ubiquitous global coverage, a
constellation similar to Kepler but with slightly larger number of orbital
planes and satellites would be sufficient. Still, NGSO constellations that aim
to provide broadband services would benefit from further increasing the
density of deployment, which would lead to greater data rates both in the
inter- and intra-plane RF ISLs.

Besides the impact of the main parameters for constellation design, we
elaborated on the major challenges and technologies to achieve global
connectivity at the physical layer, for link establishment, and routing. These
arise from the distinctive characteristics of NGSO constellations, which are
greatly dynamic, yet fully predictable large-scale infrastructures.

## Acknowledgements

This work is supported in part by the German Federal Ministry of Education and
Research (BMBF) within the project Open6GHub under grant number 16KISK016 and
by the German Research Foundation (DFG) under grant EXC 2077 (University
Allowance).

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