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Large - Scale LEO Satellite Constellation to Ground
QKD links: Feasibility Analysis
Argiris Ntanos1,2, Nikolaos K. Lyras*1,2, Saif Anwar3, Obada Alia3, Dimitris Zavitsanos1,2, Giannis Giannoulis1,2, Athanasios
D. Panagopoulos1,2, George Kanellos3, Hercules Avramopoulos1,2
1School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece
2Institute of Communication and Computer Systems, Athens, Greece
3High Performance Network Group, School of Computer Science, Electrical & Electronic Engineering and Engineering
Maths (SCEEM), University of Bristol, UK
email: ntanosargiris@mail.ntua.gr, lyrasnikos@mail.ntua.gr*, Saif.Anwar@warwick.ac.uk, obada.alia@bristol.ac.uk,
dimizavitsanos@mail.ntua.gr, jgiannou@mail.ntua.gr, thpanag@ece.ntua.gr, gt.kanellos@bristol.ac.uk, hav@mail.ntua.gr
Abstract— As Quantum Key Distribution (QKD) seems to turn
towards satellite communication infrastructure to interconnect
distant nodes aiming to a global quantum secured network, the
number of assisting satellites is expected to increase. In this work, a
feasibility analysis of a large-scale Low Earth Orbit (LEO) satellite
constellation supporting LEO to ground QKD links is presented. A
software tool to simulate the physical properties of a large-scale
satellite constellation and a link budget calculator tailored for LEO
satellite to ground QKD links have been developed. A large-scale
LEO satellite constellation with 100 satellites orbiting at 550km
altitude with 53deg inclination angle in ten different orbital planes
(10 satellites per orbital plane) has been simulated and subsatellite
points for 1 year have been obtained. Assuming, an optical ground
station network consisting of nine different optical ground stations
located in observatories across Europe, the performance of this
large-scale constellation is evaluated in terms of availability and
Secure Key Rate (SKR) employing the prepare and measure Decoy-
State BB84 QKD protocol, during nighttime, under different
atmospheric conditions including cloud coverage and turbulence
effects among others, while two different wavelengths (i.e., 800nm
and 1550nm) are examined. For each Optical Ground Station (OGS)
location, Gbits of distilled keys per year per ground station and key
rates up to Kbps are reported.
Keywords— Quantum Key Distribution (QKD), Low Earth
Orbit (LEO), Satellite Constellation, Decoy-BB84, Annual cloud
statistics, Turbulence
I. INTRODUCTION
Quantum Key Distribution (QKD), as a method of securely
generating and distributing cryptographic keys between two
nodes, is lately gaining a lot of interest. Discrete Variable
(DV-) QKD exploits the quantum nature of single photons
and specifically the fact that single photon states cannot be
copied [1], therefore the presence of an eavesdropper would
be inevitably detected, as was described by the first QKD
protocol by Bennett and Brassard, known as the BB84
protocol [2]. In contrast to classical public-key algorithms,
which are vulnerable to Shor’s algorithm [3], QKD provides
in principle security against quantum attacks.
During the last few decades, many successful QKD
experiments have been demonstrated. Both Secure Key Rate
(SKR) and distance reach of QKD links have been
tremendously improved not only in fiber [4] but also in free
space transmission [5], whereas experiments up to a network
scale have been demonstrated [6]. Towards the long-distance
QKD links, the exponential loss of optical fiber sets a
fundamental limit for the repeaterless links. Record
experiments in the range of hundreds of kilometers have been
reported using ultra-low loss optical fibers [4][7]. Exploiting
the quadratic loss of free-space and using the appropriate
telescope sizes, orders of magnitudes longer QKD links can
be realized with the equivalent attenuation loss [8].
Towards global scale quantum secured networks,
satellite communication infrastructure can play a vital role
towards successfully supporting the terrestrial Quantum
Communication Infrastructure (QCI) by delivering quantum
keys to optical ground terminals. To this end, several studies
regarding the applicability and feasibility of the QKD over
satellite optical links and especially Low Earth Orbit (LEO)
satellite-to-ground links under different atmospheric
conditions have been published [9]-[13], while some initial
experimental demonstrations have already been successfully
performed [14][15]. In general, satellite QKD overall
progress is summarized in [16]. In the majority of these
studies, either a single LEO satellite or a small size LEO
satellite constellation is investigated, resulting in reduced
visibility of order of a few minutes during each day for a
given area. To increase the satellite-to-ground link
availability and provide a global connectivity large LEO
satellite constellations can be employed.
In this paper, a feasibility analysis of a large-scale LEO
satellite constellation supporting LEO satellite-to-ground
links employing the prepare and measure Decoy-State BB84
QKD protocol is performed. A software tool to simulate the
physical properties of a large-scale satellite constellation,
such as the orbital inclination, position and the altitude of
satellites has been developed. In total, a constellation
consisting of one hundred satellites orbiting at an altitude of
550km in ten equidistant orbital planes has been simulated.
To continue, the atmospheric channel has been modeled
under the effect of turbulence, during nighttime. The cloud
influence has been integrated by calculating the Cloud Free
Line of Sight (CFLOS) probability, by employing annual
cloud coverage statistics of each Optical Ground Station
(OGS) [17][18]. Finally, both wavelengths of 1550nm and
800nm are examined for the quantum transmission. As OGS
terminals, several observatories located across Europe in
various altitudes and equipped with different receiver
telescope apertures sizes have been investigated. The results
are provided in terms of yearly distilled key per ground
station whereas SKRs of up to kbps are reported.
This paper is organized as follows. In Section II,
we present the VPython software tool that simulates the
satellite constellation’s physical structure. Section III
provides the overall system architecture as well as the
assumptions for the BB84 Decoy-State QKD protocol. In
Section IV the modeling of the satellite-to-ground link is
provided. Section V provides the selection and optimization
of the setup components as well the results of this study.
Finally, Section VI concludes this work.
II. CONSTELLATION SIMULATION TOOL
A simulation tool has been developed to model the physical
structure of a satellite network constellation with intersatellite
links and its temporal evolution. The constellation parameters
that can be adjusted are the number and inclination of the
orbital planes, the number of satellites per orbital plane, the
altitude and the mass of each satellite and finally the phase
offset.
Phase offset is defined as a value between 0 and 1 which
indicates the timing difference for when satellites in
consecutive planes cross the equator. If satellites in directly
opposing planes were to have the same initial positions, they
would collide at the equator.
The constellation structure is represented in the 3-
Dimensional space and geographical space. The center of the
Earth is denoted as the origin in the 3D space and the orbital
motion of individual satellites are calculated using the
position and physical properties of each satellite. For the
work presented in this paper, a satellite constellation with ten
orbital planes and ten satellites per plane has been simulated.
An orbital inclination of 53∘ was used with all satellites
orbiting at an altitude of 550km. Visualizations of both the 3D
space and the geographical positions of all satellites in this
constellation are shown in Fig. 1 a) and b) respectively.
The initialization of the constellation deployment is
defined to be at time 𝑡=0. The simulation is initialised in
the 3D space with the defined number of satellites deployed
at equidistant positions in a single orbital plane. The
granularity of the simulation is defined as the time interval,
𝛥𝑡, at which consecutive satellite positions are computed. For
a satellite, 𝑆, at time 𝑡 with Cartesian position vector S, the
position at time 𝑡+𝛥𝑡 is calculated as:
S
=
S
+
v
𝛥𝑡
(1)
where v is the velocity vector of 𝑆 at time 𝑡. Doing this
repeatedly allows us to define the temporal motion of all
satellites. The Cartesian positional coordinates are mapped to
the spherical coordinate system. The features of the spherical
system directly translate to geographical positions consisting
of a longitude and latitude pairing using the mapping shown
Fig. 2 and Fig. 3.
Fig. 2. Geometric relationship between the 3D Cartesian and Spherical
coordinate systems. A position in the spherical coordinate system is
described through r, φ, and θ. Translating these to a Cartesian system for a
point P, r is the 𝐿 norm from the origin to P therefore the length of line
segment OP. θ is the anticlockwise angle in the XY plane from positive X
and ranges 0 ≤ θ ≤ 360. φ is the inclination from the positive Z axis to line
segment OP and ranges 0 ≤ θ ≤ 180.
Satellites are labelled according to their plane number as well
as their position within the corresponding plane. Each
satellites geographical position is collected and saved for later
use. The simulation can be executed for a predefined period
of time, or can be set to run indefinitely and continually
collect data throughout however, this is more
computationally intensive.
Given the nature of position calculation in the
simulation, the position at any time can be calculated by
varying the ∆t value. All physical features which affect the
orbital motion and relation to the geographical positions are
accounted for such as the rotation of the Earth. However, the
Earth is assumed to be spherical with uniform gravitational
pull.
Fig. 1. a) The 3-Dimensional visualization of the satellite constellation used with the characteristics described using the developed simulation tool. b) The
geographical visualization of the satellite constellation used with the characteristics described using the developed simulation tool.
Fig. 3. Left: The mapping from θ in the 3D spherical space to longitudes in
the geographical space. Right: The mapping from φ in the 3D spherical space
to latitudes in the geographical space.
III. S
YSTEM
A
RCHITECTURE AND
QKD
P
ROTOCOL
A. Satellite and Ground Stations
In this study, a large-scale constellation consisting of one
hundred LEO satellites is assumed. The satellite nodes are
selected to host the quantum transmitter equipment, since it
is usually less bulky and less complex compared to the
quantum receiver and also since the downlink transmission
offers a higher loss budget compared to the uplink [9].
Therefore, Single Photon Detectors (SPD)s, which are used
in the receiver side, that demand more complex and advanced
mechanisms to function (e.g., cooling) are placed on the
ground stations. For the ground terminals, astronomical
observatories in Europe have been selected as possible OGS
locations taking advantage of existing facilities. Additionally,
the majority of these sites are located in high altitudes thus
providing the required clear atmosphere conditions as well as
the reduced background radiance due to absence of city stray
lights.
Through our analysis, we have investigated nine
astronomical observatories located across Europe. In Fig. 4,
the positions of these observatories are depicted.
Fig. 4. Locations of the nine OGSs over five countries across Europe.
TABLE I. provides further details about the location of each
observatory, the observatory’s altitude as well as the
telescope aperture diameter that is assumed for every ground
station.
TABLE I. OGS
S SPECIFIC CHARACTERISTICS
# Ground
Station
Country Latitude,
Longitude
Altitu
de(m)
Aperture
diameter(m)
1
Helmos
Greece
37.98
,
22.20
2340
2.3
2
Skinakas
Greece
35.21
,
24.89
1750
1.2
3
Cholomondas
Greece
40.34
,
23.50
850
0.75
4
Calar Alto
Spain
37.22
,
-
2.55
2157
1.23
5
Te
nerife
Spain
28.29
,
-
16.51
23
9
0
1
6
Villafranca
Spain
40.26
,
-
3.57
664
1
7
Santa Maria
Portugal
37
,
-
25.08
276
1
8
Matera
Italy
41.98
,
13.60
544
1.5
9
C
ote d’Azure
France
43.72
,
7.29
372
0.77
B. QKD Protocol Assumptions
In this study, the weak+vacuum Decoy-State BB84 protocol
as described in [19] was used. The quantum states are
encoded in different polarizations, since the LEO satellite to
ground polarization decoherence is known to be very low
[20]. The decoy and vacuum states are added to the traditional
BB84 protocol to counter the Photon Number Splitting (PNS)
attack, by precisely measuring the channel’s loss and the
background noise that reaches the detector. According to
[19], the SKR by employing the decoy state protocol is lower
bounded by the following inequation,
𝑆𝐾𝑅
≥
𝑓
×
𝑞
𝑄
[
1
−
𝐻
(
𝑒
)
]
−
𝑄
𝑓
𝐸
𝐻
𝛦
(
2
)
where 𝑓
is the transmitters pulse repetition rate, q is the
protocol efficiency calculated according to [19], the subscript
µ is the average photon number per signal in signal states, 𝑄
and 𝛦
are the gain and the Quantum Bit Error Rate (QBER)
of signal states, respectively, 𝑄
and 𝑒
are the gain and the
error rate of the single photon state in signal states,
respectively, f(x) is the bi-directional error correction rate and
𝐻
(𝑥) is the binary entropy function.
IV. LEO
S
ATELLITE
-T
O
-G
ROUND
L
INK
M
ODEL
This Section provides the assumptions for the modeling of the
atmospheric channel. In this study, only the case of downlink
transmission under nighttime conditions has been examined.
A. CFLOS modeling
Cloud coverage is the dominant fading mechanism for the
optical satellite communication systems. The attenuation
induced by clouds blocks the optical signal, interrupting the
QKD communication [18][21]. Therefore, the CFLOS
probability of OGSs is important for the system level
evaluation of optical satellite communication systems. For
the estimation of CFLOS, cloud coverage statistics from
ECMWF database for 4 years (2012-2015) are used and the
methodology reported in [17][18][21] is employed. TABLE
II. provides the CFLOS probability of all OGSs. The
majority of observatories selected above provide a relative
low cloud coverage probability.
TABLE II. CFLOS PROBABILITY FOR EVERY OGS
#
Ground Station
CFLOS
Probability
1
Helmos
62.5
2
Skinakas
72.3
3
Cholomondas
61.78
4
Calar Alto
71.62
5
Tenerife
81.3
6
Villafranca
62.22
7
Santa Maria
37.07
8
Matera
54
9
Cote d’Azure
61
B. Geometrical Loss
Geometrical loss constitutes one of the main loss factors in a
satellite downlink. Considering the gains of the transmitters
and receiver’s telescope apertures, the signal’s attenuation due
to its propagation in free space can be calculated as follows
[22]:
𝐴
=
𝜆
4
𝜋
𝑑
(
𝜃
)
×
𝜋
𝐷
𝜆
×
8
𝑤
,
(3)
where 𝐷 (m) is the receiver’s aperture diameter,
𝑤= 2𝜆/𝜋 𝐷 is the half-width beam divergence angle (rad)
for a gaussian beam, 𝐷 (m) is the transmitter’s aperture
diameter, λ is the wavelength of the transmitted signal and d(θ)
is the distance between the satellite and the OGS, which is
given by [23]:
𝑑
(
𝜃
)
=
𝑅
𝐻
+
𝑅
𝑅
𝑐𝑜𝑠
𝜃
−
𝑠𝑖𝑛
𝜃
,
(4)
where H (m) is the satellite’s altitude above Earth’s surface,
𝑅 (m) is the Earth’s radius and θ (rad) is the elevation angle.
C. Atmospheric Transmittance
The atmospheric transmittance is the result of molecular
absorption under clear sky and can be given as a function of
the zenith angle as follows [24]:
𝐿
=
𝐿
(
)
,
(5)
where 𝐿 is the vertical link transmittance for a particular
wavelength and 𝜁 (𝑟𝑎𝑑) is the zenith angle of the link.
D. Atmospheric Turbulence
Atmospheric turbulence is produced by changes of the
refractive indices in small air pockets that result in beam
diffraction [22], thus leading to intensity variations in the
receiver, known as scintillations. The intensity of this effect
is characterized by the value of the refractive index structure
parameter 𝐶
(𝑚/) as weak moderate and strong. To take
into consideration the various altitudes of the OGSs as well
as the elevation angle, the Hufnagel-Valley model is used
[22]. The value of 𝐶
can be calculated as follows [25]:
𝐶
(
ℎ
)
=
𝐴
exp
−
𝐻
700
exp
𝐻
−
ℎ
100
+
5
.
94
(6)
×
10
(
𝑢
27
)
ℎ
exp
−
ℎ
1000
+
2
.
7
×
10
ex
p
−
ℎ
1500
,
where 𝐴 (𝑚/) is the refractive index structure parameter
at ground level, 𝑢 (m/s) is the average wind speed along
the slant path using the Bufton model, 𝐻 (𝑚) is the OGSs
altitude and ℎ (𝑚) is the height above the ground station
altitude. The OGSs altitude is once again taken into
consideration in the expression of the Rytov index, which is
calculated as follows [22],[26]:
𝜎
=
2
.
25
𝑘
𝑠𝑒
𝑐
(
𝜁
)
𝐶
(
ℎ
)
(
ℎ
−
𝐻
)
𝑑
ℎ
,
(7)
where 𝜁 (𝑟𝑎𝑑) is the zenith angle, 𝑘 (𝑟𝑎𝑑/𝑚) is the
wavenumber and 𝐻 (𝑚) is the turbulence altitude which
is set to 20km. For higher altitudes, turbulence is considered
negligible. To continue, the scintillation index is estimated
for a plane wave approximation by using the Kolmogorov
model [22]. To take the various aperture diameters into
account, the aperture averaging effect is included according
to [27]. Finally, since the apertures in this study are relatively
large and only the downlink scenario is examined, the
scintillation effect is weak, therefore the log-normal
distribution is suitable for the calculation of the signal loss,
which is given in dB for a given outage probability 𝑝 as
follows [27]:
𝐿
=
4
.
343
[
𝑒𝑟
𝑓
(
2
𝑝
−
1
)
[
2
𝑙𝑛
(
𝜎
+
1
)
]
−
1
2
𝑙𝑛
(
𝜎
+
1
)
]
,
(8)
E. Pointing Loss
The pointing error loss is also derived for a given outage
probability from the Probability Density Function (PDF) of
the normalized intensity, which is calculated by [28] as
follows:
𝑝
𝐼
=
𝛽
𝐼
,
0
≤
𝐼
≤
1
,
(
9
)
where 𝐼 = 𝛽/(𝛽+1) and 𝛽 is the divergence pointing
ratio given by the following formula:
𝛽
=
𝑤
4
𝜎
,
(10)
where 𝑤 is the half-width divergence angle of the
transmitted beam commuted for Gaussian beams and 𝜎 is
the pointing error variance (rad). For a given outage
probability 𝑝, the pointing error loss 𝐿 is calculated as
follows [28]
𝐿
=
𝑝
/
.
(11)
F. Background Noise
Background noise is mainly a result of sky radiance. For a
SPD, the solar background radiance can be high even during
nighttime. The noise power level, measured in Watts, that is
inserted in a telescope aperture with a capture area of 𝐴 is
given by the following formula [29]:
𝑃
=
𝐻
×
𝛺
×
𝐴
×
𝛥𝜆
,
(12)
where 𝐻 (𝑊/𝑚𝑠𝑟 𝜇𝑚) corresponds to the background
radiance energy density, 𝛺 (sr) is the telescope’s Field of
View (FOV) and ∆λ (µm) is the receiver’s band pass optical
filter width. The background noise is translated into counts
per second (cps) in the SPD and consequently as erroneous
detection probability for one gate time window as follows:
𝑃
=
𝑡
×
𝑐𝑝
𝑠
=
𝑡
×
𝑃
ℎ
×
𝑓
(13)
where h×f corresponds to the energy of a single photon.
V. SIMULATION RESULTS AND DISCUSSION
A. System assumptions
In this study, only the downlink scenario was taken into
consideration. Satellite-to-ground communication was
assumed to be possible only for elevation angles greater than
20. Both wavelengths of 1550nm and 800nm have been
examined, as they exhibit good atmospheric transmittance
[22]. To simulate the effects of the atmospheric channel, we
set the refractive index structure parameter at ground level to
1.7×10 (𝑚/), the average wind speed to 10m/s, and the
pointing error variance to 0.75μrad. The scintillation and
pointing loss were calculated for an outage probability of 1%.
The vertical atmospheric transmittance 𝐿 was calculated
by the MODTRAN tool to be 0.6 and 0.8 for 800nm and
1550nm respectively. Finally, the background solar radiance
during nighttime was set to the values of 10 (𝑊/
𝑚𝑠𝑟 𝜇𝑚) and 10 (𝑊/𝑚𝑠𝑟 𝜇𝑚) at 800nm and 1550nm
respectively [9],[30],[31].
The satellites as transmitters are assumed to be equipped
with telescope aperture diameters of 0.15m. In the OGSs side,
the telescope apertures diameters are given in TABLE I. and
vary between 0.75m and 2.3m. To limit the effect of
background solar radiance, a FOV of 100μrad was assumed
[12]. Concerning the SPDs, Single Quantum technology
Superconducting Nanowires Single Photon Detectors
(SNSPD)s were assumed [32]. The values of the SNSPDs and
optical filter performance characteristics as well as the BB84
Decoy-State related parameters are given in TABLE III. .
TABLE III. OGS AND BB84 SYSTEM PARAMETERS
Variable
Value
Unit
Wavelength
800/1550
nm
SPD
Detection
efficiency
[32]
0.9/0.85
-
Dark Count Rate (
DCR
)
[32]
10/250
c
ps
Dead time
[32]
10/25
μ
s
Detector’s visibility
[32]
98
%
G
ate
duration
time
[32]
1
ns
Detector’s
setup
loss
[33]
2.65
dB
Filter passband
[34]
0.
2
nm
Filter loss
[34]
1.5
dB
Fiber
Coupling loss
[35]
5.22
dB
Polarization decoherence
[20]
0.3
dB
Mean signal photon number μ
0.56
-
Mean decoy photon ν
0.1
-
Signal
:
decoy
: vacuum ratio
[19]
16:4:1
-
Protocol efficiency
~2/5
-
Βi-direction error correction
efficiency
f(e)
[19]
1.22 -
The selected values of mean signal and decoy photon numbers
were selected in order to optimize the resulting SKR by taking
into account the calculated overall link loss.
B. Feasibility Simulation
In the downlink case, geometrical loss consists one of the main
link loss factors. To minimize its effect and to increase the link
distance, large transmitter and receiver telescope apertures
should be deployed. In Fig. 5 the overall geometrical loss over
link distance and over transmitter to receiver aperture ratio is
depicted for both wavelengths of 800nm and 1550nm.
Fig. 5. Geometrical loss over distance at a)1550nm and b)800nm, over
receiver/transmitter telescope aperture diameter ratio for a transmitter
aperture diameter of 0.15m.
It should be mentioned, that in the case of a satellite on an
orbital altitude of 550km, the maximum possible link distance
which occurs for an elevation angle of of 20 is calculated to
be about 1300km. Therefore, geometrical loss may vary for an
1m receiver telescope diameter from 14dB to 21dB for the
wavelength of 1550nm depending on the elevation angle. It is
evident by Fig. 5, that for the wavelength of 800nm lower
geometrical loss is provided for the same receiver/transmitter
aperture ratio. On the other hand, the pointing loss according
to the equations (9-11) for an outage threshold probability of
1% is calculated to be 3.4dB and 0.9dB at 800nm and 1550nm
respectively.
Besides the geometrical loss, the background noise
radiance can make the SKR distillation unfeasible. The values
of the background noise radiance may vary from 10 to
10 (𝑊/𝑚𝑠𝑟 𝜇𝑚) at 800nm depending on the moon’s
position [9], whereas the night radiance at 1550nm is assumed
to be an order of magnitude lower [31]. In Fig. 6, the
normalized SKR over the background solar radiance over the
link’s distance is depicted.
Fig. 6. Normalized SKR over link distance (550-1300km) over background
solar radiance for a)1550nm and b)800nm, with a receiver’s aperture
diameter of 1m.
Fig. 6 strongly supports that daylight QKD communication is
infeasible even with the fine bandpass filtering of 0.2nm
which we assumed. On the contrary, the values of nighttime
solar radiance seem to barely affect the QKD performance.
The maximum background solar radiance that does not
interrupt the SKR distillation is calculated to be less than 0.1
𝑊/𝑚𝑠𝑟 𝜇𝑚, which is far less from the values of the full
daylight solar radiance (up to 15 𝑊/𝑚𝑠𝑟 𝜇𝑚 at 800nm
under daytime conditions [9]). Despite this, daylight QKD
could become feasible by assuming even narrower filter
passbands as in [36], or by further reducing the FOV or the
detection time window [29]. In this study, we considered only
nighttime transmission.
Finally, Fig. 7 presents the overall link loss over the
satellite’s elevation angle for various receiver aperture sizes.
The satellite’s elevation angle drastically affects the total link
attenuation, since for lower elevation angle values the distance
increases resulting in higher geometrical loss, scintillation loss
and atmospheric loss.
As it is depicted in Fig. 7, the total link loss for elevation
angles from 20 to 90 degrees varies from 22dB to 38dB at
1550nm and from 20dB to 37.5dB at 800nm. For vertical links
(i.e., high elevation angles), the wavelength of 800nm
provides a better loss margin. At low elevation angles, due to
the increased atmospheric and scintillation loss at 800nm, no
significant difference in the overall link loss between the two
wavelengths is observed.
Fig. 7. Total link loss over elevation angle, over receiver’s aperture
diameter (0.75m-2.3m) at a)1550nm and b)800nm.
It should be noted that even for elevation angles as low as 20
degrees SKR distillation is possible, since the maximum
affordable overall loss that does not interrupt the QKD link
under nighttime conditions is calculated to be around 46.5dB
for an 1m receiver telescope aperture diameter.
C. Large-Scale Satellite Constellation Performance
a) LEO Satellite Constellation over a single OGS: For the
selected LEO altitude of 550km, a short period for each
satellite’s orbit around Earth is observed. In Fig. 8. the orbital
path of a single satellite over a day is provided.
The density of the constellation is large enough to provide
availability to almost 24 hours for every station, meaning that
most of the time for each OGS at least one satellite is visible.
Fig. 8. One out of the one hundred satellite’s orbit over a time period of one
day.
Finally, each satellite is visible about two to three times every
24 hours by every OGS.
Every satellite is visible under different elevation
angles in each pass. For this reason, a long period of time
should be examined to export the long-term average results
concerning the distilled SKRs. In the following figure, the
calculated normalized SKR for a single pass of part of the
satellite constellation over the OGS of Skinakas (Greece),
over a time period of three hours is depicted. The duration of
the QKD communication for a single satellite pass over an
OGS may last up to about five minutes provided that each
satellite reaches a high enough elevation angle.
Fig. 9. Normalized SKR over a time period of three hours between part of
the constellation (41 satellites) and the OGS of Skinakas located in Greece,
calculated for the wavelength of 1550nm.
Each different color in Fig. 9 represents an individual
satellite-OGS link. The satellite constellation is large enough
so that almost continuously a connection between a ground
station and one of the satellites is established. Despite this, it
is evident by Fig. 9 that more than one satellites can be
simultaneously visible at a given time. To resolve this issue,
we consider two possible scenarios.
In the first scenario, it is assumed that each ground
station is employed with a single telescope receiver and can
therefore communicate with up to one satellite at a time. The
satellite which is selected to be linked with each observatory
is the one that can offer the highest elevation angle. Each
satellite is assumed to be equipped with three QKD
transmitters and three transmitting telescopes, since
according to our simulation the maximum number of OGSs
which are simultaneously visible by a single satellite can be
up to three individual stations.
In the second scenario, it is assumed that the OGSs are
equipped with enough telescope apertures and thus are
capable of establishing quantum links with all satellites for
which LoS exists at a given time. In this scenario, it is once
again assumed that each satellite is equipped with three
quantum transmitter stations and three transmitter telescopes.
b) Performance Evaluation: Scenario 1: The results of
this subSection are presented in terms of distilled key Gbits
per ground station over a time period of one year. QKD
downlinks were only considered feasible during the nighttime
hours (18:00-6:00), while the different time zones of each
location had been taken into account. The calculated CFLOS
probability contributes by limiting the final estimated SKRs.
Finally, the quantum signal repetition rate was set to 100Mhz
as in [14]. In TABLE IV. , the estimated distilled key Gbits
per ground station over a period of a year are provided.
TABLE IV. S
CENARIO
I:
D
ISTILLED
K
EY
B
ITS
P
ER
G
ROUND
S
TATION
# Optical
Station
Country
Yearly
Distilled Gbits
1550nm 800nm
1
Helmos
Greece
114.216
164.437
2
Skinakas
Greece
31.932
46.790
3
Cholomondas
Greece
10.994
16.268
4
Calar Alto
Spain
34.142
49.824
5
Tenerife
Spain
22.391
34.257
6
Villafranca
Spain
20.936
31.227
7
Santa Maria
Portugal
10.862
16.111
8
Matera
Italy
47.268
69.783
9
Cote d’Azure
France
13.017
20.160
Total
305.76
448.86
It is evident by TABLE IV. that the wavelength of 800nm
provides about 30% higher distilled bits values over the
period of one year. Furthermore, it is observed that OGSs
employing a large telescope are able to distill significantly
larger key bits strings. Specifically, for the OGS of Helmos
which is assumed to be employed with the largest telescope
and for the wavelength of 800nm the maximum value of the
calculated SKR with an transmitter repetition rate of 100Mhz
is 86.2Kbps.
c) Performance Evaluation: Scenario 2: In the current
scenario, it is assumed that the observatories are employed
with up to 3 receiver telescopes of equal size. TABLE V. ,
provides the estimated distilled Gbits per ground station over
the period of one year.
TABLE V. S
CENARIO
II:
D
ISTILLED
K
EY
B
ITS
P
ER
G
ROUND
S
TATION
# Optical
Station
Country Yearly Distilled Gbits
1550nm
800nm
1
Helmos
Greece
156.
323
219.
712
2
Skinakas
Greece
41.295
59.209
3 Cholomondas Greece 14.423 21.190
4
Calar Alto
Spain
46.211
66.079
5
Tenerife
Spain
26.634
38.582
6
Villafranca
Spain
28.075
40.724
7
Santa Maria
Portugal
14.556
21.198
8
Matera
Italy
65.373
92.574
9
Cote d’Azure
France
18.701
27.672
Total
411.594
586.949
The calculated distilled SKR is higher compared to the first
scenario, since all possible QKD downlinks can be
accommodated. Similarly, to the first scenario, the OGSs
equipped with larger receiver telescope apertures are capable
of extracting more SKR bits over the same time period.
C
ONCLUSIONS
A thorough feasibility analysis of a large-scale LEO satellite
constellation to ground QKD has been presented. A unified
software tool which provides the important satellites
constellation information has been developed. By modeling
the turbulent atmospheric channel and by calculating the
CFLOS probability derived from annual cloud coverage
statistics, we were able to extract results concerning the
performance of the QKD downlinks, for nine different optical
ground terminals located in various observatories across
Europe. It has been shown that QKD links can grant high
normalized key rates during nighttime that can reach up to
8.62×10bps. Over the investigated time period of one year,
it has been shown that up to about 219.7Gbits of distilled keys
can be generated between the satellite constellation and a
single OGS. The results reported in this study aim to
contribute towards a broader understanding of the potentials
and limitations of deploying quantum satellite network
spanning across Europe.
ACKNOWLEDGMENT
Part of the research leading to this work has been supported
by the H2020-funded Flagship project UNIQORN (820474).
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