IEEE - Aerospace and Electronic Systems - April 2023 - 8

Laser Intersatellite Link Range in Free-Space Optical Satellite Networks: Impact on Latency
Figure 2.
First shortest path (i.e., the shortest path at first time slot) between New York and Istanbul over the FSOSN at 659.5 km LISL range. Note
that the lowest 659.5 km LISL range results in short LISLs between satellites and 15 hops/satellites on this path. The propagation delay,
node delay, and the latency (or network latency) of this path are 32.94, 15, and 47.94 ms, respectively. Further note that the propagation
delay of this path is the sum of the propagation delays of all links on this path [i.e., uplink (which is the link between GS at New York and
satellite x11503), 14 LISLs, and downlink (which is the link between satellite x12264 and GS at Istanbul)]; the node delay of this path is the
sum ofthe node delays of all 15 hops/satellites on this path; and the latency of this path is the sum of its propagation delay and its node delay.
satellites and GSs at a time slot, we construct a connectivity
graph for the FSOSN at that time slot and use link
propagation delays and node delays in the FSOSN as the
weights of the edges and vertices of this graph, respectively.
Subsequently, we use Dijkstra's algorithm [17] to
calculate the shortest path between two cities over the
FSOSN in terms of end-to-end latency. More precisely,
we employ Dijkstra's algorithm and use the connectivity
graph as input to calculate the shortest path over the
FSOSN between cities that minimizes the total weight of
the edges and vertices (i.e., the total latency) between the
source and the destination, i.e., the GS in the source city
on Earth and the GS in the destination city on Earth,
respectively. The latency of the shortest path at a time slot
is composed of propagation and node delays on this path
at that time slot, and the average of the latencies of the
shortest paths at all time slots has been referred to as average
network latency in this work.
FSOSNs are well-suited to provide low-latency longdistance
data communications as a premium service to the
financial centers around the world [18]. To calculate the
latency of the shortest path for New York-London, New
York-Istanbul, and New York-Sydney intercontinental
connections over the FSOSN, we use the coordinates (i.e.,
latitudes and longitudes on the Earth's surface) of the
financial stock markets (i.e., New York Stock Exchange,
London Stock Exchange, Istanbul Stock Exchange, and
Sydney Stock Exchange) for the GSs within these cities.
The latency of the shortest path between cities includes
the propagation delay of the laser link between the GS in
the source city on Earth and a satellite in space, the
8
propagation delays of the laser satellite-to-satellite links
and the node delays of the satellites on this path, and the
propagation delay of the laser link between a satellite in
space and the GS in the destination city on Earth.
The range of GSs at New York, London, Istanbul, and
Sydney Stock Exchanges is fixed and is assumed as 1000 km.
For Starlink Phase I, the gateways (or GSs) communicate
only with satellites above a minimum elevation angle. This
angle is specified as 25 for Phase I ofStarlink by SpaceX in
its FCC filing [7]. It is also mentioned in this filing that this
angle will be 40 when the constellation is fully deployed.
Based on these elevation angles of25 and 40, the GS range
can be calculated as 1123 km and 812 km, respectively. The
GS range of 1000 km is, therefore, a reasonable range to
assume since it lies between these two ranges.
The satellites in Starlink's Phase I constellation orbit at
speeds of approximately 7.6 km/s. Due to this high-speed
movement of satellites, GS-to-satellite link, satellite-to-satellite
links, and satellite-to-GS link (and/or their propagation
delays) are constantly changing. As a result, the shortest path
over the FSOSN between two cities (and/or its latency)
changes at every second (or time slot). Figures 2-4 show
first shortest paths (i.e., shortest paths at first time slot)
between New York and Istanbul at different LISL ranges.
For example, Figure 2 illustrates the first shortest path over
the FSOSN at 659.5 km LISL range, and this path consists
of the GS at New York Stock Exchange, satellites x11503,
x11504, x11505, x11506, x11507, x11508, x11509, x11607,
x11608, x11609, x11610, x11611, x11612, x11613,and
x12264, and GS at Istanbul Stock Exchange. The shortest
path is shown in yellow color while the markers and labels
IEEE A&E SYSTEMS MAGAZINE
APRIL 2023

IEEE - Aerospace and Electronic Systems - April 2023

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