This article compares the downlink performance in a gross average sense between space and ground network support of low-Earth orbiters. The purpose is to assess what the demand for DSN support of future small, low-cost missions might be, if data storage for spacecraft becomes reliable enough and small enough to support the storage requirements needed to enable support only a fraction of the time. It is shown that the link advantage of the DSN over space reception in an average sense is enormous for low-Earth orbiters. The much shorter distances needed to communicate with the ground network more than make up for the speedup in data rate needed to compensate for the short contact times with the DSN that low-Earth orbiters have. The result is that more and more requests for DSN-only support of low-Earth orbiters can be expected

Posner, E. C.

English

NASA Technical Reports Server

TDA ProgressReport42-111 November 15, 1992
A Model to Compare Performance of Space and Ground
Network Support of Low-Earth Orbiters
E. C. Posner
Office of Telecommunications and Data Acquisition
This article compares the downlink performance in a gross average sense between
space and ground network support of low-Earth orbiters. The purpose is to assess
what the demand for DSN support of future smMl low-cost missions might be, if
data storage for spacecraft becomes reliable enough and small enough to support
the storage requirements needed to enable support only a fraction of the time. It
is shown that the link advantage of the DSN over space reception in an average
sense is enormous for low-Earth orbiters. The much shorter distances needed to
communicate with the ground network more than make up for the speedup in data
rate needed to compensate for the short contact times with the DSN that low-Earth
orbiters have. The result is that more and more requests for DSN-only support of
low-Earth orbiters can be expected.
I. Introduction
NASA's Tracking and Data Relay Satellite System
(TDRSS) can support low-Earth orbiters, providing con-
tinuous coverage when necessary, for example, for piloted
missions. Due to the synchronous altitude of TDRSS, the
communication path length to a low-Earth orbiter is about
equal to the synchronous altitude, or 36,000 km. The com-
munication path from an Earth station such as the DSN
to a low-Earth orbiter is much less, resulting in a huge
reduction in path loss. On the other hand, the visibility
(fraction) of a low-Earth orbiter reduction to a ground net-
work of only three locations, such as the DSN, is much less
than 1, i.e., the fraction of the time a low-Earth orbiter
is visible to the DSN is small. This means that the data
must be stored and then dumped over the station during
the orbiter's passes or times of visibility. This means an
increase in the required data rate, to partially offset the
gain from the shorter communication path.
For example, in a typical case of a 400-kin circular orbit
at a random inclination, ignoring station masks, the net-
work sees the orbiter 8.8 percent of the time, for a required
increase in image data rate of 1/0.088 = 11.36, a 10.6-dB
loss as accounted for in this article. This loss is much more
than made up for by the gain due to shorter communica-
tion paths. The distance at rise or set for a 400-kin orbit
is 2298 kin. This gives a gain at rise or set relative to the
36,000-kin synchronous altitude of (36000/2298) 2 = 245.5
or 23.9 dB. The data rate can be varied during a pass, i.e.,
increased as the spacecraft rises and decreased as it sets.
Although continuous rate variation is assumed below, it
turns out that most of the improvement can be realized
333
https://ntrs.nasa.gov/search.jsp?R=19930009736 2020-03-17T07:20:38+00:00Z
with only two rate changes. On average, data volume for
400-km orbits improves an average increased factor of 3.61,
or 5.6 dB, as is shown below. The total average improve-
ment for using an Earth station instead of one at a syn-
chronous altitude for a random 400-kin circular orbit is
then (23.9 + 5.6- 10.6) dB = 18.9 dB.
The 18.9-dB average improvement does not consider
that a ground station will typically have a greater aperture
than a space relay spacecraft, and can also have a much
lower noise temperature than that which could be pro-
vided by any space low-noise reception technology forsee-
able over the next decade. For example, a 26-m ground
station such as in the DSN has an advantage in gain of
14.3 dB over a 5-m TDRSS-style space-based antenna, as-
suming equal antenna efficiencies, yet ignoring any noise
temperature differences, which tend to favor ground-based
antennas. Also, the space system may not use its highest
gain antenna to support simpler missions, but rather its
multiple-access capability. The multiple-access capability
allows several spacecraft to be supported at once, which
may allow the continuous support assumed here, but at
a still greater advantage to the ground than the 14.3 dB
quoted above.
The effect of frequency selection needs to be considered.
Here, roughly the same frequency is assumed for the space
network as for the ground network. The space network
could ultimately make use of a relay frequency of 60 GHz,
or even of an optical frequency. These choices could change
some of the considerations. On the other hand, receiver
improvements are much easier to make in a ground station
than in a space relay station, once launched. In fact, ser-
vicing a synchronous spacecraft will be very difficult and is
certainly not foreseen for at least 20 years. The rest of the
article, therefore, assumes roughly the same frequencies
for the space network as for the ground network.
Other factors ignored in this article, which is not in-
tended to substitute for a system engineering trade-off
study, are any costs to the using spacecraft of the access
protocol to use a multiple-access capability on the space-
based relay platform, implementation cost differences be-
tween space-based and ground-based reception capabilities
and likewise any operations cost differences, the ability to
upgrade a ground station during its lifetime, the number
of spacecraft practically supportable by a space or ground
network capability, the differential costs of onboard data
storage by using the ground-based capability, and finally
the costs of the using spacecraft communications package
to produce the required effective isotropic radiated power
(EIRP) in the two cases. The assumption of random cir-
cular orbits would also have to be replaced by realistic or-
bits and mission requirements in a more detailed analysis,
which would also include realistic station masks.
Nevertheless, the potential gain of (18.9 + 14.3) dB =
33.2 dB or more (a factor of 2100) will be attractive to
using spacecraft as a cost, size, and weight reduction, as-
suming the availability of data storage that can overcome
the low visibility from the ground. This will apply then
to robotic missions that do not have very high average
data acquisition rates. Many missions may be included
in the set of potential users in coming years as spacecraft
are downsized. Such spacecraft may use the 33.2-dB or
more average decrease in required spacecraft EIRP in sev-
eral ways, or use all these ways at once: lower spacecraft
power, a lower gain or even an omnidirectional spacecraft
antenna, less or no restrictions on spacecraft attitude, and
a general relaxation of the constraints on the spacecraft
radio. The mass reduction allows a smaller launch vehicle,
which could open up whole new mission opportunities.
There are corresponding uplink and navigation im-
provements as well, which are not considered in this ar-
ticle. Overall, the result of support of low-Earth orbiters
by the ground will be the provision of a communications
capability that will result in smaller, cheaper, and lighter
spacecraft of the same capability. Thus, it can be expected
that in coming years there will be more and more low-
Earth orbiters that are designed for support exclusively
by the DSN.
The remainder of this article is organized as follows.
Section II presents the sinaple model of random circular
orbits that is being considered. Section III calculates the
average visibility of a low-Earth orbiter to the DSN, and
thus the amount of data storage that must be provided on
board the using spacecraft. Section IV finds the average
improvement in the data volume received when using the
ground network as opposed to the space network. Finally,
Section V summarizes the results and computes the aver-
age advantage of ground versus space network support for
low-Earth orbiters, considering both communication dis-
tance and spacecraft visibility.
II. Model of Random Circular Orbits
Here random circular orbits are assumed. Real orbits
are only sometimes circular. Moreover, certain inclina-
tions are often preferred, due for example to the require-
ment of keeping the line of apsides fixed or to provide Sun
synchronism. The location of a single tracking station on
Earth may as well be assmned fixed, given random orbits.
The rotation of the Earth can also then be ignored, since
334
one is in effect assuming a random phase of the orbiter in
its orbit. The DSN has its communication complexes far
enough apart so that there is never simultaneous visibility
of low-Earth orbiters. Thus, visibilities from a single sta-
tion, when multiplied by 3, the number of complexes, give
the long-term average visibility to the entire DSN with its
present complex locations.
The radius of the Earth, r, is taken in calculations as
6400 kin. The altitude above Earth of the circular orbit is
h; in calculations, h is taken as 400 km. The fraction of
time that a spacecraft in random circular orbit at distance
h above the Earth is visible to a given ground station on
a spherical Earth of radius r is found in the next section.
III. Average Visibility of a Low-Earth Orbiter
Since the spacecraft is in a random circular orbit, ran-
dom phase and inclination, it is at a given time at a ran-
dom (uniform) point on a sphere of radius r + h centered
at the Earth's center. A given tracking station sees a cer-
tain fraction of the surface area of the larger sphere, and
that fraction is clearly the average visibility from a single
station. The single station may as well be random too,
since the average visibility is clearly independent of the
station's location. By the same reasoning, the spacecraft
may as well be considered fixed. Thus, the visibility of a
spacecraft from a single Earth station is just the fraction
of the Earth's area seen by a fixed spacecraft.
The fraction of the area on the Earth seen by a space-
craft at height h above the Earth is now easily found (see
Fig. 1). A tangent is drawn from the spacecraft to the
Earth, and the area of the spherical cap is sought. Let 0
be the angle subtended by the spacecraft tangent, so that
0 -- arc°s (r_h)
Let ¢ be the angle of integration between a point on
the cap and the center of the Earth. This angle goes from
0, the angle corresponding to the spacecraft location at
zenith, to the edge of Earth visibility at angle 0. The per-
pendicular radius of the circle at ¢ is rsin¢, and its cir-
cumference is 27rr sin ¢. The slant length of the differential
ring corresponding to angle d¢ around ¢ is rd¢. Thus, the
area dA of the differential ring is
dA = 27rr sin ¢. rd¢ = 2rr 2 sin ¢d¢
The area of the cap A is then
0
A = 2rr2 sin 5d¢
=0
-----2rrr 2 (-- cos ¢)_=0
= 2vr 2 (1 -- cos O)
so that
The area of the surface of the Earth is 47rr 2, so the
visibility V from a single station is
h )/4rr 2V = 2rr 2
h
Y=--
2(r+h)
With h = 400 km and r = 6400 kin, V = 1/34. The
visibility from the entire network of three complexes is 3
times this, or 3/34 = 8.8 percent. This is a long-term
average. It does not of course mean that the DSN will see
8.8 percent of every or any orbit.
Assuming the orbiter is gathering data even while trans-
mitting, it must transmit 34/3 = 11.33 times as fast
(10.5 dB more link is needed) as a spacecraft that can al-
ways be seen and is continually serviced by a synchronous
relay satellite system. Such a data rate is supportable even
by present technology for satellites whose data acquisition
rate is up to several megabits per second. This is because
all the data can be dumped if during a pass there is an
average data rate of tens of megabits per second, which
is compatible with current technology. Future data acqui-
sition digital equipment in the signal processing centers
of the DSN is expected to be able to accommodate even
higher peak rates.
What about data storage requirements? Maximum
storage requirements cannot be found from the averaging
techniques used here. Nevertheless, the following discus-
sion is of some interest. The orbital period for a low-Earth
335
orbiter is about 90 minutes (5400 sec). This means, on av-
erage, a pass every 1800 sec or so, with a three-complex
network, assuming every pass is supported as in the as-
sumption here. If the spacecraft transmits while also ac-
quiring and recording more data, then 1800 sec, say 2000
sec, of data must be stored. If the storage on board is
limited to 10 gigabits, today's technology, a maximum
spacecraft data acquisition rate of 5 megabits per second
can then be supported. Future terabit onboard storage
could support 100 times this data acquisition rate, or 500
megabits/sec downlink. The link, not the storage, would
then become the limiting factor. The storage and dump
mode is clearly feasible for small low-Earth orbiters from
the standpoint of data storage technology.
Now that the average visibility is known, one can find
the link improvements, using the method given in the next
section.
IV. Average Link Improvement
The average link improvement is readily calculated
from the average inverse squared distance to the Earth
tracking station from the low-Earth orbiter. Recall that it
is being assumed that the distance to a space relay station
is essentially constant at 36,000 km. Thus, the decibel
improvement due to the distance effect is correctly calcu-
lated in terms of data volume received as the product of
36,000 km squared times the average inverse squared dis-
tance. This gain must be de-rated by the visibility factor,
i.e., the fraction of time that the low-Earth orbiter is visi-
ble to the ground tracking network. The resulting product
is the average link improvement taking both communica-
tion distance and visibility into account.
The calculation to follow assumes that the data rate is
varied by an onboard stored sequence during a pass as the
spacecraft distance to the Earth station changes. The goal
is to make the data rate as large as possible at all times.
This is similar to deep space support, where the rate can
be varied during a pass, but with more frequent changes
during a near-Earth pass. Rate changing results in a max-
imum to minimum data rate in an overhead 400-km orbit
of (2298/400) _ = 33.0 or 15.2 dB. If the minimum data
rate is 2 megabits/sec, the maximum rate when the space-
craft is directly overhead would be 66 megabits/sec. So
the high maximum-minimum ratio is not an insurmount-
able problem, except perhaps at the highest average data
acquisition rates.
The calculation shall proceed by calculating the aver-
age improvement factor F relative to distance squared at
spacecraft rise or set:
F = [(r + h) 2 - r 2] x average inverse squared distance
This is used for ease of correctness testing later. Referring
to Fig. 2, it is seen, as in the previous section, that with
0 = arcos (rl (r + h))
as before, and normalizing over the area of the cap,
0 2a.r 2 sinCd¢/(2vr2h/(r + h))F = h(2r + h) l_ (1)
=0
Here I is the distance from the spacecraft to what is
now thought of as the randomly situated tracking station,
found from a vector diagram (Fig. 3) to be
12 = (r + h) 2 + r 2- 2r(r + h) cos¢ (2)
12 =2r 2+2rh+r 2-2r(r+h) cos¢ (3)
Substituting Eq. (2) into Eq. (1) and using sin ¢d¢ =
-dcos¢, Eq. (1) becomes
0 -dcos¢F = (2r + h)(r + h)
=0 2r2 + 2rh +-_'_ 2r(r + h) cos ¢
(4)
Using cos 0 = r/(r + h), Eq. (4) becomes, with u = cos ¢,
fr = (2r + h)(r + h) du
=_._ 2r 2 + 2rh + h 2 - 2r(r + h)u
(5)
and so
F= (2r+h)(r+h)
2r 2 + 2rh + h _-
f[ dux
=___ 1 - 2r(r + h)u/(2r _ + 2rh + h 2) (6)
Make the substitution
336
v = 2r(r + h)u/(2r _+ 2rh+ h2) (7)
so that Eq. (6) becomes
F = (2. + h)(_+ h) (2._+ 2_h+ h_)
(2r 2 + 2rh + h2) 2r(r + h)
2r(r+h)/(2r'+2rh+h_) dv (8)
=2r_/(2r_+2rh+h _) 1 -- V
Using
dv _ In(l-v) (9)1--v
Eq. (8) becomes
F = 1 + _r - V)l_=2r(,+h)/(2,2+2_h+h_ ) (10)
or
(2rh +
F= (1+ h)In \ )_ h2) (11)
or
This is the desired result on the average improvement fac-
tor F.
Several checks are in order. First F is always greater
than 1, since
(l+l) ln(l+x) >1 for x >0
i.e., (1 + x) ln(1 + x) > x. This is because the derivative
of the left-hand side, 1 + ln(1 + z), is greater than 1, the
derivative of the right-hand side, if z > 0. Second, it is
clear from the geometry that F ought to be decreasing in
h, i.e., less improvement for higher orbits. This amounts
to (1 + l/x) ln(1 + z) increasing in x as x increases from
0. The derivative of this with respect to z is
x - ln(x + 1)
X 2
whose numerator is obviously and well-known to be posi-
tive for z > 0, as required.
Another check is that F clearly approaches 1 from
above as h approaches 0¢, from the geometry. This easily
follows algebraically from Eq. (12):
2T
F- 1+_- I 1 as h ---, oo
It is interesting to note that, as h ---* 0, the improvement
F becomes infinite as In (2r/h).
For orbits conditioned to pass directly overhead, it is
clear that the improvement factor is even greater than that
given by Eq. (12). For example, for 400-kin orbits condi-
tioned to go overhead, the improvement factor is 10 dB
instead of the 5.6 dB to be derived below. This aspect will
not be pursued.
V. Summary
For 400-km orbits, the average improvement factor F
is found from Eq. (13) to be
33
F=_In33=3.605=5.6dB
The distance at rise or set is 2298 km, so the gain relative
to a 36,000-kin path, ignoring temporarily the visibility
loss, is
F = (3.605) = 884.7 = 29.5 dB
This is to be de-rated by the visibility loss of Section III,
0.088-dB or 10.5-dB loss, to get the average gain of 19.0 dB
reported in Section I.
To recapitulate, the average link gain factor G for Earth
reception over full-time synchronous space reception, con-
sidering distances, variable data rates, and visibilities, is
given for random circular orbits and a three-station ground
network by
337
d 3h (13)V-h(2 +h) In 1+ orbit in kilometers. This G is easily seen to be decreasingas h increases, as is reasonable.
using Eq. (12) and the equation for the visibility V from a
single Earth station derived in Section II. The factor of 3
occurs because expected values add together, and no two
DSN stations ever see the same low-Earth orbiter at the
same time. Equation (13) simplifies to
G- 4 r(r-t-h) In 1 q- (14)
Here d is synchronous altitude, 36,000 km, r is the radius
of the Earth, 6400 km, and h is the height of the circular
In summary, small Earth orbiters will more and more
find it advantageous to be supported by the ground net-
work rather than by the space network. The advantage
of lowered communications package mass, size, and power
consumption, resulting from smaller communication dis-
tances capitalized upon by available onboard data storage,
is amplified by the greater figure of merit (gain divided by
noise temperature) of ground stations compared to space
relay stations. Overall, NASA costs are expected to be
lower as well, but this article does not attempt a formal
trade-off study. Nevertheless, the DSN can expect to be
supporting more and more low-Earth orbiters.
338
r+ h)2- [ 2
SP_A_ECRAFT
1°
Fig. 1. The geometry of visibility.
SPACECRAFT h
Fig. 2. The average Inverse squared distance.
STATION
SPACEC RAFT
II _11=r, II yll =r+h,
IL y-Ell =_
_02=11yll 2 +11Eli2 -2(y._)
AND
y._=il Ell -II yil cos_
CENTER OF
EARTH
Fig. 3. The distance between the spacecraft and the tracking
station.
339


A model to compare performance of space and ground network support of low-Earth orbiters

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