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Acta Astronautica
Acta Astronautica 84 (2013) 15–23
0094-57
http://d
$ Thin Corr
E-m
(P.P. Su
C.J.M.Ve
journal homepage: www.elsevier.com/locate/actaastro
Enhancing ground communication of distributed space systems$
P.P. Sundaramoorthy a,n, E. Gill b, C.J.M. Verhoeven b
a Electronic Research Laboratory, Faculty of Electrical Engineering, Mathematics & Computer Science, Delft University of Technology,
Mekelweg 4, 2628 CD Delft, The Netherlandsb Chair of Space Systems Engineering, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands
a r t i c l e i n f o
Article history:
Received 29 February 2012
Received in revised form
31 August 2012
Accepted 22 October 2012Available online 3 December 2012
Keywords:
Femto-satellites
Distributed space segment
Phased array in space
Communication enhancement
Scalable systems
65/$ - see front matter & 2012 IAA. Publish
x.doi.org/10.1016/j.actaastro.2012.10.032
s paper was presented during the 62nd IAC
esponding author. Tel.: þ31 15 2786098; fa
ail addresses: [email protected]
ndaramoorthy), [email protected] (E. Gill)
[email protected] (C.J.M. Verhoeven).
a b s t r a c t
The functionality of a distributed system can be significantly enhanced by exploring
non-traditional approaches that leverage on inherent aspects of distributed systems in
space. Till now, the benefit of distributed systems in space has been limited to enhancing
coverage, multipoint sensing, creating virtual baselines (e.g. interferometry) or to
enhance redundancy. The list of benefits can be further expanded by understanding
the nature of distributed systems and by productively incorporating it into mission and
spacecraft design. For example, prior knowledge of the spatial evolution of such systems
can lead to innovative communication architectures for these distributed systems. In this
paper, different communication scenarios are investigated that can enhance the
communication link between the distributed system and ground.
The increasing trend towards highly miniaturized spacecraft (nano- to femto-
satellites) and proposals to launch hundreds or even thousands of them in massively
distributed space missions have expanded the interest in distributed systems with
miniature spacecraft. It is important to understand how and which, functionalities and
systems, scale with size and number. Scalable systems are defined and addressed at a
basic level and the utility of scaling rules and trends in identifying optimal configurations
of distributed systems is explored.
In this paper we focus on the communication capability and identify methods to
enhance the communication link between a distributed space segment, consisting of a
number of simplistic, resource limited femto-satellites, and earth. As an example, the
concept of forming a dynamic phased array in space with the elements of a distributed
space system in low-earth orbit is investigated. At the ground receiver, the signals from
different satellites forming the array should not differ in phase by more than one-third
the transmission wavelength, to ensure constructive superposition. Realizing such a
phased array places strict accuracy requirements on time synchronization and knowl-
edge of relative separation between the satellites with respect to the ground receiver.
These constraints are derived and discussed.
& 2012 IAA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
The trend towards highly miniaturized spacecraft haspropelled femto-satellites as candidates for massively
ed by Elsevier Ltd. All right
in Cape Town.
x: þ31 15 2785322.
l
,
distributed space systems [1,2]. Femto-satellites have amass of less than 0.1 kg and are seen to form the nextclass of miniature spacecraft that will innovate spacecraftsystems engineering and exploit space mission design torealize novel distributed space missions.
Miniature systems are advantageous by virtue of theirsmall size (packaging of more functional components),low mass and hence low mechanical inertia (precisionmovements and rapid actuation), ability to be mass pro-duced and less material requirements among others [3].
s reserved.
Thro
ughp
ut
Dimension
Linear
Sub-linear
Super-linear
Fig. 1. Throughput as a function of dimension, showing linear, sub-
linear and super-linear scaling.
1 The ratio of the effective output to the total input in any system.2 Output or production over a period of time.
P.P. Sundaramoorthy et al. / Acta Astronautica 84 (2013) 15–2316
Miniature spacecraft will enjoy all these benefits and addmore aspects like low spacecraft cost, low launch cost, andfast development time.
Distributed systems enjoy features such as redun-dancy, robustness, reliability, ability for incrementalgrowth but also suffer from security issues, networkproblems and operating software. A distributed networkof miniature systems will ideally combine the advantagesof miniaturization and distributed systems to realize anefficient and effective system.
In space, distributed systems have been primarilyemployed to increase coverage, enhance redundancy,create virtual baselines or for simultaneous multipointsensing. Apart from these benefits, typical functionalitiesof spacecraft like communication, attitude control, orbitmaneuvering, etc. maybe enhanced by exploring non-traditional approaches that leverage on inherent aspectsof distributed systems in space. For example, envision adeployment mechanism that can launch hundreds ofspacecraft with a statistical probability of a fixed fractionof these spacecraft facing the Earth at any given time.Depending on the mission scenario, this could obviate theneed for an explicit attitude control system.
Distributed systems and miniature systems are essen-tially systems that are scaled. While distributed systemsare scaled up in quantity or units, miniature systems arescaled down with respect to size. In Section 2, a briefdiscussion is presented on scalable systems and how toidentify functionalities and systems that favor miniatur-ization and distributed nature.
This study concentrates on the communication func-tionality and investigates, in particular, how the commu-nication capability varies as the number of elements inthe system increase. As a first step, the communicationcapability of an individual element of the distributedsystem – the femto-satellite, is characterized. To thisend, in Section 3, a power budget is derived for a typicalfemto-satellite, which serves as an input for the commu-nication link analysis in Section 4. Section 5 identifies andexplores scenarios for communication link enhancementbetween distributed femto-satellites and the groundstation.
As an example for communication enhancement, theconcept of forming a dynamic phased array in space withthe elements of a distributed space system in low-earthorbit is investigated. The basic principles of a phasedarray, its utility for distributed space systems andconstraints are addressed in Section 6. Section 7 brieflyaddresses inferences with respect to scaling trends.Conclusions with respect to communication enhancementand constraints are presented in Section 8.
2. Scalable systems
Scalable systems are systems that are capable ofoperating over the entire scale of a dimension (mass, size,number). Similarly, scalable models are those that workeffectively over the entire range of the dimension ininterest.
Some systems are not scalable at all and some othersscale over the entire range, but typically a number of
systems are scalable within a specific range. While theefficiency1 of some systems and functionalities are scaleinvariant (isometric systems), others show an increase ordecrease in performance with scale (allometric systems).Identifying and classifying these systems accordingly isvital in recognizing which systems benefit from decreas-ing size (miniaturization) and increasing numbers(multiple entities). To this end, we broadly classify scal-able systems into three kinds – systems that scalelinearly; systems that scale sub-linearly; and ones thatscale super-linearly with the dimension of interest.
If we define a metric for throughput2 ‘T’ related to adimension ‘D’, such that
TpDxð1Þ
then,
x¼1; leads to linear scaling,xo1; leads to sub-linear scaling andx41; leads to super-linear scaling (Figs. 1 and 2).
Depending on the dimension of interest, inferences canbe drawn on the trend lines. If the dimension is related tosize (e.g. Mass, volume and length), then a sub-lineartrend implies a pro-micro system (systems whoseefficiency benefits with miniaturization) and a super-linear trend implies a pro-macro system. On the otherhand, if the dimension of interest is the number of units,then a super-linear trend indicates a pro-multiple config-uration (configurations where multiple systems improveefficiency) and a sub-linear trend indicates pro-singleconfiguration. Ideally, for massively distributed systemswith miniature satellites we would use systems that scalesub-linearly with size and super-linearly with number.The trend lines can be used to identify systems that favorminiaturization and functionalities that benefit frommultiple entities. Such laws can be established on acomponent level, but must be finally integrated to the
Perf
orm
ance
/Eff
icie
ncy
Dimension
Linear Sub-linear Super-linear
Fig. 2. Efficiency as function of dimension showing linear (scale-invariant
performance), sub-linear (pro-micro; pro-single) and super-linear (pro-
macro; pro-multiple) trends.
y = xR2 = 1
y = 1.1004x0.8455
R2 = 0.99820
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2
Nor
mal
ized
Gai
n
Normalized Mass
Uniform thickness
Varying thickness
Fig. 3. Normalized gain as a function of normalized mass for a parabolic
dish antenna. (l¼ 0:1 m; Z¼ 0:55; r¼ 8000 kg=m3; for uniform thick-
ness t¼0.8 mm and for varying thickness t¼0.375 to 0.8 mm).
0.80.9
1m
entu
m
P.P. Sundaramoorthy et al. / Acta Astronautica 84 (2013) 15–23 17
sub-system and then system level to get the comprehen-sive overview of the scaling trend. These curves can beobtained through statistical data, physical principles orother established theories as shown in the following threeexamples.
00.10.20.30.40.50.60.7
0 0.2 0.4 0.6 0.8 1
Nor
mal
ized
Sto
red
Ang
ular
Mo
Normalized Mass
Fig. 4. Increase in the stored angular momentum against the normalized
mass of the reaction wheel.
2.1. Mass of parabolic antenna vs. gain of the parabolic
antenna
The gain of a parabolic antenna Gr can be expressed as
Gr ¼ p2D2Z=l2ð2Þ
where, D is the diameter of the dish, l is the wavelengthused for transmission and Z is the antenna efficiency.
Considering a solid dish antenna, the mass of the dishMd can be expressed as the product of the dish surfacearea S, the thickness of the dish which is a function of themass t(Md) and the density r of the material used.
Md ¼ S t Mdð Þr ð3Þ
and the surface area of a paraboloid is given by
S¼pr
6h2r2þ4h2� �3
2�r3
� �ð4Þ
where r is the radius of the dish and h is the height(or depth) of the dish.
If we assume a constant density and thickness (thick-ness independent of QUOTE ) of the dish then we see alinear increase in gain with respect to the mass. However,if we consider the thickness of the dish to increase withmass and hence size of the dish we get a sub-linear trendline, indicating a pro-micro system. Hence for a solid dishantenna, a smaller dish is more mass efficient withrespect to gain compared to a larger dish (Fig. 3).
2.2. Mass of reaction wheel vs. stored angular momentum
A power-law to establish the best fit curve based onstatistical data relating reaction wheel mass (includingwheel electronics) M in kg and stored angular momentum
H in Nms is shown in Eq. (5), [4].
M¼ 2:018 H0:4483ð5Þ
The co-efficient 2.018 in Eq. (5) has a dimension ofkg Nms�0.4493. This can be rewritten as Eq. (6).
H¼ 0:209 M2:231ð6Þ
This shows that the performance of the reaction wheelexhibits a super-linear trend with the mass of the reactionwheel, favouring scaling up rather than scaling down(Fig. 4).
2.3. Unit cost vs. production
Economies of scale [5] is a popular economic principleand refers to the reduction in unit cost as the number ofunits produced increases. Therefore, the cost efficiencyagainst number of units will show a super-linear trend,with the degree of super-linearity varying according toeach individual case.
P.P. Sundaramoorthy et al. / Acta Astronautica 84 (2013) 15–2318
3. Power budget of a femto-satellite
A femto-satellite is defined as having a mass rangebetween 10 and 100 g. Using the 100 g upper limit, apower budget is derived for a femto-satellite at 500 kmaltitude. SMAD [6] has been used as the source for thetypical values with respect to power allocation, massallocation and performance of components. The actualvalues could deviate considerably based on advances intechnology and implementation, so this approachprovides conservative numbers to get a preliminary budget.
Tables 1 and 2 show the mass distribution and powerbudget for a femto-satellite without battery and withbattery respectively. The power budget is also worked outfor the case with battery to assess the feasibility of havinga battery in a femto-satellite and evaluate how muchenergy can be harvested in one orbit. Including a batterycould be an attractive option for many mission scenarios.
Table 1Mass distribution and power budget for a femto-satellite witho
Parameters
Total mass of spacecraft (g)
Mass available for power system, MP (g)
Power generation (solar array), Ms (g)
Power storage (battery), Mb (g)
Power control, Mc (g)
Power regulation, Mr (g)
Power distribution, Md (g)
Parameters
Specific performance of solar array, Ssa (W/kg)
Power output with planar solar array, Ppsa (W)
Power output with omnidirectional solar array, P (W)
Orbital period, To (hr)
Maximum possible energy in one orbit (W h)
Power available for communication subsystem, PC (W)
Power available for transmission, Pt (W)
Transmitter efficiency, ZOutput power to transmitting antenna (W)
Table 2Mass distribution and power budget for a femto-satellite with
Parameters
Total mass of spacecraft
Mass available for power system
Power generation (solar array), Ms (g)
Power storage (battery), Mb (g)
Power control, Mc (g)
Power regulation, Mr (g)
Power distribution, Md (g)
Parameters
Specific performance of solar array, Ssa (W/kg)
Power output with planar solar array, Ppsa (W)
Power output with omnidirectional solar array, P (W)
Orbital period, To (h)
Maximum Eclipse duration, Te (h)
Maximum energy storage in one orbit (W h)
Battery performance (W h/kg)
Battery capacity (W h)
Minimum energy available per orbit (W h)
The above approach, as shown in Table 1, results in anavailable power of 29 mW for the communication sub-system. The communication subsystem of the femto-satellite developed by Barnhart et al. [1] is based oncommercially available products and has an estimatedtypical power consumption of 20 mW (for a much smallerrange than 500 km). The 7.35 mW output power to thetransmitting antenna established in Table 1 provides astarting point for the link analysis in Section 4.
4. Downlink budget for a femto-satellite
A sample downlink budget for a femto-satellite isshown in Table 3. The starting value for the transmittedpower is taken from the last row of the power budget inTable 1. The aim is to get an estimate of the downlinkmargin. The required margin is assumed as 5 dB.
ut battery (orbit altitude¼500 km).
Equations & typical values Mass (g)
100
28% of spacecraft mass 28
MP�Mb�Mc�Mr�Md 22.4
0
0.02 kg/W� P 0
0.025 kg/W� P 3.5
2% of spacecraft mass 2
Equations & typical values Power (W)
25
Ms� Ssa 0.56
1/4th of Ppsa 0.14
1.576
P� To¼0.221
21% of P 0.0294
Assume 100% of PC 0.0294
25%
Pt�Z 0.00735
battery (orbit altitude¼500 km).
Equations & typical values Mass (g)
100
28% of spacecraft mass 28
MP�Mb�Mc�Mr�Md 17
Through iteration 4
0.02 kg/W�P 2.125
0.025 kg/W� P 2.65625
2% of spacecraft mass 2
Equations & typical values Power (W)
25
Ms� Ssa 0.425
1/4th of Ppsa 0.10625
1.576
(35.75 min) 0.596
P� To¼0.168
40
Mb�Battery performance¼0.16
P(To�Te)¼0.104
Table 3Sample downlink budget for a femto-satellite (f¼3 GHz; Max. range¼
500 km).
Parameter Value Value (dB)
Transmitted power (W) 0.0074 �21.34
Transmitter to antenna loss, Ll (�) 1
Transmitting antenna gain, Gt 1 0
Receiving antenna gain, Gr
(0.1 m diameter; efficiency 0.55)
7.35
Pointing loss (�) 3
Connector loss (�) 2
Free space loss, LS 3E-16 (�) 155.96
Path loss, La (�) 1
System noise, Ts (K) 135.0 (�) 21.30
Data rate, R (bps) 50 (�) 16.99
Boltzmann constant, k 228.6
Required Eb/N0 (BPSK; PE¼10�5) (�) 9.6
Margin 3.75
-4 -2 0 2 4 6 8 10 12 1410-10
10-8
10-6
10-4
10-2
100
Eb/No [dB]
Prob
abili
ty o
f err
or P
e
BPSKBFSKQPSK/MSK
-1.6 dBShannon limit
Region I
Region II
Region III
Fig. 5. Probability of error vs. Eb/N0 for simple modulation schemes.
P.P. Sundaramoorthy et al. / Acta Astronautica 84 (2013) 15–23 19
The link is sensitive to a number of parameters as shownin Eq. (7) [6]. The symbols are elaborated in Table 3. QUOTEincludes all losses except the free space loss. Additionally, anumber of parameters like the receiving antenna gain, datarate, maximum range and frequency of operation can showconsiderable deviation than what is shown in the sampledownlink budget in Table 3. Eq. (7) gives a clear idea of theimpact that these parameters have on the link. FromTable 3, it is clear that the required margin of 5 dB is notattainable for the chosen scenario.
Eb
N0¼
PtGtGrLsL
kTsRð7Þ
5. Scenarios for enhanced communication
In this section we will explore scenarios which maybenefit from enhancing downlink communication usingmultiple satellites. Enhancing the downlink implies eitherestablishing the link through multiple satellites whenindividual satellites fail to establish the link or increasingthe throughput of multiple satellites to more than thecombined throughput of the individual satellites.
Fig. 5 shows a typical graph of received Eb/N0 againstprobability of error. Three different regions depending onthe received Eb/N0 are also indicated in Fig. 5 and arediscussed in the subsequent sub-sections. In each region,the benefits of enhancing the downlink are explored.
5.1. Region I
In this region, Eb/N0 is less than �1.6 dB, the Shannonlimit below which no error-free communication at anyinformation rate can take place.
C ¼ B log2 1þSNRð Þ ð8Þ
Eq. (8) is the Shannon’s channel capacity theorem [7],where C is the channel capacity, B is the channel band-width and SNR denotes the received signal-to-noise ratio.In the limiting case when the channel bandwidth isinfinitely large, implying data rate to bandwidth is tend-ing to zero, from Eq. (8), the corresponding limit on Eb/N0
is �1.6 dB, which is referred to as the Shannon limit.
In this power-limited region, no communication cantake place with a single femto-satellite and no coding orshaping techniques can enable communication. When thelink results in an Eb/N0 that lies in this region, there is aclear need to explore schemes that will improve Eb/N0 bycombining power resources from multiple satellites.
5.2. Region II
In this region the Eb/N0 is greater than �1.6 dB but lessthan the value required for receiving the signal with givenprobability of error (using simple modulation and codingschemes). Here, advanced and complex coding techniquesand modulation schemes, supplemented with constellationshaping techniques, can reduce the requirement on Eb/N0
and bring it closer to the ultimate Shannon capacity limit[8]. The implementation of such high performing codes andalgorithms on simplistic femto-satellites will be a challenge.Therefore, in this region also, downlink enhancement withmultiple femto-satellites becomes attractive. The downlinkcan be enhanced in two contexts:
Basic improvement of Eb/N0 to achieve requiredmargin and ensure a communication link
Improvement of Eb/N0 to increase throughput byensuring operation through optimal elevation angles(i.e., increasing Eb/N0 beyond what is required to achievethe margin and increasing the range of the link to operatewith optimal ground contact time).
Fig. 6 shows throughput (downlink data volume in onesatellite pass) as a function elevation angle. It can be seenthat maximum throughput is achieved for an elevationangle of around 451 for zenith pass and around 301 for asatellite pass which is 501 off zenith. An analytical treat-ment of optimizing throughput can be found in Gill et al.[9]. If the individual satellite link cannot achieve therequired Eb/N0 to operate in this region, then multiplesatellites can increase throughput by cooperating tocollectively operate in this optimal region.
5.3. Region III
The Eb/N0 is sufficient to establish the communicationlink. The scope for communication enhancement withmultiple satellites will be to improve Eb/N0 to ensure
0
0.2
0.4
0.6
0.8
1
1.2
5 15 25 35 45 55 65 75 85
Nor
mal
ized
Dat
a Th
roug
hput
Elevation Angle [degrees]
Zenith pass 50° off
Fig. 6. Normalized throughput as a function of minimum elevation
angle.
P.P. Sundaramoorthy et al. / Acta Astronautica 84 (2013) 15–2320
operation in optimal elevation angles, if existing link doesnot allow it.
The challenge in this region will primarily be in estab-lishing multiple accesses from multiple satellites to groundstation leading to solutions such as frequency division, timedivision and code division multiple access (FDMA, TDMAand CDMA). Single ground station and overlap in satellitetimes of view is another scenario where multiple satellitescan cooperate to increase throughput.
6. Phased array with multiple satellites
One option to enhance the link is to combine thetransmitter powers by realizing a phased array with themultiple satellites. Cooperative transmission from multi-ple antennas has been investigated for terrestrial wirelesssensors [10–12], but limited mainly to static configura-tions. In this section the concept of phased arrays withmultiple satellites will be explored.
A phased array is a group of antennas in which therelative phases of the respective signals feeding theantennas are varied in such a way that the effectiveradiation pattern of the array is reinforced in a desireddirection and suppressed in undesired directions. Withrespect to the receiver this implies constructive super-position of the signals coming from the different trans-mitters at the receiver. Such an array will require somemeans of phase synchronization to achieve this.
Phase synchronization in its simplest explanation issome means to synchronize the antennas to ensure thesignals arriving or leaving the antennas have the requiredrelative phases. This phase synchronization is withrespect to a preferred direction or just a point in space.When the array is used for transmission, the synchroniza-tion should be such that the signals from all the spatiallydistributed antennas reach the desired receiver in phase,enabling constructive interference of the signals.Likewise, when the array is used for reception, the phasesynchronization should ensure that the entire array isfocused in the direction of interest.
The other pre-requisite for such a phased array isexchange of data between the satellites, so that allsatellites have the common data before they start trans-mitting in phase. In this study, we will not focus onapproaches for inter-satellite data transfer, but recognizethat this data transfer will require a finite energy, andthere are many network algorithms which can beemployed to optimize the energy.
6.1. Theory: superposition of signals
Consider r1, r2, rn as the signals at the receiver from n
satellite transmitters defined as,
r1 ¼ A1sin otþa1ð Þ
r2 ¼ A2sin otþa2ð Þ
rn ¼ Ansin wtþanð Þ
ð9Þ
where A, o and a represent the amplitude, angularfrequency and phase offset of the received signals, thenthe superposition of these signals would result in,
Xn
i ¼ 1
ri ¼ A1sin otþa1ð Þ þ A2sin otþa2ð Þþ . . . þAnsin otþa3ð Þ
ð10Þ
This can be written as
Xn
i ¼ 1
ri ¼ A1cosa1þA2cosa2þ . . .þAncosanð Þ sin ot
þ A1sina1þA2sina2þ . . .þAnsinanð Þcos ot ð11Þ
Due to the close proximity of the satellites in orbit theassociated signal decay will be comparable for the differentsignals reaching the receiver. Therefore, we assume A1¼A2
¼y¼An¼A, to simplify the analysis and get the amplitudeof the superposed signal as
Xn
i ¼ 1
ri
����������¼ A
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficosa1þcosa2þ . . .þcosanð Þ
2þ sina1þsina2þ . . .þsinanð Þ
2q
ð12Þ
The Normalized received signal amplitude withrespect to A can then be written as
~A ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficosa1þcosa2þ . . .þcosanð Þ
2þ sina1þsina2þ . . .þsinanð Þ
2q
ð13Þ
The above equation relates the phase differences a tothe received signal amplitude. Note that the assumptionof equal amplitude for the received signals to get Eq. (12)is solely to get a more intuitive understanding of theeffect of the phase differences on the superimposed signalamplitude and is not a requirement. In a distributednetwork of satellites that are transmitting simulta-neously, the phase difference at the receiver arises dueto the errors in clock synchronization and difference inthe relative position of these transmitters with respect tothe receiver.
Assuming we can compensate for these phase differ-ences, then the accuracy with which we know the relativeposition of the transmitters with respect to the receiverand the accuracy of time synchronization will directlyimpact the strength of the received signal. Fig. 7 showsthe normalized amplitude of the superposed received
P.P. Sundaramoorthy et al. / Acta Astronautica 84 (2013) 15–23 21
signal as a function of the number of transmitters fordifferent accuracies of phase synchronization
6.2. Enhancing throughput with a phased array of femto-
satellites
Considering femto-sateliites with a link budget as givenin Table 3, with a lower limit on date rate of 50 bps, we get athroughput vs. number of satellites plot as shown in Fig. 8for a satellite pass which is 501 off zenith. It is assumedthere are no errors in phase synchronization and thetransmitter powers of the individual satellites can be addedup as the satellites increase. The link is not realized with asingle femto-satellite which results in zero throughput. Twofemto-satellites result in a throughput of around 1000 bitsand three femto-satellites realize 6000 bits. There on thethroughput increases by around 2000 bits per additionalsatellite. A super-linear trend can be seen in the throughputincrease from zero through 1000 to 6000 bits as the numberof femto-satellites increase from one to two and then three.Further increase in the number of satellites results in alinear increase in throughput. Three satellites represents thepoint where the trend changes from a pro-multiple systemto a scale invariant system and this number of satellites
0 5 10 15 20 25 30 35 40 45 500
5
10
15
20
25
30
35
40
45
50
No. of Satellites
Nor
mal
ized
Am
plitu
de o
f rec
eive
d sig
nal Perfect sync
Sync accuracy λ/10 Sync accuracy λ/5 Sync accuracy λ/3
Fig. 7. Normalized amplitude of the received signal as a function of the
number of satellite transmitters for different accuracies of phase
synchronization (l is the wavelength of transmission).
02000400060008000
10000120001400016000
0 2 4 6 8
Thro
ughp
ut [b
its]
Number of Satellites
Fig. 8. Increase in throughput with increase in number of satellites,
assuming perfect synchronization in the phased array, for a satellite pass
which is 501 off zenith.
gives the minimal size for optimal throughput of thedistributed system. The throughput of a system withoptimal number of elements will be higher than thesummed throughput of systems formed of elements lessthan the optimal number. The finite network overheadwhich has been neglected till now that increases with thenumber of elements is the motivation to keep the systemsize as low as possible making the transition point theoptimal size. Fig. 9 shows the increasing throughput withnumber of satellites for different accuracies of phasesynchronization.
6.3. Feasibility of the phased array
The main challenge to increase the throughput byincreasing the number of satellites as shown in Fig. 9, isachieving the required levels of phase synchronization.The accuracy with which we can determine the relativepositions of the satellites, referred to as localization, andthe accuracy of time synchronization together should bewithin the limits indicated in Table 4. For the l/3 case at3 GHz, the required accuracy is 3.3 cm or 0.11 ns. Thismeans that if the relative position accuracy for e.g. is1 cm, then the accuracy of time synchronization should bewithin 2.3 cm (when considered as correlated errors orwithin 3.15 cm for uncorrelated errors) or equivalently0.076 ns. Depending on what level of phase synchroniza-tion is achievable at a certain frequency of operation, thethroughput can be derived from a graph as shown inFig. 9.
Femto-satellites with current technology will barely beable to meet the phase synchronization requirements byachieving the necessary time synchronization and locali-zation. Time synchronization and localization are popularconcepts in terrestrial wireless sensor systems. Motivatedby advances in large-scale highly distributed terrestrialwireless sensor systems, there has been a lot of effort indeveloping time synchronization methods that are mind-ful of the resource constraints of such systems [13]. Timesynchronized COTS platforms have also been consideredfor applications such as beam forming [14]. There aremultiple ways to achieve localization within a sensornetwork. GPS satellites based positioning and rangingare popular methods for localization. In ranging, the
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0 5 10 15 20
Thro
ughp
ut [b
its]
Number of Satellites
Perfect Sync.
λ/3λ /5
Fig. 9. Throughput vs. number of satellites for different accuracy levels
of phase synchronization for a satellite pass which is 501 off zenith.
Table 4Requirements on phase synchronization accuracy translated into equivalent distance (relative positions) and time.
Frequency of operation (GHz) Wavelength (m) l/10 l/5 l/3
distance (cm) Time (ns) Distance (cm) Time (ns) Distance (cm) Time (ns)
3 0.1 1 0.033 2 0.066 3.3 0.11
1 0.3 3 0.1 6 0.2 10 0.33
0.3 1 10 0.33 20 0.66 33 1.1
P.P. Sundaramoorthy et al. / Acta Astronautica 84 (2013) 15–2322
accuracy of relative range estimation is a fraction of thewavelength used for ranging. Currently there is consider-able interest in miniaturize GPS receivers to port them onsmall satellites. Another challenging aspect in localizationis the prediction of the satellite dynamics, and inparticular relative orbital prediction. Once phase synchro-nization is established the prediction in relative dynamicsbetween the spacecraft will play a crucial role in deter-mining the duration for which the synchronization isvalid. The prediction accuracy of relative positions of thespacecraft will determine update rate from sensors usedfor positioning.
Advancing these methods and technology to meet thestringent requirements of phase synchronization andadopting them for space applications with miniaturedynamic satellites will be the key challenge with respectto achieving the required levels of time synchronizationand localization. The stringency on these requirementscan be reduced by choosing lower frequencies of opera-tion. However, this will impact the bandwidth used andthe antenna size employed.
7. Discussion
The scaling trend – linear, sub-linear or super-linear,dictates the benefit in increasing the number of entities toenhance a particular functionality. In the phased arrayexample (see Fig. 9), the initial trend is super-linearfollowed by a linear increase in throughput. Dependingon network implementation, the trend could be differentif the energy expenditure to realize a distributed networkis included in the analysis. This analysis assumed a zerooverhead for network realization.
The transition point from super-linear to linear trendacquires significance as this defines the region where thebenefit of combining multiple entities reaches saturation.In Fig. 9 the transition occurs when the number ofsatellites reaches three. As discussed in Section 1, asuper-linear trend implies improvement in efficiency withincreasing elements, a linear trend implies constantefficiency and a sub-linear trend implies decrease inefficiency for distributed systems. Therefore, when weaccount for the finite network overhead that increaseswith the number of entities in the network, then optimallink performance is achieved by limiting the network tothe number of satellites at the transition point, in thiscase three. In a massively distributed system of femto-satellites with the above established scenario, a conclu-sive implication of this result is that for enhancing groundcommunication, sub-groups of three femto-satellitescommunicating cooperatively is optimal. In general, the
scaling trend identifies regions and subsequently numberof elements that are optimal for distributed networks.
8. Conclusion
Highly miniaturized spacecraft such as femto-satellitesare excellent candidates to realize massively distributedsystems in space. Scaling rules which use the size ofindividual satellites and their number in a system areefficient to characterize the performance of highlydistributed massively miniaturized space systems. More-over, scaling trends can help identify optimal size andnumbers of elements in a distributed network.
While the typical benefit of distributed systems inspace originates from features as coverage, redundancy,baselines and multipoint sensing, the enhancement of thedownlink communication capability of a distributedsystem of femto-satellites to a ground station wasexplored. To this end, the benefits of a phased array inspace formed by multiple femto-satellites have beenstudied. It was shown that although individual satellitemay not be able to communicate to the ground station, thephased array enables communication. The challenge ofthis approach is to achieve phase synchronisation betweenthe satellites which necessitates a sufficient time synchro-nization and localization in a dynamic environment.
Femto-satellites were chosen as candidates forresource limited spacecraft and low-earth orbit as apotential mission scenario. However, the concept andconclusion apply to all missions involving multiple satel-lites that aim to combine resources to extend or enhancethe individual spacecraft capabilities.
Acknowledgement
The financial support from the Dutch MicroNed andNanoNextNL Programmes during the course of this studyis highly appreciated and acknowledged.
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Prem Sundaramoorthy received his Bachelordegree in Telecommunication Engineeringfrom Bangalore University, Bangalore, Indiain 2001. This was followed by a three yearresearch assignment in the area ofunmanned air vehicles at the AeronauticalDevelopment Establishment, Bangalore,India. He received his M.Sc. Degree fromthe chair of Astrodynamics and SatelliteSystems at the Delft University of Technol-ogy, Netherlands in 2007. He is currentlypursuing his Ph.D. at the Delft University of
Technology in the Chair of Space SystemsEngineering. His current research interests include space missionanalysis, femto-satellites, cooperative communication and distributedsystems in space.
Eberhard Gill was born in Germany in 1961.He received the diploma in physics and thePh.D. degree in theoretical astrophysics fromthe Eberhard-Karls University Tuebingen,Tuebingen, Germany. He has been workingas a Researcher with the German AerospaceCenter (DLR), in the field of precise satelliteorbit determination, autonomous navigationand spacecraft formation flying. He hasdeveloped a GPS-based onboard navigationsystem for the BIRD microsatellite. Dr. Gillhas been Co-Investigator on International
missions, including Mars94/96, Mars-Express, Rosetta, Equator-S, Champ, and PRISMA. Since 2007, he holdsthe Chair of Space Systems Engineering of the Delft University ofTechnology, Delft, The Netherlands, which developed the nano-satelliteDelfi-C3. He has authored or coauthored over 150 journal articles andconference papers, three text books, and one patent.
Chris Verhoeven is an associate professor inthe Department of Microelectronics at theDelft University of Technology. In February1990 he obtained his Ph.D. degree from theDelft University of Technology on the topicof oscillators. His research interests includesystematic analog design, RF circuits, adap-tive front-ends, oscillator design and space-qualified electronics for nano-satellites.Educational activities include courses insystematic design of analog circuits, space-born electronic systems, space mechatronics
and ethics. Since 2007 he is part-time employed at the Faculty ofAerospace Engineering in the Space Systems Engineering Department.He was involved in the design and implementation of the Delfi-C3 nano-satellite that was successfully launched in 2008 and is now involved inthe development of the Delfi-n3Xt satellite of the TU-Delft and he is oneof the initiators of the national OLFAR (Orbiting Low Frequency Array)project, a moon-orbiting radio telescope based on a swarm of nano-satellites.
