GEOSTATIONARY SATELLITE LINK AVAILABILITY OFAIRBORNE COMMUNICATION NODES

Peter H. WuMIT Lincoln Laboratory

244 Wood St. Lexington, MA 02420wu@ll.mit.edu

ABSTRACTSatellite links are essentialfor an airborne communicationnode to maintain connectivity to the Global InformationGrid (GIG) infrastructure. Satellite links may not alwaysbe available due to the limited antenna scanning capabilityand the aircraft's maneuvering. Link outage can bealleviated by increasing the scanning capability, whichmay be realized by placing more antennas on the aircraft.This leads to several important questions in the systemdesign. in order to keep the links highly available, howmany antennas are needed? How much scanningcapability of each antenna is required? And where shouldthese antennas be installed on the aircraft? In this paper,we propose a novel analysis approach to address theseissues. The analysis is based on the aircraft-centricgeometric framework. The link availability is computedand averaged over all the aircraft locations, which areassumed uniformly distributed in the earth coveragefootprint of a geostationary satellite. The analysis alsoprovides guidelines to configure the antennas for thedesired link availability.

1 INTRODUCTION

In the GIG vision, airborne nodes play an important roleto relay the theater information back to the CONUS. Inthe relay path, the links between the airborne nodes andthe satellite need to be well maintained because linkoutage often imposes threats to time critical operations.

One misconception about link outage is that the link isblocked by the wings as the aircraft maneuvers. This istrue only if the antenna can look beneath the wing. Ingeneral, the antenna looks above the horizon, i.e., the lookangle (elevation angle) is greater than zero. Therefore, asillustrated in Figure 1 that as the aircraft banks, the link isout because the satellite is not in the antenna's view, notbecause of the wing blockage. Throughout the paper, we

This work was sponsored by the Department of the Air Force underAF Contract FA8721-05-C-0002. Opinions, interpretations,conclusions, and recommendations are those of the authors and are notnecessarily endorsed by the United States Government.

assume that the antenna's look (elevation) angle is alwaysgreater than zero.

The most straightforward way to determine the linkavailability is to simulate an aircraft flying along a specificrace track, at a specific location on the earth, with multipleantennas of specific system parameters. The simulationmay require the use of a complex software package, suchas Satellite Tool Kit, and will take much effort to cover allpossible cases. Therefore, it is motivated to have a quickand simple analysis for the link availability problem. Witha few reasonable assumptions, the methodology proposedin this paper is able to provide accurate results withouttremendous simulation efforts. The methodology isgeneral and flexible that it can be extended to differentoperational scenarios.

The paper is organized as follows. A novel linkavailability analysis is proposed in Section 2, where themethodology aimed to evaluate the average linkavailability is described and illustrated in detail.Extensions of the methodology to some operationscenarios are considered. In Section 3 the analysis isapplied to the systems with one or multiple antennas.Average link availability is evaluated and systemparameters are selected according to the results. Section 4concludes the analysis and results.

Figure 1: Link outage is due to the satellite being out ofthe antenna view, not due to the wing blockage.

2 METHODOLOGY

Here we propose an "aircraft-centric" view of theproblem. Instead of having a stationary satellite and amoving aircraft, we fix the aircraft's location and let thesatellite move. Figure 2 illustrates the concept. In Figure

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2(a) the airplane is positioned at three locations that givethe elevation angles OEL=00, 450, and 900, respectively.The airplane will have these elevation angles when it is atany position along the corresponding dashed-linesindicated in this figure. Equivalently, using the aircraft-centric viewpoint, these "equal elevation lines" can betranslated into the satellite orbiting paths on theGeostationary Hemisphere (GH) as depicted in Figure 2(b).

(b)Figure 2: (a) Satellite-centric view vs. (b) Aircraft-centric view. In the aircraft-centric view, the satellite isorbiting on the Geostationary Hemisphere.

Now consider the antenna scanning characteristic andthe link availability in the context of the aircraft-centricview. The antenna's scanning capability can becharacterized by a scanning cone; the beam can be steeredto any angle within the cone. Looking down from the topof the GH, we see a scanning cone projection on the GH,which is termed the Scanning Field of View (SFOV) in thepaper. The link availability can be computed by thepercentage that the satellite comes across the SFOV.Figure 3 illustrates this concept with one scanning antenna.The SFOV rotates as the aircraft changes its heading, butthe SFOV does not shift as shown in Figure 3(a). As theaircraft makes turns, it often banks and the SFOV shiftsaccording to the bank angle as shown in Figure 3(b).Through out this paper, we consider the aircraft's bankingas rolling, i.e., the bank angle is the roll angle.

Suppose that the aircraft travels along a circular racetrack, its heading would change from 00 to 3600 whencompleting the race track, and the SFOV will rotate by thesame amount. To demonstrate how the satellite is coveredby the SFOV, we consider an aircraft flying throughout therace track with banking; the motion of the SFOV is shownin Figure 4. As the aircraft flies along the race track, thesatellite will be in and out of the SFOV as shown. Again,from the aircraft-centric view, the aircraft is fixed and thesatellite is traveling along a circle. The link availabilitycan be calculated by the arc length within the SFOVdivided by the circumference, as shown in Figure 5.

SFOV -*

(a)

(b)Figure 3: (a) As the aircraft changes its heading, theSFOV rotates. (b) As the aircraft banks, the SFOVshifts. The SFOVs viewed from the top of the GH arethe yellow shaded area shown on right.

An important assumption is made here: the race track issmall enough that as the aircraft travels along the racetrack, the SFOV only shifts insignificantly, and the majormotion of the SFOV is rotation. This assumption issupported by the nominal operation for which the racetrack is likely to be within 100 miles in diameter. In suchcase, the traveling of the aircraft from one end to the othercauses only 1.40 difference in latitude. From the GHviewpoint, the SFOV is shifted only by this amount. Sincethis shift is insignificant compared to that caused bybanking, it is reasonable to assume that the SFOV onlyundergoes a rotation during the aircraft's flight along therace track.

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mapped into the PDF of the satellite location on the GH,again from the aircraft-centric viewpoint. If the PDF ofthe satellite location can be described as a function of theelevation angle, the average link availability (ALA) can beobtained by integrating the LAP over the PDF:

ALA = f LAP (0) foL (0) dO (1)

where 0 is a value of OEL, the elevation angle.

Figure 4: The motion of the SFOV as the aircraft fliesalong a race track. The race track is shown on theupper right corners. Note that when SFOV covers thesatellite, the link is available; the link is out otherwise.

Figure 5: The link availability is calculated as the ratioof the intersection of the satellite's traveling path andthe SFOV (shown by the solid arc) with respect to thecircumference.

Based on the assumption and the aircraft-centric view,the link availability is easy to calculate just compute theratio of the arc covered by the SFOV with respect to thecircumference. Since different aircraft locations givedifferent elevation angles, which in turn vary the linkavailability as demonstrated in Figure 6. The circlerepresents the satellite traveling path on which the aircraftwill have the same elevation angle. From the top view ofthe GH, the outmost circle corresponds to OEL=0° and theinner circles correspond to higher elevation angles up to900, as depicted in Figure 6. These circles are termed theElevation Contours (ELC) in this paper. As shown inFigure 6, the intersections of the ELCs and the SFOV are

different depending on the elevation angle. Therefore, we

can view the link availability as a function of the elevationangle. This function is termed the link availability profile(LAP).

It is important to know the average link availability over

all possible aircraft locations within the satellite's footprint.Assuming a certain probability distribution function (PDF)of the aircraft location on earth, this PDF can then be

Figure 6: The link availability is evaluated with respectto the elevation angle. For each elevation angle, thesatellite orbits along a corresponding ElevationContour (ELC).

2.1 LAP examples of a two-antenna system

These examples show how the methodology can beapplied to a multiple-antenna system. Figure 7 illustrates a

two-antenna system with its two SFOVs on the GH. Thesatellite location can be described by a vector Vsat,originating from the center of the aircraft to the satellite.The orientation of the antennas defines the SFOV centervectors VI and V2. The angle between V1 (or V2) and thez-axis of the aircraft is called the antenna orientationangle Oant. As the satellite orbits along the ELC, the anglesbetween Vsat and V1, and Vsat and V2 are computed. Thesetwo angles, +j and °2, are compared with the antenna scan

angle Oscan. Note that the scan angle is defined by theangle between the edge and the center of the scanning cone.

If either of the two angles is smaller than the scan angle,the satellite is within the SFOV. The portion of thesatellite within the SFOV determines the link availabilityassociated with the elevation angle of the correspondingELC, and the LAP can be determined. The LAP can vary

from one set of system design parameters to the other. It isalso heavily dependent on the bank angle of the aircraft.Figure 8 shows the LAP for a two-antenna system withoant=450 and Oscan=300, with or without banking (Obank=300or O0).

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location G determines the elevation angle OEL* Theprobability that the elevation angle is greater than 0 equalsto the probability that the satellite is located within thecorresponding spherical cap, i.e.,

Pr{OEL > O} = Pr{Satellite is within the spherical cap}(2)2zTh(OEL 0)

2;Th (OEL 0)

where h is the height of the spherical cap,

h(OEL =0) =RG[1 COc(OEL 0)]

Figure 7: Illustration of evaluating the LAP for a two-antenna system.

LAP for 2-antenna system: O.nt=450 oscan=300

bank=

0 300obank

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08

a 0.64

03

7L- 0.5

0.41

0.3

0.2-

0. 1

(3)

The angle O is the angle between the vectors VCA and VCG.

Now we need to relate the elevation angle 0 with Oc. Thecoordinates of these locations are

A:(O,RE), G:(RGsinO0,RGcosO0), C:(O,O) (4)

The elevation angle 0 and the angle Oc are related by

Co rO+i VAG VAC( RE- RGcosO0, (5)( 2) VAG A (RGSinc) +(RGCosOc -RE)2

Using (2), (3), and (5), the PDF of the satellite location interms of the elevation angle can be evaluated by

foEL (0) d Pr{OEL <O}dOd

{ -Pr{OEL > O}} (6)

The PDF of the elevation angle based on the uniformlydistributed aircraft locations on the earth coveragefootprint is shown in Figure 10. Integrating the LAP withthe elevation angle PDF (6) gives the ALA.

10 20 30 40 50 60Elevation Angle (deg)

70 80 90

Figure 8: The LAP examples of a two-antenna system.The antennas are installed at 450 away from the z-axisof the aircraft body. Each antenna can scan up to 300.The red and blue lines are the LAPs for the aircraftflying with and without banking. The bank angle is 300.

2.2 PDF of sateite location

Assuming the aircraft is uniformly located on the earthcoverage footprint, from the aircraft-centric view it isequivalent to that the satellite is uniformly located on theGH surface. This does not mean that the satellite locationPDF is uniformly distributed with respect to the elevationangle. The satellite location PDF with respect to theelevation angle is shown below. Figure 9 gives thegeometry of the earth and the GH, where A, G, and C arethe aircraft location, the geostationary satellite location,and the earth center, respectively. Let RE be the earthradius and RG the GH radius. RG=6.61RE. The satellite

SphericalCap,/+ s~~~~~~~

GH A:((OX RE)

Z-axis

hR G (R Gsin0C,RGCOSOC)

RG

E

)

)

Figure 9: Geometry for computing the PDF of theelevation angle.

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vector and the z-axis, is the same for all SFOV centervectors. In addition, the projections of the N SFOV centervectors on the azimuth plane are assumed evenly separated.For example, the azimuth separation is 1200 for a three-antenna system, as shown in Figure 11. Theseassumptions help to characterize the antenna installationby just one parameter-- the antenna orientation angle.

10 20 30 40 50 60 70 80 90

Figure 10: The PDF of the elevation angle based on theassumption that the aircraft location is uniformlydistributed within the earth coverage footprint.

2.3 Extension for operational scenarios

This methodology can be extended to differentoperational scenarios. In a scenario where a phased array

antenna is implemented, one should consider the effectivescanning capability with the link margin. The phased array

antenna gain in the pointing direction becomes smallerthan the boresight gain due to the decreasing effectivearray area. The effective array area is proportional toI/cos2(p), where p is the off-boresight angle. If the linkmargin is known, the effective scanning capability can becomputed. For example, if the link margin 3 dB, theeffective scanning capability is 450 even though the phasedarray may be able to scan up to 600. In this case, 45°scanning angle should be considered in calculating theALA.

Some communication scenarios require the minimumelevation angle OmMn for operation. This means the aircraftwill operate only in the areas where the elevation angle isgreater than the requirement. Therefore, the operationregion is smaller than earth coverage footprint. Toevaluate the ALA, one can still apply the methodologywith a modified elevation angle PDF, i.e., Eq(2) should bemodified as

2{OTOh(hOEL- 0)Prlo ~ 2zThQ'EL =

min ) (7)

As discussed in Section 2.1 this methodology can beextended to N antennas, N>1. The angles between thesatellite vector and N SFOV center vectors are computedand compared with the scan angle. There are many ways

to configure the N antennas on the aircraft's body. Tosimplify the analysis, we assume that the antennaorientation angle, Oant, the angle between a SFOV center

Figure 11: Antenna orientation angle for a 3-antennasystem. Assuming even separation in azimuth, theSFOV center vectors can be specified by the antennaorientation angle.

3 RESULTS

As discussed above that the link availability depends on

the following factors: the aircraft location (elevation angle),the aircraft orientation (the bank angle and heading whiletraveling along the race track), the antenna scanningcapability (the scan angle), and the antenna orientation (theantenna orientation angle). We have shown how toaverage the link availability over a race track and over allthe aircraft locations on the earth coverage footprint.Therefore, after averaging, the ALA is a function of threevariables, the bank angle, Obank, the scan angle, Oscan,, andthe antenna angle, Oant. The following results show theeffects of these factors on the ALA. For analysis purposes,

we assume that each antenna has the same scanningcapability in the multi-antenna cases. For the single-antenna system, the antenna is always installed on the topof the aircraft body (Oant0=0). When a particular bankangle is assumed, the aircraft flies with this bank (or roll)angle all the time all along the race track.

Figure 12 shows the ALA for 1 to 4 antennas as a

function of 0ant and Osca11 without banking (Obank=00). Thepurpose is to find out the optimal antenna orientation. Asthe scan angle increases, the ALA approaches to unitydepicted by the red plateau. One can reach higher ALAwith limited scanning capabilities by adjusting the antennaorientation. This means that by installing the antenna on

proper places of the aircraft body, one can relax theantenna scanning requirement, and thus save the cost.

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0.025

0.02 f

0.015

0.01

0.005-

O _0

Using more antennas increases the red plateau area,implying more design choices are available to achieve100% average link availability.

From Figure 12 (b)-(d) the best antenna orientationangle for 2-4 antennas is between 500 and 600. Since thereis not much difference in ALA, we choose 550 forperformance comparison. Figure 13 shows the ALA vs.the scan angle with the optimal antenna angle, Oant=550. Itillustrates that given a scanning capability for each antenna,one can observe the ALA improvements by having moreantennas. On the other hand, given an ALA requirement,one can make a trade off between the number antenna andthe scanning capability. For example, if more than 90% ofALA is required and the phased-array antenna is to beimplemented, the 3-antenna system is the best choice. The2-antenna system is difficult to implement because its scanangle has to be wider than 700. While the 4-antennasystem can meet the requirement with a smaller scan angle,the cost may be an issue.

Based on the same approach, the best orientation angleof 600 is observed for the bank angle of 300. With thisantenna orientation angle, Figure 14 plots the ALA vs. thescan angle. For this bank angle, the single-antenna systemcan never achieve more than 90% link availability, thusmore antennas are needed. Similar to the case of nobanking, there is diminishing return using more than threeantennas. Since these results assume that the aircraft flieswith 300 banking all the time along the race track, theyprovide the lower bound. In reality, if the banking takesa0% of time, one can evaluate the ALA byo% *ALA(Obank=300)+(10-00%)*ALA(Obank=00).

Average Link Availabiliy for 2 antennas at Bank Angle = 0 degMinimum Elevation Angle = 0 deg

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Average Link Availabiliy for 3 antennas at Bank Angle = 0 degMinimum Elevation Angle = 0 deg

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(c) 3 antennas

Average Link Availabiliy for 4 antennas at Bank Angle = 0 degMinimum Elevation Angle = 0 deg

(a) 1 antenna

Figure 12: Average Link Availability as a function ofthe antenna orientation angle and the scan angle. Nobanking. (a) 1 antenna, (b) 2 antennas, (c) 3 antennas,and (d) 4 antennas. The optimal antenna orientationangle is 550 for the multiple antenna cases.

(d) 4 antennas

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05

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03

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0.1

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1 Z

0

Scan Angle (deg)

Antenna Orientationt Angle (deg)

Average Link Availability at Bank Angle = 0 degAntenna Orientation Angle=55 deg sizes and the scanning losses associated with phased arrayMinimum Elevation Angle = 0 deg

0 9 r ~~~~~~~~~~implementation.RrSr fX 09 The analysis can be applied to evaluate the ALA of

0.8 different antenna configurations, including the design07 parameters of the number of antennas, the orientation of06 antennas, and the scanning capability. It is found that for05 multiple-antenna systems, the ALA is optimized when the

antenna boresight is 550 apart from the normal vector (z-,,04 _ ,< X Xa' - axis) of the aircraft. With the optimal antenna orientation030 and the required ALA greater than 90%, the most cost02 X /Aeffective and feasible solution is to use three antennas,O. 1' -e- 2 1Antennas each scans more than 500.

3 Antennas4 Antennas

20 30 40 50 60 70 80 90Scan Angle (deg) 5 ACKNOWLEDGEMENTS

Figure 13: Average link availability vs. the scan angle The author would like to thank Dr. Ron Bauer for valuablefor 1 to 4 antennas. No banking. The optimal antenna discussions on the methodology.orientation angle is 550 for multiple-antenna cases.

Average Link Availability at Bank Angle = 30 degAntenna Orientation Angle = 60 degMinimum Elevation Angle = 0 deg

0.9 _

08

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06

05

0.4-

03 /

0.21 Antenna

01e 2 Antennas-3 Antennas

C' 4 Antennas

20 30 40 50 60 70 80 90Scan Angle (deg)

Figure 14: Average link availability vs. the scan anglefor 1 to 4 antennas with 300 banking. The optimalantenna orientation angle of 600 is assumed.

4 CONCLUSIONS

In this paper we propose a novel analysis on theavailability of a communication link between an airbornenode and a geostationary satellite. Instead of evaluatingthe link availability associated with a race track at aparticular location, the analysis evaluates average linkavailability (ALA) over a race track and all locationswithin the earth coverage footprint. The analysis isaccurate for small race tracks with the radius less than 100miles. The analysis can be easily extended to variousrealistic operational scenarios, such as different footprint

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