How Many GNSS Satellites areToo Many?

GRACE XINGXIN GAO, Member, IEEEUniversity of Illinois at Urbana—Champaign

PER ENGE, Fellow, IEEEStanford University

Global Navigation Satellite Systems (GNSS) are growing

from the current US GPS and Russian GLONASS to additional

European Galileo and Chinese Compass systems. Along with

the growth of the systems, the number of satellites will also

increase. The whole family of GNSS is projected to consist of

about 120 satellites by 2030. Moreover, the new satellites are

capable of transmitting multiple signals in multiple frequency

bands. Altogether there will be more than 300 GNSS signals

broadcast in the future.

The growing number of GNSS satellites and signals enable

greater redundancy for positioning. On the other hand, the

signals interfere with each other due to overlapping frequency

bands. Here we answer the question: how many satellites are

too many? We assess the self-interference within GNSS, and

hence establish their multiple access capacity, by examining

the code interactions between satellites. This analysis considers

cross-correlation properties of the codes at all possible Doppler

frequency offsets between satellites. We first approach the

question theoretically by calculating auto- and cross-correlation

properties of random sequences with binary phase shift keying

(BPSK) modulation and binary offset carrier (BOC) modulation.

With the theoretical result of pure random sequences as a

guideline, we then use real broadcast pseudorandom noise (PRN)

codes of the current Galileo GIOVE and Compass-M1 satellites

to further analyze various correlation properties over a range of

Doppler frequency offset. We ultimately establish the multiple

access capacity of GNSS.

Manuscript received November 26, 2010; revised July 25, 2011;released for publication August 18, 2011.

IEEE Log No. T-AES/48/4/944178.

Refereeing of this contribution was handled by M. Braasch.

Authors’ address: GPS Lab, Stanford University, 496 Lomita Mall,Stanford, CA 94345, E-mail: (gracegao@stanford.edu).

0018-9251/12/$26.00 c° 2012 IEEE

I. INTRODUCTIONGlobal Navigation Satellite Systems (GNSS) are

experiencing a new era. Until now, there have beenonly two operational systems, the United States’Global Positioning System (GPS) [1] and Russia’sGLONASS [2]. The original satellites of both systemseach transmitted just a single civil signal in onefrequency band.In recent years the significance and value of

global satellite navigation has been recognized bymore countries. In particular, the European Unionis developing their Galileo system [3]. The first twotest satellites of the Galileo system, Galileo In-OrbitValidation Elements, GIOVE-A and GIOVE-B, werelaunched on December 28, 2005 [4, 5], and April 27,2008 [6], respectively.China was involved in the initial stages of Galileo

[7], but later began development of its own system,Compass [8]. The first, and so far, only mediumEarth orbit (MEO) satellite of the Compass system,Compass-M1 was launched on April 14, 2007 [9].At full development, the Galileo and Compass

systems are intended to have about 27 and 35satellites, respectively. As shown in Table I, the wholefamily of GNSS is projected to consist of about 120satellites by 2030. Moreover, the new satellites arecapable of transmitting multiple signals in multiplefrequency bands. Altogether there will be more than300 GNSS signals broadcast in the future. The GNSSworld is growing from a couple of dominant playersto four complete systems, from 32 satellites to about120 satellites, and from simple signals to an array ofcomplicated signals.

TABLE IGNSS Past, Present and Future, MEO Satellites Only

Nation System 2002 2010 2030

USA GPS 24 satellites 31 satellites » 31 satellitesEU Galileo – 2 satellites » 27 satellitesChina Compass – 1 satellite » 27 satellitesRussia GLONASS 8 satellites 26 satellites » 24 satellites

Total 32 satellites 60 satellites » 120 satellites

Named after the Italian astronomer, Galileo Galilei,the Galileo system is the planned European GNSS.The 3.4 billion euro project is a joint initiative of theEuropean Commission (EC) and the European SpaceAgency (ESA). It is an alternative and complementarycounterpart to the current GNSS, such as the U.S.GPS and the Russian GLONASS. The Galileo systemaims to provide a highly accurate, guaranteed globalpositioning service under civilian control [10]. Whenfully deployed, the Galileo system will have 30satellites in MEO at an altitude of 23222 km. Therewill be three orbital planes inclined at an angle of 56±

to the equator. Ten satellites will occupy each orbital

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 48, NO. 4 OCTOBER 2012 2865

plane. Nine of them will be operational satellites andone spare for failover redundancy [11]. The Galileosystem is a code division multiple access (CDMA)system [12]. All the Galileo satellites will share thesame nominal frequency but with different spreadspectrum codes to identify themselves.The first test satellite of the Galileo system,

GIOVE-A (Galileo In Orbit Validation Element-A)was launched on December 28, 2005. It secures theGalileo frequencies allocated by the InternationalTelecommunication Union (ITU) and also testscertain Galileo satellite components [5]. GIOVE-Astarted to broadcast Galileo signals on January12, 2006. GIOVE-A is capable of transmittingon two frequencies at once from an availableset of L1 (1575.42 MHz), E5 (1191.80 MHz),and E6 (1278.75 MHz) bands. The E5 bandhas two sub-bands, E5a (1176.45 MHz) andE5b (1207.14 MHz) band. GIOVE-A was firstbroadcasting on L1 and E6 bands. Based on ourobservation, it switched to L1 and E5 bands in August2006 for a few weeks and switched back to L1 andE6 frequencies in September 2006. Since October25, 2006, it has been again transmitting on L1 andE5 bands.The Compass navigation satellite system (CNSS),

which is also known as Beidou II, is China’s entryinto the realm of GNSS. The current design plansfor 27 MEO satellites, 5 geostationary orbit (GEO)satellites, and 3 inclined geosynchronous satellite orbit(IGSO) satellites. The MEO satellites will operatein six orbital planes to provide global navigationcoverage [8]. Compass will share many featuresin common with GPS and Galileo, providing thepotential for low-cost integration of these signals intocombined GPS/Galileo/Compass receivers. Thesecommonalities include multiple frequencies, signalstructure, and services.The Compass-M1 satellite, launched on April 14,

2007, represents the first of the next generation ofChinese navigation satellites and differs significantlyfrom China’s previous Beidou navigation satellites.Those earlier satellites were considered experimental,and were developed for two-dimensional positioningusing the radio determination satellite service (RDSS)concept pioneered by Geostar [13]. Compass-M1 isalso China’s first MEO navigation satellite. Geostarwas based on two-way ranging, whereas Compass-M1is based on one-way pseudoranging. Previous Beidousatellites were geostationary and only providedcoverage over China. The global implications of thissatellite and the new GNSS it represents make thesatellite of great interest to navigation experts.Compass will provide two services: an

open civilian service and a higher precisionmilitary/authorized user service [8]. Compass-M1satellite currently broadcasts in three frequency bandsknown as E2, E6, and E5b [9]. Table II provides

Fig. 1. Frequency occupation of GPS, Galileo and Compass,adapted from [9].

TABLE IICompass-M1 Broadcast Frequencies

Frequency Band Center Frequency (MHz)

E2 1561.10E6 1268.52E5b 1207.14

center frequencies of the signal transmission bands.Figure 1, adapted from [9], shows the overlap infrequency of the Compass signals with those of GPSand Galileo. Like GPS and Galileo, the Compassnavigation signals are CDMA signals. They use binaryor quadrature phase shift keying (BPSK, QPSK,respectively) [1].The growing number of GNSS satellites and

signals enable greater redundancy for positioning. Onthe other hand, the signals interfere with each otherdue to overlapping frequency bands. In this paperwe answer the question: how many satellites are toomany? The previous satellite capacity study of the USGPS system is based on BPSK modulation. However,the signals of the new GNSS such as Galileo andCompass use binary offset carrier (BOC) in additionto BPSK modulation. We begin by introducing BOCmodulation in Section II. We conduct theoreticalanalysis for auto- and cross-correlation properties ofrandom sequences with BPSK and BOC modulationsin Section III. Next we study various properties ofthe GIOVE and Compass pseudorandom noise (PRN)codes across Doppler frequency offset from ¡10 KHzto 10 KHz. As GIOVE-A and GIOVE-B codes aresimilar, for brevity, we only show the results forGIOVE-A. We ultimately establish the multiple accesscapacity of GNSS in Section VI, and conclude thepaper in Section VII.

II. BINARY OFFSET CARRIER

The GPS L1 coarse acquisition (C/A) signal usesBPSK modulation [1], in which the PRN code chipshape is a square wave. So do the Galileo civiliansignals in E6, E5a, and E5b bands [14]. In contrast,

2866 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 48, NO. 4 OCTOBER 2012

Fig. 2. PRN code chip with BPSK and BOC(1,1) modulation,respectively. BOC(1,1) coding is same as Manchester coding [16].

Fig. 3. Spectrum of BPSK and BOC(1,1) modulation.

Galileo L1 signals use BOC modulation [14]. TheBOC modulation was originally devised by Spilker,et al. [15], and named split spectrum modulation asa generalization of Manchester coding [16]. LaterBetz, et al. called it BOC modulation or BOC coding[17, 18]. In BOC(n,m) modulation, the PRN codechip shape is a square subcarrier of frequency nmultiples of 1.023 MHz, where the BPSK chip rateis m multiples of 1.023 MHz [19]. The Galileo openservice signal in L1 band has BOC(1,1) modulation.Figure 2 compares a PRN code chip of the GPS L1C/A signal using BPSK modulation with the GalileoL1 signal using BOC(1,1) modulation. The chipshapes in Fig. 2 are theoretical, infinite bandwidthrepresentations, which do not take filtering intoaccount.A feature of BOC modulation is that it splits the

spectrum from one mainlobe in the middle into twosidelobes as shown in Fig. 3. The dashed curve showsthe GPS C/A signal with BPSK modulation, while thesolid curve is the Galileo L1 signal with BOC(1,1)modulation. Although GPS and Galileo share the sameL1 frequency band, the split spectrum of the GalileoBOC(1,1) signal mitigates interference with the GPSL1 signal by using different spectral occupation.BOC modulation also increases the Gabor

bandwidth [2, 20] by pushing the signal energyto the edges of the bandwidth. This has the effectof sharpening the correlator peak. Figure 4 showsthe correlation function of BPSK and BOC(1,1)modulation. The sharper correlation peak improves

Fig. 4. Correlation function of BPSK and BOC(1,1) modulation.

tracking sensitivity, but the side peaks may confusethe receiver tracking loops in noisy environments.

III. CORRELATION PROPERTIES OF RANDOMSEQUENCES

The auto- and cross-correlations of the PRNcodes determine their system’s robustness to noiseand interference. In a noisy environment, theauto-correlation side peaks or the cross-correlationpeaks with other PRN codes can exceed the mainauto-correlation peak and thus confuse receiveracquisition and tracking loops. In this section weanalyze the statistical correlation properties of randomsequences, modulated by BPSK and BOC(1,1). LetX = (x1,x2, : : : ,xN) and Y = (y1,y2, : : : ,yN) be sequencesof N independent and identically distributed (IID)random variables, taking values §1 equiprobably.Note that this section focuses on theoretical analysisof ideal random sequences. In reality, the PRN codesequences are pseudo random. We show the resultsof current broadcast Galileo and Compass codes inthe next section. Moreover, the codes are quantizedand passed through band-limited filters in practicalsystems.

A. Auto-Correlation of BPSK Random Sequence

Suppose that X is modulated by BPSK with chipduration Tc, so that the overall period of the codeTcode =NTc. The auto-correlation RX(t) of this signalhas the following properties, derived in [1]: RX(0) = 1deterministically and RX(iTc) (where i 6= 0) has mean0 and variance 1=N. The mean and variance of thisauto-correlation are plotted in Figs. 5 and 6. Note that,between integer multiples of Tc, the mean and varianceare linear [1]. Since the auto-correlation mean is zeroaway from the main peak, the variance characterizesthe robustness of a random sequence used as a PRNcode. Reducing the variance away from the main peak(by increasing the length N) improves the likelihoodthat the main peak will be found by the receiver.

B. Cross-Correlation of BPSK Random Sequences

Now suppose that X and Y are both modulatedby BPSK. The mean of the cross-correlation RXY(t)is 0, since the sequences are IID and zero mean. Wenow derive the cross-correlation variance at integermultiples of the chip duration Tc.

GAO & ENGE: HOW MANY GNSS SATELLITES ARE TOO MANY? 2867

Fig. 5. Auto-correlation mean of random sequence of length Nwith BPSK modulation.

Fig. 6. Auto-correlation variance of random sequence of lengthN with BPSK modulation.

Ef(RXY(iTc)¡EfRXY(iTc)g)2g= Ef(RXY(iTc)2g

=T2cT2code

E

(N¡1Xm=0

xmym+i

N¡1Xn=0

xnyn+i

)

=1N2

N¡1Xm=0

N¡1Xn=0

Efxmxnym+iyn+ig

=1N

(1)

since

Efxmxnym+iyn+ig=½1 if m= n

0 otherwise: (2)

The cross-correlation variance is plotted in Fig. 7, andits value is the same as the auto-correlation varianceaway from the main peak.

C. Cross-Correlation of BOC(1,1) and BPSK RandomSequences

The BPSK cross-correlation variance characterizesthe level of self-interference within the GPS system.However, the Galileo L1 signal uses BOC(1,1)modulation. So, we now consider the cross-correlationbetween BOC(1,1) and BPSK random sequences.Suppose that X is modulated by BOC(1,1) to producethe signal XBOC(t) and that Y is modulated by BPSK

Fig. 7. Cross-correlation variance of random sequences of lengthN, both modulated by BPSK.

Fig. 8. Illustration of BOC modulated random sequence XBOC(t)and BPSK modulated random sequence Y(t).

to produce the signal Y(t), as illustrated in Fig. 8.We represent XBOC(t) as X1(t) +X2(t), where X1(t)captures the first halves of the chips and X2(t)captures the second halves of the chips.As in the case of BPSK cross-correlation, the

cross-correlation mean is zero since the randomsequences are IID and zero mean. The cross-correlation variance is

Ef(RXY(t))2g

= E

(μ1Tcode

Z Tcode0

XBOC(t)Y(t¡ ¿)d¿¶2)

= E

(μ1Tcode

Z Tcode0

X1(t)Y(t¡ ¿) +X2(t)Y(t¡ ¿)d¿¶2)

:

(3)When the signals are offset by an integer multipleof Tc, the chips of X1(t) cancel out the chips of X2(t)within each chip duration of Y(t). So, the variancebecomes

Ef(RXY(iTc))2g

=(Tc=2)

2

T2codeE

8

Fig. 9. Variation of cross-correlation of random sequences oflength N, BOC(1,1) versus BPSK.

Fig. 10. Cross-correlation variance of random sequences oflength N , both modulated by BOC(1,1).

When the signals are offset by an additional half achip, the correlated chips of X1(t) and X2(t) overlapdifferent chips of Y(t). The variance is

Ef(RXY((i+ 12 )Tc))2g

=(Tc=2)

2

T2codeE

8

Fig. 11. Maximum correlation sidelobes of GIOVE-A L1 codeauto-correlation.

Fig. 12. Maximum correlation sidelobes of GIOVE-A E6 codeauto-correlation.

TABLE VMaximum Sidelobes of Compass-M1 Auto-Correlation

Auto-Correlation SidelobeCompass-M1 Code Sidelobes (dB) Variance (dB)

E2/E5b ¡23:68 ¡33:11E6 ¡29:83 ¡40:10

two periods of the B codes are used to accommodatethe C code lengths. Table V shows the Compass-M1maximum auto-correlation sidelobes. We also comparethe maximum auto-correlation sidelobes with randomcode sidelobe variances as computed in the previoussection. Sidelobe variance represents an averagebehavior, while maximum auto-correlation sidelobeis the worst case. It is shown that the worst caseself-interference is about 10 to 12 dB higher than theaverage case.Doppler residuals always exist in satellite signals.

This causes frequency offset between the incomingsignal and the local replica. Therefore, we needto investigate the correlation performance notonly at zero frequency, but also at all frequencyoffsets ranging from ¡10 KHz to 10 KHz. The

Fig. 13. Max correlation sidelobes of GIOVE-A E5a codeauto-correlation.

Fig. 14. Maximum correlation sidelobes of GIOVE-A E5b codeauto-correlation.

auto-correlation performance of the GIOVE-A L1,E6, E5a, and E5b codes is shown in Figs. 11—14. Theauto-correlation performance of the Compass-M1E2/E5b and E6 codes is shown in Fig. 15. In thesefigures the decibel values are referenced to thecorrelation main peak value. For the GIOVE-AL1 and E6 bands, the C codes have 3 dB betterperformance than the B codes, since the C codesare twice as long as the B codes. The Compass E6code has roughly 7 dB better performance than theCompass E2/E5b code, because the length of the E6code is 5 times that of the E2/E5b code.

V. CROSS-CORRELATION BETWEEN SYSTEMS

The Galileo L1 band overlaps with that of GPS,and the Galileo E5b band overlaps with that ofCompass as described in Section I. When acquiringor tracking a Galileo signal, the signals from othersatellites in the same frequency bands behave asinterference. In return, the Galileo signals in thecommon frequency bands also interfere with otherGNSS systems. The coexistence of Galileo andeither GPS or Compass is characterized by thecross-correlation functions between the GIOVE-A

2870 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 48, NO. 4 OCTOBER 2012

Fig. 15. Maximum correlation sidelobes of Compass E2/E5b andE6 code auto-correlation.

PRN codes and the GPS or Compass PRN codes. Inaddition, since the satellites are orbiting, the relativevelocity between two satellites results in a frequencyoffset between the PRN code of one incoming satellitesignal and the PRN code of the local replica ofanother satellite. This frequency offset ranges from¡10 KHz to 10 KHz.Figure 16 shows the maximum sidelobes of

cross-correlation between the GIOVE-A and GPSPRN codes in L1 band. Since there are 32 PRN codesassigned for the GPS L1 C/A signal, the maximumsidelobe is plotted among all 32 correlation functionsat each frequency offset. BOC modulation of theGIOVE-A signal is considered, and the GPS C/Acodes are repeated 4 and 8 times to accommodatethe length of the GIOVE-A L1-B and L1-C codes,respectively. The performance of the L1-B code is3 dB worse than that of the L1-C code, because theL1-B code is half the length of the L1-C code.The maximum sidelobes of cross-correlation

between the GIOVE-A and Compass PRN codes inE5b band is shown in Fig. 17.

VI. MULTIPLE ACCESS CAPACITY OF GNSS

Although the new satellites and signals providegreater redundancy for positioning, it is not always acase of “the more, the merrier.” The previous sectionshowed that the GNSS satellites interfere with eachother, because they share frequency bands. Whena receiver processes the signal from a particularsatellite, other visible satellite signals contribute tothe correlation sidelobes. If there are too many visiblesatellites, the correlation side peaks may exceedthe main peak, confuse the receiver, and cause thepositioning to fail.Beyond what number of satellites would a

receiver fail? The question is not easy to answer,because receiver performance depends on a varietyof parameters, such as integration time, coherentor noncoherent integration, receiver filters, lowernoise amplifier (LNA) noise figure, etc. We choose

Fig. 16. Maximum sidelobes of cross-correlation betweenGIOVE-A L1 codes and GPS codes.

Fig. 17. Maximum sidelobes of cross-correlation betweenGIOVE-A E5b codes and Compass E5b code.

Fig. 18. Received C/A code signal power available from isotropicantenna as function of elevation angle for user on surface of the

Earth [1].

to measure the level of the satellite self-interferencerelative to the thermal noise floor. This metric is thusgeneral and independent of receiver design.The GNSS satellite transmission power is

estimated based on GPS transmission power andthe similarity among the GPS, Galileo and Compasssystems. The GPS L1 C/A signal power available

GAO & ENGE: HOW MANY GNSS SATELLITES ARE TOO MANY? 2871

Fig. 19. Commercial L1 antenna gain pattern. Predicted patternfor standard patch antenna mounted on four-wavelength-diameter

circular ground plane (Courtesy of Frank Bauregger,Novariant, Inc.).

Fig. 20. Received C/A code signal power subject to gain ofpatch antenna.

from an isotropic antenna is shown in Fig. 18. Thepower is not flat over the whole range of elevationangles in order to accommodate nonisotropic patchantenna gains. Patch antennas are the most popularantenna for commercial receivers due to their lowcost and small size. Therefore, we use patch antennapattern in our analysis. Note that better choices ofantennas can improve interpretability. For instance,directional antennas suppress the interference fromother satellites in view by pointing the antenna to thetarget satellite. An example of a patch antenna gainis shown in Fig. 19. It reaches a maximum towardszenith, an elevation of 90±. The received GPS L1signal power, shown in Fig. 20, is roughly flat from20± to 160±, after being subject to the commercialpatch antenna gain.To model the interference, we assume that GNSS

satellites are uniformly distributed around the Earth.We also assume that the PRN codes are randomsequences. According to our discussion in Section III,correlation sidelobe variance is upper bounded by10log10 1=N dB for both BPSK and BOC(1,1)

Fig. 21. Average-case multiple satellite self-interference, L1 band.

Fig. 22. Average-case multiple satellite self-interference, L5 band.

modulation, where N is the code sequence length.We use the upper bound for our computations fortwo reasons. First, we consider up to 2000 satellites inthe future, and it is uncertain how many of them willuse BOC(1,1) and how many use BPSK modulation.Second, for a GPS L1 receiver with sampling rate1.023 MHz, the incoming Galileo L1 BOC signal isdown sampled and appears to be BPSK modulated.We compare the satellite self-interference with

thermal noise floor, for which we use the value of¡201 dB/Hz in this paper. We believe comparing theinter-satellite interference with thermal noise flooris a reasonable metric. Most mass market receiversusing low-cost antennas can still function with 3 dBof SNR loss. More importantly, signals from differentnavigation satellites are not only competitive, but alsocooperative. Although some high-precision surveyreceivers can tolerate only small increase of thenoise floor, there are algorithms to take advantage ofthe cooperative nature of the signals from differentsatellites, such as vector lock loops [2].Figures 21 and 22 show the average-case GNSS

satellite self-interference power level with respect

2872 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 48, NO. 4 OCTOBER 2012

to the thermal noise power level. We first considerthe case where the new satellites will have the sameradiated power as the current satellites, and plot theinterference as the blue solid curves. In L1 band,the satellite self-interference power reaches that ofthermal noise when there are 329 GNSS satellites.In L5 band, the self-interference power will notexceed the noise floor until there are 817 GNSSsatellites. The L5 band can tolerate a larger numberof satellites than the L1 band, because the L5 bandis 10 times as wide as the L1 band. When bothGalileo and Compass systems are fully deployed,there will be about 120 satellites. Even for L1 band,the self-interference then is still 4.5 dB below thethermal noise power level. So, we conclude that 120satellites can coexist if their transmitted power is thesame as current GPS satellites. If the radiated powerof the satellites is increased by 3 dB or 6 dB, theirinterference is shown as the magenta dashdot or theblack dashed curves, respectively. For L5 band, evenif the new satellites transmit 6 dB more power, thesatellite self-interference power still will not reach thethermal noise floor until there are as many as 204satellites. However, in the L1 band, we only need82 satellites to have the satellite self-interferencepower exceed the noise floor, if the new satellitesare 6 dB more powerful. Hence, we have to becareful when designing more powerful new GNSSsatellites.

VII. CONCLUSION

We analyzed GNSS PRN code properties withrespect to correlation. We presented theoreticalvariation of cross-correlation of random sequenceswith BPSK or BOC modulation. With the theoreticalperformance of pure random sequences as a guideline,we also evaluated the correlation performance ofbroadcast PRN codes of the current Galileo andCompass systems at different frequency offsets.We also studied the self-interference among theGNSS satellites with respect to the number of GNSSsatellites, and compared with the thermal noise levelfor both GPS L1 and L5 bands. When Galileo andCompass are completely deployed, we conclude thatthe total 120 navigation satellites from all GNSSsystems can coexist if the radiated power of the newsatellites remains the same as that of the currentsatellites. Special care and consideration towardssatellite interoperability and coexistence need to betaken if designing new satellites with more radiatedpower.

REFERENCES

[1] Misra, P. and Enge, P.Global Positioning System: Signals, Measurements, andPerformance.Lincoln, MA: Ganga-Jamuna Press, 2006.

[2] Parkinson, B. W. and Spilker, Jr., J. J.Global Positioning System: Theory and Applications.Reston, VA: AIAA, 1996.

[3] Hein, G. W. and Wallner, S.Development and design of Galileo.In Proceedings of the ION Annual Meeting, Cambridge,MA, June 2005.

[4] First Galileo satellites named ‘GIOVE.’ESA Press Release, Nov. 9, 2005.

[5] Amos, J.Europe launches Galileo satellite.BBC News, Dec. 28, 2005.

[6] ESA’s most advanced navigation satellite launched tonight.ESA Press Release, Apr. 27, 2008.

[7] China’s state company obtains contract to develop Galileotechnologies.People’s Daily, Mar. 30, 2005.

[8] China to build global satellite navigation system.People’s Daily, Apr. 16, 2007.

[9] Grelier, T., et al.Initial observations and analysis of Compass MEOsatellite signal.Inside GNSS, (May/June 2007).

[10] Benedicto, J., et al.GALILEO: Satellite system design and technologydevelopments.ESA Documentation, July 17, 2007.

[11] How to build up a constellation of 30 navigation satellites.ESA Documentation, July 17, 2007.

[12] Hein, G. W., et al.Galileo broadcast E5 codes and their application toacquisition and tracking.In Proceedings of the ION GPS Conference, Portland, OR,Sept. 2002.

[13] Bian, S. Z. F. and Jin, J.The Beidou satellite positioning system and itspositioning accuracy.Navigation, 52, 3 (2005).

[14] GIOVE-A navigation signal-in-space interface controldocument.ESA Galileo Documentation, Nov. 2000.

[15] Spilker, Jr., J. J., Martin, E., and Parkinson, B. W.A family of split spectrum GPS civil signals.In Proceedings of the 11th International Technical Meetingof the Satellite Division of the Institute of Navigation (IONGPS), Nashville, TN, Sept. 1998.

[16] Spilker, Jr., J. J.Digital Communications by Satellite (Prentice-HallInformation Theory Series).Upper Saddle River, NJ: Prentice-Hall, 1977.

[17] Betz, J. W.A note on offset carrier signals.MITRE Product MP98B14, Mar. 1998.

[18] Betz, J. W.The offset carrier modulation for GPS modernization.In Proceedings of the ION NTM Conference, San Diego,CA, Jan. 1999.

[19] Pratt, A. R. and Owen, J. I. R.BOC modulation waveforms.In Proceedings of the ION GPS Conference, Portland, OR,Sept. 2003.

[20] Weill, L. R.Multipath mitigation, how good can it get with newsignals?GPS World, (June 2003).

[21] Gao, G. X.Towards navigation based on 120 satellites: Analyzing thenew signals.Ph.D. Thesis, Stanford University, 2008.

GAO & ENGE: HOW MANY GNSS SATELLITES ARE TOO MANY? 2873

Grace Xingxin Gao (M’08) received her B.S. degree in mechanical engineeringin 2001 and her M.S. degree in electrical engineering in 2003, both at TsinghuaUniversity, China. She obtained her Ph.D. degree in electrical engineering atStanford University in 2008.Dr. Gao is an Assistant Professor of Aerospace Engineering at the University

of Illinois at Urbana—Champaign. She was a research associate in the GPS labof Stanford University from 2008 to 2012. Her current research interests includeGPS integrity, GNSS modernization, and GNSS receiver architectures.

Per Enge (F’04) received his Ph.D. from the University of Illinois.He is a Professor of Aeronautics and Astronautics at Stanford University,

where he is the Kleiner-Perkins, Mayfield, Sequoia Capital Professor in theSchool of Engineering. He directs the GPS Research Laboratory, which developssatellite navigation systems based on the Global Positioning System (GPS). Hehas been involved in the development of Federal Aviation Administration’s GPSWide Area Augmentation System (WAAS) and Local Area Augmentation System(LAAS) for the FAA.Professor Enge has received the Kepler, Thurlow, and Burka Awards from the

Institute of Navigation. He is a Member of the National Academy of Engineeringand a Fellow of the Institution of Navigation.

2874 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 48, NO. 4 OCTOBER 2012