GPS Solutions

, Volume 17, Issue 4, pp 499–510 | Cite as

On the distribution of GPS signal amplitudes during low-latitude ionospheric scintillation

  • Alison de Oliveira MoraesEmail author
  • Eurico Rodrigues de Paula
  • Waldecir João Perrella
  • Fabiano da Silveira Rodrigues
Original Article


Ionospheric scintillations are fluctuations in the phase and/or amplitude of trans-ionospheric radio signals caused by electron density irregularities in the ionosphere that affect the performance of Global Navigation Satellite Systems receivers. We used an entire month of high-rate (50 Hz) measurements of the GPS L1 (1.575 GHz) signal amplitude to investigate the statistics of L-Band signals during ionospheric scintillation events. The scintillation measurements used in this study were made by a GPS-based scintillation monitor installed in Sao Jose dos Campos, Brazil, near the equatorial anomaly peak. The observations were made over 32 days during high solar flux conditions when typical values of F10.7 were above 150 × 10−22 W/m2/Hz. This data set allowed us to test the Nakagami-m and Rice probability density functions (PDFs) in the description of the distribution of L-Band scintillating signals with better statistical confidence than previously possible. In addition, we parameterized and tested the ability of the α–μ distribution, which is a more general and yet simple and flexible fading model to describe the distribution of signal amplitudes during scintillation events. The results show a slight advantage of the Nakagami-m PDF over the Rice distribution. We also show that the α–μ PDF outperforms the Nakagami-m and Rice PDFs in the statistical characterization of amplitude scintillation. The reason for such a performance is the fact that the α–μ model was specially tailored to the ionospheric scintillation events, resulting in a better fit with experimental data, specifically in the region of small amplitudes, which is particularly interesting for scintillation studies.


Ionospheric scintillation α–μ distribution Fading distributions Propagation channel modeling 



The authors are grateful to Prof. Michel D. Yacoub from Universidade Estadual de Campinas (UNICAMP) for the discussions concerning the application of the α–μ model. AOM wishes to thank the Brazilian Institute of Aeronautics and Space (IAE), where he works as a research engineer, for supporting and assisting his doctoral studies at ITA. FSR would like to thank the support from NSF through Award AGS-1024849, which allowed this collaborative work with INPE and IAE.


  1. Aarons J (1982) Global morphology of ionospheric scintillations. Proc IEEE 70(4):360–378CrossRefGoogle Scholar
  2. Aarons J (1991) The role of the ring current in the generation or inhibition of equatorial F layer irregularities during magnetic storms. Radio Sci 26(4):1131–1149. doi: 10.1029/91RS00473 CrossRefGoogle Scholar
  3. Abdu MA, Souza JR, Batista IS, Sobral JHA (2003) Equatorial spread F statistics and empirical representation for IRI: a regional model for the Brazilian longitude sector. Adv Space Res 31(3):703–716. doi: 10.1016/S0273-1177(03)00031-0 CrossRefGoogle Scholar
  4. Aquino M, Andreotti M, Dodson A, Strangeways H (2007) On the use of ionospheric scintillation indices as input to receiver tracking models. Adv Space Res 40(3):426–435. doi: 10.1016/j.asr.2007.05.035 CrossRefGoogle Scholar
  5. Aquino M, Monico J, Dodson A, Marques H, De Franceschi G, Alfonsi L, Romano V, Andreotti M (2009) Improving the GNSS positioning stochastic model in the presence of ionospheric scintillation. J Geodesy 83:953–966. doi: 10.1007/s00190-009-0313-6 CrossRefGoogle Scholar
  6. Beach TL (1998) Global positioning system studies of equatorial scintillations. Ph.D. Thesis, Cornell UniversityGoogle Scholar
  7. Beach TL, Kintner PM (2001) Development and use of a GPS ionospheric scintillation monitor. IEEE Trans on Geosci Remote Sens 39:918–928. doi: 10.1109/36.921409 CrossRefGoogle Scholar
  8. Beniguel Y, Forte B, Radicella SM, Strangeways HJ, Gherm VE, Zernov NN (2004) Scintillations effects on satellite to earth links for telecommunication and navigation purposes. Ann Geophys 47:1179–1199. doi: Google Scholar
  9. Briggs BH, Parkin IA (1963) On the variation of radio star and satellite scintillations with zenith angle. J Atmos Terr Phys 25:339–366. doi: 10.1016/0021-9169(63)90150-8 CrossRefGoogle Scholar
  10. Carrano CS, Groves KM (2010) Temporal decorrelation of GPS satellite signals due to multiple scattering from ionospheric irregularities. In: Proceedings of the ION GNSS-10, Portland, OR, Institute of Navigation, pp 361–374Google Scholar
  11. Conker RS, El-Arini MB, Hegarty CJ, Hsiao T (2003) Modeling the effects of ionospheric scintillation on GPS/satellite-based augmentation system availability. Radio Sci 38:23. doi: 10.1029/2000RS002604
  12. Dana RA (1997) Effects of ionospheric scintillation on differential demodulation of GPS data. IEEE Trans Aerosp Electron Syst 33:893–902. doi: 10.1109/7.599264 CrossRefGoogle Scholar
  13. Fontán FP, Espiñeira PM (2008) Modelling the wireless propagation channel: a simulation approach with MATLAB. Wiley, New YorkCrossRefGoogle Scholar
  14. Fremouw EJ, Livingston RC, Miller DA (1980) On the statistics of scintillating signals. J Atmos Terr Phys 42:717–731CrossRefGoogle Scholar
  15. Humphreys TE, Psiaki ML, Hinks JC, Kintner PM Jr (2009) Simulating ionosphere-induced scintillation for testing GPS receiver phase tracking loops. IEEE J Sel Top Signal Process 3:707–715. doi: 10.1109/JSTSP.2009.2024130 CrossRefGoogle Scholar
  16. Humphreys TE, Psiaki ML, Kintner PM Jr (2010a) Modeling the effects of ionospheric scintillation on GPS carrier phase tracking. IEEE Trans Aerosp Electron Syst 46:1624–1637. doi: 10.1109/TAES.2010.5595583 CrossRefGoogle Scholar
  17. Humphreys TE, Psiaki ML, Ledvina BM, Cerruti AP, Kintner PM (2010b) Data-driven testbed for evaluating GPS carrier tracking loops in ionospheric scintillation. IEEE Trans Aerosp Electron Syst 46:1609–1623. doi: 10.1109/TAES.2010.5595582 CrossRefGoogle Scholar
  18. Kintner PM, Kil H, Beach TL, de Paula ER (2001) Fading timescales associated with GPS signals and potential consequences. Radio Sci 36:731–743. doi: 10.1029/1999RS002310 CrossRefGoogle Scholar
  19. Kintner PM, Ledvina BM, de Paula ER, Kantor IJ (2004) Size, shape, orientation, speed, and duration of GPS equatorial anomaly scintillations. Radio Sci 39:RS2012. doi: 10.1029/2003RS002878
  20. Kintner PM, Ledvina BM, Paula ER (2007) GPS and ionospheric scintillations. Space Weather 5:S09003. doi: 10.1029/2006SW000260 CrossRefGoogle Scholar
  21. Ledvina BM, Makela JJ, Kintner PM (2002) First observations of intense GPS L1 amplitude scintillations at midlatitude. Geophys Res Lett 29(14):1659. doi: 10.1029/2002GL014770 CrossRefGoogle Scholar
  22. Moraes AO, Rodrigues FS, Perrella WJ, Paula ER (2011) Analysis of the characteristics of low-latitude GPS amplitude scintillation measured during solar maximum conditions and implications for receiver performance. Surv Geophys 33(5):1107–1131. doi: 10.1007/s10712-011-9161-z CrossRefGoogle Scholar
  23. Morris JM (1992) Burst error statistics of simulated viterbi decoded BPSK on fading and scintillating channels. IEEE Trans Commun 40:34–41. doi: 10.1109/26.126705 CrossRefGoogle Scholar
  24. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C: the art of scientific computing. Chapter 15. Cambridge University Press, CambridgeGoogle Scholar
  25. Simon MK, Alouini M (2006) Digital communications over fading channels. Wiley, New YorkGoogle Scholar
  26. Sobral JHA, Abdu MA, Takahashi H, Taylor MJ, de Paula ER, Zamlutti CJ, Aquino MG, Borba GL (2002) Ionospheric plasma bubble climatology over Brazil based on 22 years (1977–1998) of 630 nm airglow observations. J Atmos Sol Terr Phys 64(12–14):1517–1524. doi: 10.1016/S1364-6826(02)00089-5 CrossRefGoogle Scholar
  27. Stein S (1987) Fading channel issues in system engineering. IEEE J Sel Areas Commun SAC 5:6869Google Scholar
  28. Woodman RF (2009) Spread F—an old equatorial aeronomy problem finally resolved? Ann Geophys 27:1915–1934CrossRefGoogle Scholar
  29. Yacoub MD (2002) The α–μ distribution: a general fading distribution. In: Proceedings of 13th international symposium on personal, indoor and mobile radio communications PIMRC, Lisboa, PortugalGoogle Scholar
  30. Yacoub MD (2007) The α–μ distribution: a physical fading model for the stacy distribution. IEEE Trans Veh Technol 56:24–27. doi: 10.1109/TVT.2006.883753 CrossRefGoogle Scholar
  31. Yang L, Elmas Z, Hill C, Aquino M, Moore T (2011) An innovative approach for atmospheric error mitigation using new GNSS signals. J Navig 64:211–232. doi: 10.1017/S0373463311000373 CrossRefGoogle Scholar
  32. Yeh KC, Liu CH (1982) Radio wave scintillations in the ionosphere. Proc IEEE 70(4):324–360. doi: 10.1109/PROC.1982.12313 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alison de Oliveira Moraes
    • 1
    • 2
    Email author
  • Eurico Rodrigues de Paula
    • 3
  • Waldecir João Perrella
    • 2
  • Fabiano da Silveira Rodrigues
    • 4
  1. 1.Instituto de Aeronáutica e Espaço, IAESão José dos CamposBrazil
  2. 2.Instituto Tecnológico de Aeronáutica, ITASão José dos CamposBrazil
  3. 3.Instituto Nacional de Pesquisas Espaciais, INPESão José dos CamposBrazil
  4. 4.William B. Hanson Center for Space SciencesUniversity of Texas at DallasUTD, RichardsonUSA

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