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A Modified Loo Model with Partially Blocked and Three Dimensional Multipath Scattering: Analysis, Simulation and Validation

Abstract

This paper presents a novel mobile fading channel model, belonging to the class of Loo models, in which the multipath power arrives both in three dimensions (3-D) and in two angular sectors at the azimuth receiver’s plane. Moreover shadowing affects the amplitude of the line of sight (LOS) component, making it time varying and following a lognormal distribution, as required for a Loo model. The Doppler power spectral density (PSD) is analytically calculated, after Fourier transforming the closed form autocorrelation function. Afterwards exact solutions for the probability density function (PDF) of the envelope and phase are presented. What follows are approximate solutions for the second order statistics, i.e. the level crossing rate (LCR) and the average duration of fades (ADF’s). A new, appropriate for 3-D scattering cases, deterministic simulation scheme is developed, which implements the analytical model on a digital computer and is used to test the validity of the approximate solutions. Moreover the deterministic model is thoroughly investigated for all the possible cases, in terms of its convergence to the analytical one. Finally a curve fitting of the LCR to real world data, drawn from channel measurements, will demonstrate the flexibility and usefulness of the modified Loo model.

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References

  1. 1.

    Aulin T. (1979) A modified model for the fading signal at a mobile radio channel. IEEE Transactions Vehicular Technology 28(3): 182–203

  2. 2.

    Durgin, G. D. (2003). Space-time wireless channels. T. S. Rappaport, Series Editor. USA: Prentice Hall.

  3. 3.

    Durgin G.D., Rappaport T.S. (2000) Theory of multipath shape factors for small-scale fading wireless channels. IEEE Transactions on Antennas and Propagation 48(5): 682–693

  4. 4.

    Patzold M. (2002) Mobile fading channels. Wiley, Chichester, UK

  5. 5.

    Olenko A.Y., Wong K.T., Qasmi S.A., Ahmadi-Shokouh J. (2006) Analytically derived uplink/downlink TOA and 2-D-DOA distributions with scatterers in a 3-D hemispheroid surrounding the mobile. IEEE Transactions on Antennas and Propagation 54(9): 2446–2454

  6. 6.

    Bevan D.D.N., Ermolayev V.T., Flaksman A.G., Averin I.M. (2004) Gaussian channel model for mobile multipath environment. Eurasip Journal of Applied Signal Processing 9: 1321–1329

  7. 7.

    Castrellon M., Muñoz D., Vargas C., Lopez C., Covarrubias D. (2007) Doppler spread for Gaussian scatter density environments employing smart antennas. International Journal of Electronic Communication 61(9): 631–636

  8. 8.

    Lopez C., Covarrubias D., Muñoz D., Panduro M.A. (2005) Statistical cellular Gaussian scatter density channel model employing a directional antenna for mobile environments. International Journal of Electronic Communication 59(3): 195–199

  9. 9.

    Le K.N. (2007) A new formula for the angle-of-arrival probability density function in mobile environment. Signal Processing 87(6): 1314–1325

  10. 10.

    Mahmoud S.S., Al-Qahtani F.S., Hussain Z.M., Gopalakrishnan A. (2008) Spatial and temporal statistics for the geometrical-based hyperbolic macrocell channel model. Digital Signal Processing 18(2): 151–167

  11. 11.

    Jiang L., Tan S.Y. (2007) Geometrically based statistical channel models for outdoor and indoor propagation environments. IEEE Transactions on Vehicular Technology 56(6): 3587–3593

  12. 12.

    Khan N.M., Simsim M.T., Rapajic P.B. (2008) A generalized model for the spatial characteristics of the cellular mobile channel. IEEE Transactions on Vehicular Technology 57(1): 22–37

  13. 13.

    Karadimas, P., Vagenas, E. D., & Kotsopoulos, S. A. (2008, Jan. 10–12). A small scale fading model with sectored and three dimensional diffuse scattering. 5th IEEE Consumer Communications and Networking Conference, 2008-CCNC 2008 (pp. 943–947). Las Vegas, USA.

  14. 14.

    Pal, A., Beach, M., & Nix, A. (2006). A novel quantification of 3D directional spread from small-scale fading analysis. IEEE International Conference on Communication ICC ‘06 (Vol. 4, pp. 1699–1704).

  15. 15.

    Abdi A., Barger J.A., Kaveh M. (2002) A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station. IEEE Transactions on Vehicular Technology 51(3): 425–434

  16. 16.

    Tepedelenlioglu C., Giannakis G.B. (2001) On velocity estimation and correlation properties of narrow-band mobile communication channels. IEEE Transactions on Vehicular Technology 50(4): 1039–1052

  17. 17.

    Tepedelenlioglu C., Abdi A., Giannakis G., Kaveh M. (2001) Estimation of Doppler spread and signal strength in mobile communications with applications to handoff and adaptive transmission. Wireless Communication and Mobile Computing 1: 221–242

  18. 18.

    Loo C. (1985) A statistical model for a land mobile satellite link. IEEE Transactions on Vehicular Technology, 34(3): 122–127

  19. 19.

    Loo C., Secord N. (1991) Computer models for fading channels with applications to digital transmissions. IEEE Transactions on Vehicular Technology 40(4): 700–707

  20. 20.

    Suzuki H. (1977) A statistical model for urban radio propagation. IEEE Transactions on Communication 25(7): 673–680

  21. 21.

    Hansen F., Meno F.I. (1977) Mobile fading—Rayleigh and lognormal superimposed. IEEE Transactions on Vehicular Technology 26(4): 332–335

  22. 22.

    Krantzik A., Wolf D. (1990) Distribution of the fading-intervals of modified Suzuki processes. In: Torres L., Masgrau E., Lagunas M.A. (eds) Signal processing V: Theories and applications. Elsevier, Amsterdam, The Netherlands, pp 361–364

  23. 23.

    Patzold M., Li Y., Laue F. (1998) A study of a land mobile satellite channel model with asymmetrical Doppler power spectrum and lognormally distributed line of sight component. IEEE Transactions on Vehicular Technology 47(1): 297–310

  24. 24.

    Karadimas, P., & Kotsopoulos, S. A. (2007, May). A modified Loo model with sectored and three dimensional multipath scattering. Delson Group Inc. 8th world wireless congress-WWC, San Francisco, USA (pp. 25–30).

  25. 25.

    Corazza G.E., Vatalaro F. (1994) A statistical model for land mobile satellite channels and its application to nongeostationary orbit systems. IEEE Transactions on Vehicular Technology 43(3): 738–742

  26. 26.

    Patzold M., Killat U., Laue F. (1998) An extended Suzuki model for land mobile satellite channels and its statistical properties. IEEE Transactions on Vehicular Technology 47(2): 617–630

  27. 27.

    Patzold M., Killat U., Li Y., Laue F. (1997) Modeling, analysis and simulation of nonfrequency- selective mobile radio channels with asymmetrical Doppler power spectral density shapes. IEEE Transactions on Vehicular Technology 46(2): 494–507

  28. 28.

    Li, Y., Patzold, M., Killat, U., & Laue, F. (1996, Apr./May). An efficient deterministic simulation model for land mobile satellite channels. Proceedings IEEE 46th Vehicular Technology Conference, VTC 96 (pp. 1028–1032). Atlanta, Georgia, USA.

  29. 29.

    Clarke R.H. (1968) A statistical theory of mobile–radio reception. Bell System Technical Journal 47: 957–1000

  30. 30.

    Karadimas P., Kotsopoulos S.A. (2008) A generalized modified Suzuki model with sectored and inhomogeneous diffuse scattering component. Wireless Personal Communications 47(4): 449–469. doi:10.1007/s11277-008-9493-2

  31. 31.

    Vatalaro F. (1995) Generalized rice-lognormal channel model for wireless communications. Electronics Letters 31(22): 1899–1900

  32. 32.

    Vatalaro F., Mazzenga F., De Maio G., Forcella A. (2002) The generalized rice lognormal channel model-first and second order statistical characterization and simulation. International Journal on Satellite Communication 20(1): 29–45

  33. 33.

    Hwang, S. H., Kim, K. J., Ahn, J. Y., & Whang, K. C. (1997, May). A channel model for nongeostationary orbiting satellite system. Proceedings IEEE 47th Vehicular Technology Conference, VTC 97, Phoenix, Arizona, USA (pp. 41–45).

  34. 34.

    Abdi A., Lau W.C., Alouini M.S., Kaveh M. (2003) A new simple model for land mobile satellite channels: First- and second-order statistics. IEEE Transaction on Wireless Communication 2(3): 519–528

  35. 35.

    Barts R.M., Stutzman W.L. (1992) Modeling and simulation of mobile satellite propagation. IEEE Transactions on Antennas and Propagation 40(4): 375–382

  36. 36.

    Karasawa Y., Kimura K., Minamisono K. (1997) Analysis of availability improvement in LMSS by means of satellite diversity based on three-state propagation channel model. IEEE Transactions Vehicular Technology 46(4): 1047–1056

  37. 37.

    Fontan F.P., Gonzalez J.P., Ferreiro M.J.S., Castro A.V., Buonomo S., & Baptista J.P. (1997) Complex envelope three-state Markov model based simulator for the narrow-band LMS channel. International Journal on Satellite Communication 15(1): 1–15

  38. 38.

    Fontan F.P., Vasquez-Castro M., Cabado C.E., Garcia J.P., Kubista E. (2001) Statistical modeling of the LMS channel. IEEE Transactions Vehicular Technology 50(6): 1549–1567

  39. 39.

    Patzold, M., Killat, U., Laue, F., & Li, Y. (1996, Apr./May). A new and optimal method for the derivation of deterministic simulation models for mobile radio channels. Proceedings IEEE 46th Vehicular Technology Conference, VTC 96 (pp. 1423–1427). Atlanta, Georgia, USA.

  40. 40.

    Patzold M., Killat U., Laue F., Li Y. (1998) On the statistical properties of deterministic simulation models for mobile fading channels. IEEE Transactions Vehicular Technology 47(1): 254–269

  41. 41.

    Wang C-X., Patzold M., Yuan D. (2007) Accurate and efficient simulation of multiple uncorrelated Rayleigh fading waveforms. IEEE Transaction on Wireless Communication 6(3): 833–839

  42. 42.

    Patzold, M., & Nquyen, V. D. (2004, Sept.). A spatial simulation model for shadow fading processes in mobile radio channels. IEEE international symposium on personal, indoor and mobile radio communications, IEEE PIMRC 2004, Barcelona, Spain (05.-08, Vol. 3, pp. 1832–1838).

  43. 43.

    Patzold, M., & Yang, K. (2006, Sept. 5–8). An exact solution for the level crossing rate of shadow fading processes modeled by using the sum of sinusoids principle. Proceeding 9th international symposium on wireless multimedia communications, WPMC 2006 (pp. 188–193). San Diego, USA.

  44. 44.

    Butterworth, J. S., & Matt, E.E. (1983, June). The characterization of propagation effects for land mobile satellite services. International conference satellite systems for mobile communication navigations (pp. 51–54).

  45. 45.

    Gradshteyn I.S., Ryzhik I.M. (2000) Tables of integrals, series and products (6th ed). Academic, New York

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Correspondence to Petros Karadimas.

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Karadimas, P., Kotsopoulos, S.A. A Modified Loo Model with Partially Blocked and Three Dimensional Multipath Scattering: Analysis, Simulation and Validation. Wireless Pers Commun 53, 503–528 (2010). https://doi.org/10.1007/s11277-009-9698-z

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Keywords

  • Blocked multipath power
  • Deterministic simulation
  • Loo model
  • Shadow fading
  • Three dimensional (3-D) multipath scattering