An Exact Solution for the Level-Crossing Rate of Shadow Fading Processes Modelled by Using the Sum-of-Sinusoids Principle

  • Matthias Pätzold
  • Kun Yang


The focus of this paper is on the higher order statistics of spatial simulation models for shadowing processes. Such processes are generally assumed to follow the lognormal distribution. The proposed spatial simulation model is derived from a non-realizable lognormal reference model with given correlation properties by using Rice’s sum-of-sinusoids. Both exact and approximate expressions are presented for the level-crossing rate (LCR) and the average duration of fades (ADF) of the simulation model. It is pointed out that Gudmundson’s correlation model results in an infinite LCR. To avoid this problem, two alternative spatial correlation models are proposed. Illustrative examples of the dynamic behavior of shadow fading processes are presented for all three types of correlation models. Emphasis will be placed on two realistic propagation scenarios capturing the shadowing effects in suburban and urban areas.


Mobile fading channels Shadowing effects Spatial shadowing processes Lognormal processes Level-crossing rate 


  1. 1.
    Okumura Y., Ohmori E., Kawano T. and Fukuda K. (1968). Field strength and its variability in VHF and UHF land mobile radio services. Review of the Electrical Communications Laboratory 16: 825–873 Google Scholar
  2. 2.
    Reudink D.O. (1972). Comparison of radio transmission at X-band frequencies in suburban and urban areas. IEEE Transactions on Antennas and Propagation 20: 470–473 CrossRefGoogle Scholar
  3. 3.
    Black D.M. and Reudink D.O. (1972). Some characteristics of mobile radio propagation at 836 MHz in the Philadelphia area. IEEE Transactions on Vehicular Technology 21: 45–51 CrossRefGoogle Scholar
  4. 4.
    Ibrahim M.F. and Parsons J.D. (1983). Signal strength prediction in built-up areas. IEE Proceedings 130F(5): 377–384 Google Scholar
  5. 5.
    Suzuki H. (1977). A statistical model for urban radio propagation. IEEE Transactions on Communications 25(7): 673–680 CrossRefGoogle Scholar
  6. 6.
    Loo C. (1987). Measurements and models of a land mobile satellite channel and their applications to MSK signals. IEEE Transactions on Vehicular Technology 35(3): 114–121 Google Scholar
  7. 7.
    Pollini G.P. (1996). Trends in handover design. IEEE Communications Magazine 34(3): 82–90 CrossRefGoogle Scholar
  8. 8.
    Zhang N. and Holtzman J.M. (1996). Analysis of handoff algorithms using both absolute and relative measurements. IEEE Transactions on Vehicular Technology 45(1): 174–179 CrossRefGoogle Scholar
  9. 9.
    Mogensen, P. E., Eggers, P., Jensen, C., & Andersen, J. B. (1991). Urban area radio propagation measurements at 955 and 1845 MHz for small and micro cells. In IEEE Global Communication Conference (pp. 1297–1302). Phoenix, AZ, Dec. 1991.Google Scholar
  10. 10.
    Gudmundson M. (1991). Correlation model for shadow fading in mobile radio systems. Electronics Letters 27(23): 2145–2146 CrossRefGoogle Scholar
  11. 11.
    Marsan M. and Hess G. (1990). Shadow variablility in an urban land mobile radio environment. Electronics Letters 26: 646–648 CrossRefGoogle Scholar
  12. 12.
    Giancristofaro D. (1996). Correlation model for shadow fading in mobile radio channels. Electronics Letters 32: 958–959 CrossRefGoogle Scholar
  13. 13.
    Universal Mobile Telecommunications System (UMTS); Selection procedures for the choice of radio transmission technologies of the UMTS (UMTS 30.03 version 3.2.0) (2004). Technical Report TR 101 112 V3.2.0 (1998-04), ETSI, 2004.Google Scholar
  14. 14.
    Pätzold, M., & Nguyen, V. D. (2004). A spatial simulation model for shadow fading processes in mobile radio channels. In Proceedings of the 15th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2004 (Vol. 3, pp. 1832–1838). Barcelona, Spain, Sept. 2004.Google Scholar
  15. 15.
    Jakes W.C. (Ed.) (1994). Microwave mobile communications. IEEE Press, Piscataway, NJGoogle Scholar
  16. 16.
    Pätzold M. (2002). Mobile fading channels. Wiley, Chichester CrossRefGoogle Scholar
  17. 17.
    Bennett W.R. (1948). Distribution of the sum of randomly phased components. Quaterly of Applied Mathematics 5: 385–393 Google Scholar
  18. 18.
    Rice S.O. (1944). Mathematical analysis of random noise. Bell System Technical Journal 23: 282–332 MATHMathSciNetGoogle Scholar
  19. 19.
    Rice S.O. (1945). Mathematical analysis of random noise. Bell System Technical Journal 24: 46–156 MATHMathSciNetGoogle Scholar
  20. 20.
    Papoulis A. and Pillai S.U. (2002). Probability, random variables and stochastic processes (4th Ed). McGraw-Hill, New York Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Faculty of Engineering and ScienceUniversity of AgderGrimstadNorway

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