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Wireless Personal Communications

, Volume 57, Issue 4, pp 735–751 | Cite as

The α − λ − μ and α − η − μ Small-Scale General Fading Distributions: A Unified Approach

  • Anastasios K. Papazafeiropoulos
  • Stavros A. Kotsopoulos
Article

Abstract

In this paper, a general small-scale fading model for wireless communications, that explores the nonlinearity and at the same time the inhomogeneous nature of the propagation medium, is presented, studied in terms of its first-order statistics of the envelope, and validated by means of field measurements and the Monte Carlo simulation. It is indeed a novel distribution with many advantages such as its generality, its physical interpretation that is directly associated with the propagation channel, and its mathematical tractability due to its simple and closed-form expression. By fitting to measurement data, it has been shown that the proposed distribution outperforms the widely known fading distributions. Namely, the α − λ − μ model, which can be in fact called α − η − μ format 2 model, can also be obtained from the α − η − μ format 1 model by a rotation of the axes. Both formats are combined, in order to result to a unified model in a closed form that may describe the propagation environment in a variety of different fading conditions. Its physical background is hidden behind the names of its parameters. The unified model includes the already known general distributions α − μ′, η − μ, λ − μ (η − μ format 2), and their inclusive ones as special cases.

Keywords

Fading channels Correlation α − μ′ Distribution Nakagami-m distribution Weibull distribution 

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References

  1. 1.
    Hoyt R. S. (1947) Probability functions for the modulus and angle of the normal complex variate. Bell System Technical Journal 26: 318–359MathSciNetGoogle Scholar
  2. 2.
    Nakagami M. (1960) The m-distribution–a general formula of intensity distribution of rapid fading. In: Hoffman W. C. (eds) Statistical methods in radio wave propagation. Pergamon, Elmsford, NYGoogle Scholar
  3. 3.
    Weibull W. (1951) A statistical distribution function of wide applicability. Journal of Applied Mechanics 27: 292–297Google Scholar
  4. 4.
    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 Transactions on Wireless Communications 2(3): 519–528CrossRefGoogle Scholar
  5. 5.
    Fraidenraich, G., & Yacoub, M. D. (2003). The λ − μ general fading distribution. In IEEE microwave and optoelectronics Conference, IMOC 2003. Proceedings of the SBMO/IEEE MTT-S international (Vol. 1, pp. 49–54).Google Scholar
  6. 6.
    Braun W. R., Dersch U. (1991) A physical mobile radio channel model. IEEE Transactions on Vehicular Technology 40(2): 27–34CrossRefGoogle Scholar
  7. 7.
    Yacoub M. D. (2007) The α −μ distribution: A physical fading model for the stacy distribution. IEEE Transactions on Vehicular Technology 56(1): 27–34CrossRefGoogle Scholar
  8. 8.
    Stacy E. W. (1962) A generalization of the gamma distribution. The Annals of Mathematical Statistics 33(3): 1187–1192CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Sagias N. C., Mathiopoulos P. T. (2005) Switched diversity receivers over generalized gamma fading channels. IEEE Communications Letters 9(10): 871–873CrossRefGoogle Scholar
  10. 10.
    Yacoub M. D. (2007) The η − μ and the η − κ distribution. IEEE Antennas Propagation Magazine 49(1): 68–81CrossRefGoogle Scholar
  11. 11.
    Yacoub, M. D., & Fraidenraich, G. (2006). The α − η − μ and α − κ − μ fading distributions. In IEEE ninth international symposium on spread spectrum techniques and applications (pp. 16–20).Google Scholar
  12. 12.
    Abramowitz M., Stegun I. A. (Eds) (1972) Handbook of mathematical functions with formulas, graphs, and mathematical tables. NewYork, Dover.zbMATHGoogle Scholar
  13. 13.
    Asplund, H., Molisch, A. F., Steinbauer, M., & Mehta, N. B. (2002). Clustering of scatterers in mobile radio channels—evaluation and modeling in the COST259 directional channel model. In IEEE international conference on communications, ICC 2002, New York.Google Scholar
  14. 14.
    Butterworth, J. S., & Matt, E. E. (1983). The characterization of propagation effects for land mobile satellite services. In International conference on satellite systems for mobile communication and navigations (pp. 51–54).Google Scholar
  15. 15.
    Abouraddy A. F., Elnoubi S. M. (2000) Statistical modeling of the indoor radio channel at 10 GHz through propagation measurements—part I: Narrow-band measurements and modeling. IEEE Transactions on Vehicular Technology 49(5): 1491–1507CrossRefGoogle Scholar
  16. 16.
    Smith, H., Barton, S. K., Gardiner, J. G., & Sforza, M. (1992). Characterization of the land mobile-satellite (LMS) channel at L and S bands: Narrowband measurements. Bradford, ESA AOPs 104 433/114 473.Google Scholar
  17. 17.
    Jakes W. C. (1974) Microwave mobile communications. Wiley, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  • Anastasios K. Papazafeiropoulos
    • 1
  • Stavros A. Kotsopoulos
    • 1
  1. 1.Department of Electrical and Computer Engineering, Wireless Telecommunications LaboratoryUniversity of PatrasPatrasGreece

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