Abstract
A unified analysis of statistical models for describing fading, shadowing, and shadowed fading channels is presented from a pedagogical viewpoint. The different probability density functions such the Rayleigh, Nakagami, gamma, generalized gamma, Weibull, lognormal, Nakagami-lognormal, K distribution, generalized K distribution, and Nakagami inverse Gaussian distribution are presented and the relationships among them are detailed. These density functions are compared in terms of two quantitative measures, namely the amount of fading and outage probability. A general approach to fading and shadowed fading channels using a cluster based approach is also presented to link several of the distributions. It is expected that this overview will be very helpful to students and educators who are engaged in the study of wireless systems and the adverse impact of fading and shadowing in wireless data transmission.
Similar content being viewed by others
References
Simon M. K., Alouni M.-S.: Digital communication over fading channels: A unified approach to performance analysis (2nd ed.). Wiley, Hoboken (2005)
Saleh A., Valenzuela R. A.: A statistical model for indoor multipath propagation. IEEE Journal on elected Area in Communications 5, 128–137 (1987)
Andersen, J. B. (2002). Statistical distributions in mobile communications using multiple scattering. Presented at the 27th URSI General Assembly, Maastricht, Netherlands.
Coulson A. J., Williamson A. G., Vaughan R. G.: A statistical basis for lognormal shadowing effects in multipath fading channels. IEEE Transactions on Communications 46(4), 494–502 (1998)
Papoulis A., Pillai S. U.: Probability, random variables and stochastic Processes (4th ed.). McGraw-Hill, New York (2002)
Nakagami M.: 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 (1960)
Shankar P. M.: A general statistical model for ultrasonic scattering from tissues. IEEE Transactions on Ultrasound, Ferroelectrics, and Frequency Control 47(3), 727–736 (2000)
Yacoub M. D., Bautista J. E. V., Guedes L.: On higher order statistics of the Nakagami-m distribution. IEEE Transactions on Vehicular Technology 48(3), 790–794 (1999)
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 Proceedings of IEEE ICC (pp. 901–905). New York, Apr./May, 2002.
Yacoub M. D.: The α-μ distribution: A physical fading model for the stacy distribution. IEEE Transactions on Vehicular Technology 56(1), 27–34 (2007)
Shankar P. M.: Ultrasonic tissue characterization using a generalized Nakagami model. IEEE Transactions on Ultrasound, Ferroelectrics, and Frequency Control 48, 1716–1720 (2001)
Aalo V. A., Piboongungon T., Iskander C.-D.: Bit-error rate of binary digital modulation schemes in generalized gamma fading channels. IEEE Communications Letters 9(2), 139–141 (2005)
Sagias N. C., Mathiopoulos P. T.: Switched diversity receivers over generalized gamma fading channels. IEEE Communications Letters 9(10), 871–873 (2005)
Sagias N. C., Varzakas P., Tombras G. S., Karagiannidis G. K.: Spectral efficiency for selection combining RAKE receivers over Weibull fading channels. Journal of the Franklin Institute 342, 7–13 (2005)
Sagias N. C., Karagiannidis G. K.: Gaussian class multivariate Weibull distributions: Theory and applications in fading channels. IEEE Transactions of Information Theory 51(10), 3608–3619 (2005)
Clark J. R., Karp S.: Approximations for lognormally fading optical signals. Proceedings of the IEEE 58, 1964–1965 (1970)
Suzuki H.: A statistical model for urban radio propagation. IEEE Transactions on Communications 25(7), 673–679 (1975)
Ohta M., Koizumi T.: Intensity fluctuation of stationary random noise containing an arbitrary signal wave. Proceedings of the IEEE 57, 1231–1232 (1969)
Gradshteyn I. S., Ryzhik I. M.: Table of integrals, series, and products (5th ed.). Academic, San Diego (1994)
Abdi A., Kaveh M. K.: Distribution: An approximate substitute for Rayleigh-lognormal distribution in fading-shadowing wireless channels. Electronics Letters 34, 851–852 (1998)
Shankar P. M.: Error rates in generalized shadowed fading channels. Wireless Personal Communications 28, 233–238 (2004)
Bithas P. S., Sagias N. C., Mathiopoulos P. T., Karagiannidis G. K., Rontogiannis A. A.: On the performance analysis of digital communications over generalized-K fading channels. IEEE Communications Letters 10, 353–355 (2006)
Laourine, A., Alouini, M.-S., Affes, S. & Stephenne, A. (2007). On the capacity of generalized-K Fading channels. Proceedings of IEEE GLOBECOM (pp. 3306–3310).
Karmeshu S., Agrawal R.: On the efficacy of Rayleigh-inverse Gaussian distribution over K-distribution for wireless fading channels. Wireless Communications and Mobile Computing 7(1), 1–7 (2007)
Laourine A., Alouini M.-S., Affes S., Stéphenne A.: On the performance analysis of composite multipath/shadowing channels using the G-distribution. IEEE Transactions on Communications 57(4), 1162–1170 (2009)
Erceg V., Fortune S. J., Ling J., Rustako A. J. Jr., Valenzuela R. A.: Comparisons of a computer-based propagation prediction tool with experimental data collected in urban microcellular environments. IEEE Journal on Selected areas in Communications 15(4), 677–684 (1997)
Salo J., El-Sallabi H. M., Vainikainen P.: The distribution of the product of independent Rayleigh random variables. IEEE Transactions on Antennas and Propagation 54, 639–643 (2006)
Karagiannidis G. K., Sagias N. C., Mathiopoulos P. T.: ‘N*Nakagami: A novel stochastic model for cascaded fading channels. IEEE Transactions on Communications 55, 1453–1458 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shankar, P.M. Statistical Models for Fading and Shadowed Fading Channels in Wireless Systems: A Pedagogical Perspective. Wireless Pers Commun 60, 191–213 (2011). https://doi.org/10.1007/s11277-010-9938-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-010-9938-2