The κ-μ Extreme/Gamma Distribution: A Physical Composite Fading Model

This article presents the introduction, formulation and derivation of the κ-μ Extreme/gamma distribution. This is a composite statistical model that is capable of characterizing effectively the simultaneous occurrence of shadowing and severe multipath fading. Novel explicit relationships for the probability density function and the cumulative distribution function of this model are derived. The offered results are validated through comparisons with results obtained from numerical integrations. Importantly, these expressions have a relatively tractable algebraic form and therefore they convenient to handle both analytically and numerically. As a result, they can find meaningful applications in analytic studies related to digital communications over κ-μ Extreme/gamma fading channels.

[1]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[2]  P. Mohana Shankar,et al.  Error Rates in Generalized Shadowed Fading Channels , 2004, Wirel. Pers. Commun..

[3]  P. Bithas.  Weibull-gamma composite distribution: alternative multipath/shadowing fading model , 2009 .

[4]  Ali Abdi,et al.  K distribution: an appropriate substitute for Rayleigh-lognormal distribution in fading-shadowing wireless channels , 1998 .

[5]  M.D. Yacoub,et al.  The $\alpha$-$\mu$ Distribution: A Physical Fading Model for the Stacy Distribution , 2007, IEEE Transactions on Vehicular Technology.

[6]  D. B. da Costa,et al.  Joint statistics for two correlated Weibull variates , 2005, IEEE Antennas and Wireless Propagation Letters.

[7]  Theodore S. Rappaport,et al.  New analytical models and probability density functions for fading in wireless communications , 2002, IEEE Trans. Commun..

[8]  F. Li,et al.  A new polynomial approximation for Jν Bessel functions , 2006, Appl. Math. Comput..

[9]  M. Nakagami.  The m-Distribution—A General Formula of Intensity Distribution of Rapid Fading , 1960 .

[10]  M. Yacoub,et al.  The к-μ Extreme distribution: Characterizing severe fading conditions , 2009, 2009 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC).

[11]  Paschalis C. Sofotasios,et al.  The η-μ/gamma composite fading model , 2010, 2010 IEEE International Conference on Wireless Information Technology and Systems.

[12]  M.D. Yacoub,et al.  The κ-μ distribution and the η-μ distribution , 2007, IEEE Antennas and Propagation Magazine.

[13]  Jeff Frolik.  On appropriate models for characterizing hyper-rayleigh fading , 2008, IEEE Transactions on Wireless Communications.

[14]  P. T. Mathiopoulos,et al.  Weibull-Gamma composite distribution : An alternative multipath / shadowing fading model , 2009 .

[15]  Mohamed-Slim Alouini,et al.  Digital Communication over Fading Channels: Simon/Digital Communications 2e , 2004 .

[16]  Halim Yanikomeroglu,et al.  On the approximation of the generalized-Κ distribution by a gamma distribution for modeling composite fading channels , 2010, IEEE Transactions on Wireless Communications.

[17]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[18]  Jeff Frolik,et al.  Diversity gains in two-ray fading channels , 2009, IEEE Transactions on Wireless Communications.

[19]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[20]  I. M. Pyshik,et al.  Table of integrals, series, and products , 1965 .

[21]  Jeff Frolik,et al.  A case for considering hyper-Rayleigh fading channels , 2007, IEEE Transactions on Wireless Communications.

[22]  W. C. Jakes,et al.  Microwave Mobile Communications , 1974 .