The Product of Two α-μ Variates and the Composite α-μ Multipath–Shadowing Model

In this paper, the product of two independent and nonidentically distributed (i.n.i.d.) α-μ variates is considered. Exact reasonably simple closed-form expressions for the probability density function (pdf), the cumulative distribution function (cdf) , and the moments of the resulting random variable (RV) are derived. These results find a wide range of applications in a number of fields, such as radar communications, multihop systems, multiple-input–multiple-input links, and cascaded communications in general. In particular, they are used here to describe a novel α-μ/α-μ composite multipath–shadowing fading model. Because the α-μ model alone comprises a substantial number of useful fading environments, its α-μ/α-μ composite version leads to a variety and an immense amount of composite fading distributions. The novel expressions for this rather flexible scenario compute instantaneously, constituting a powerful tool to characterize wireless fading channels.

[1]  Michel Daoud Yacoub,et al.  On the α-μ Autocorrelation and Power Spectrum Functions: Field Trials and Validation , 2009, GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference.

[2]  Ali Abdi,et al.  On the utility of gamma PDF in modeling shadow fading (slow fading) , 1999, 1999 IEEE 49th Vehicular Technology Conference (Cat. No.99CH36363).

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

[4]  Michail Matthaiou,et al.  Performance Analysis of Digital Communication Systems Over Composite η-μ/Gamma Fading Channels , 2012, IEEE Trans. Veh. Technol..

[5]  José F. Paris.  Statistical Characterization of $\kappa{ - }\mu$ Shadowed Fading , 2014, IEEE Transactions on Vehicular Technology.

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

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

[8]  Paschalis C. Sofotasios,et al.  The κ-μ Extreme/Gamma Distribution: A Physical Composite Fading Model , 2011, 2011 IEEE Wireless Communications and Networking Conference.

[9]  C. Baker,et al.  Maritime surveillance radar Part 1 : Radar scattering from the ocean surface , 1990 .

[10]  George K. Karagiannidis,et al.  On the Distribution of the Sum of Gamma-Gamma Variates and Applications in RF and Optical Wireless Communications , 2009, IEEE Transactions on Communications.

[11]  Sofiène Affes,et al.  Performance analysis of mobile radio systems over composite fading/shadowing channels with co-located interference , 2009, IEEE Transactions on Wireless Communications.

[12]  D. Lewinski.  Nonstationary probabilistic target and clutter scattering models , 1983 .

[13]  David W. Matolak,et al.  5-GHz-Band Vehicle-to-Vehicle Channels: Models for Multiple Values of Channel Bandwidth , 2010, IEEE Transactions on Vehicular Technology.

[14]  G. Matz,et al.  On non-WSSUS wireless fading channels , 2005, IEEE Transactions on Wireless Communications.

[15]  Yu. A. Brychkov,et al.  Integrals and series , 1992 .

[16]  Simon L. Cotton,et al.  An experimental investigation into the influence of user state and environment on fading characteristics in wireless body area networks at 2.45 GHz , 2009, IEEE Transactions on Wireless Communications.

[17]  Simon L. Cotton,et al.  Body shadowing mitigation using differentiated LOS / NLOS channel models for RSSI-based Monte Carlo personnel localization , 2012, 2012 IEEE Wireless Communications and Networking Conference (WCNC).

[18]  Daeyoung Kim,et al.  Wind-Blown Foliage and Human-Induced Fading in Ground-Surface Narrowband Communications at 400 MHz , 2011, IEEE Transactions on Vehicular Technology.

[19]  Paschalis C. Sofotasios,et al.  On the κ-μ/gamma composite distribution: A generalized multipath/shadowing fading model , 2011, 2011 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC 2011).

[20]  Jonathan Ling,et al.  Comparisons of a Computer-Based Propagation Prediction Tool with Experimental Data Collected in Urban Microcelluar Environments , 1997, IEEE J. Sel. Areas Commun..

[21]  T. Zervos,et al.  The influence of the wearable antenna type on the on-body channel modeling at 2.45 GHz , 2013, 2013 7th European Conference on Antennas and Propagation (EuCAP).

[22]  Lorenzo Rubio,et al.  Estimation of the Composite Fast Fading and Shadowing Distribution Using the Log-Moments in Wireless Communications , 2013, IEEE Transactions on Wireless Communications.

[23]  George K. Karagiannidis,et al.  $N{\ast}$Nakagami: A Novel Stochastic Model for Cascaded Fading Channels , 2007, IEEE Transactions on Communications.

[24]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

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

[26]  Fredrik Tufvesson,et al.  Multi-dimensional K-factor analysis for V2V radio channels in open sub-urban street crossings , 2010, 21st Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications.

[27]  T. Zervos,et al.  Statistical Analysis for On-Body Spatial Diversity Communications at 2.45 GHz , 2012, IEEE Transactions on Antennas and Propagation.

[28]  Mikko Valkama,et al.  The kappa-#181;/Ig Composite Statistical Distribution in RF and FSO Wireless Channels , 2013, 2013 IEEE 78th Vehicular Technology Conference (VTC Fall).

[29]  Claude Oestges,et al.  Non-Stationary Narrowband MIMO Inter-Vehicle Channel Characterization in the 5-GHz Band , 2010, IEEE Transactions on Vehicular Technology.

[30]  Stavros A. Kotsopoulos,et al.  On the Scatterers' Mobility and Second Order Statistics of Narrowband Fixed Outdoor Wireless Channels , 2010, IEEE Transactions on Wireless Communications.