Premium
New results on the sum of Gamma random variates with application to the performance of wireless communication systems over Nakagami‐ m fading channels
Author(s) -
Ansari Imran Shafique,
Yilmaz Ferkan,
Alouini MohamedSlim,
Kucur Oğuz
Publication year - 2017
Publication title -
transactions on emerging telecommunications technologies
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.366
H-Index - 47
ISSN - 2161-3915
DOI - 10.1002/ett.2912
Subject(s) - fading , nakagami distribution , mathematics , independent and identically distributed random variables , cumulative distribution function , probability density function , integer (computer science) , random variable , function (biology) , statistics , fading distribution , discrete mathematics , computer science , rayleigh fading , decoding methods , evolutionary biology , biology , programming language
The probability density function (PDF) and cumulative distribution function of the sum of L ‐independent but not necessarily identically distributed Gamma variates, applicable to the output statistics of maximal ratio combining receiver operating over Nakagami‐ m fading channels or in other words to the statistical analysis of the scenario where the sum of squared Nakagami‐ m distributions is user‐of‐interest, are presented in closed form in terms of well‐known Meijer's G function and easily computable Fox's H̄ function for integer‐valued and non‐integer‐valued m fading parameters. Further analysis, particularly on bit error rate via a PDF‐based approach, is also offered in closed form in terms of Meijer's G function and Fox's H̄ function for integer‐valued fading parameters and extended Fox's H̄ function (H ̂ ) for non‐integer‐valued fading parameters. Our proposed results complement previous known results that are either expressed in terms of infinite sums, nested sums or higher‐order derivatives of the fading parameter m . Copyright © 2014 John Wiley & Sons, Ltd.