New results on the sum of Gamma random variates with application to the performance of wireless communication systems over Nakagami‐m fading channels1. Issue 1 (4th December 2014)

• Record Type: Journal Article
• Authors: Ansari, Imran Shafique; Yilmaz, Ferkan; Alouini, Mohamed‐Slim; Kucur, Oğuz
• Is Part Of: Transactions on emerging telecommunications technologies. Volume 28:Issue 1(2017:Jan.)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2014-12-04
• Subjects: Telecommunication -- Periodicals; 384.05
• DOI: 10.1002/ett.2912
• Languages: English
• ISSNs: 2161-5748

Abstract

Abstract: 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. Abstract : The probability density function (PDF) and the 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, are presented in closed form in terms of well‐known Meijer's G and Fox's H̄ functions. Further analysis, particularly on bit error rate via a PDF‐based approach, is also offered in closed form in terms of Meijer's G, Fox's H̄, and extended Fox's H̄( Ĥ ) functions.