On the Sum of Gamma Random Variates With Application to the Performance of Maximal Ratio Combining over Nakagami-m Fading Channels

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Ansari I. S., Yilmaz F., Alouini M., Kucur O.

13th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Cesme, Turkey, 17 - 20 June 2012, pp.394-398 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1109/spawc.2012.6292935
  • City: Cesme
  • Country: Turkey
  • Page Numbers: pp.394-398
  • Keywords: Gamma variates, cellular mobile radio systems, non-integer parameters, diversity, maximal ratio combining (MRC), binary modulation schemes, bit error rate (BER), Fox H-function distribution, Meijer G-function distribution, Fox (H)over-bar function distribution, Extended Fox (H)over-bar-function ((H)over-cap) distribution, MRC, RECEIVERS, SYSTEMS
  • Yıldız Technical University Affiliated: No


The probability distribution function (PDF) and cumulative density function of the sum of L independent but not necessarily identically distributed gamma variates, applicable to maximal ratio combining receiver outputs or in other words applicable to the performance analysis of diversity combining receivers operating over Nakagami-m fading channels, is presented in closed form in terms of Meijer G-function and Fox (H) over bar -function for integer valued fading parameters and non-integer valued fading parameters, respectively. Further analysis, particularly on bit error rate via PDF-based approach, too is represented in closed form in terms of Meijer G-function and Fox (H) over bar -function for integer-order fading parameters, and extended Fox (H) over bar -function ((H) over cap) for non-integer-order fading parameters. The proposed results complement previous results that are either evolved in closed-form, or expressed in terms of infinite sums or higher order derivatives of the fading parameter m.