On the sum of fisher-snedecor F variates and its application to maximal-ratio combining

Osamah S. Badarneh, Daniel B. Da Costa, Paschalis C. Sofotasios, Sami Muhaidat, Simon L. Cotton

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60 Scopus citations


In this letter, we investigate the sum of independent but not identically distributed (i.n.i.d.) Fisher-Snedecor F variates. First, a novel closed-form expression is derived for the moment generating function of the instantaneous signal-to-noise ratio. Based on this, the corresponding probability density function and cumulative distribution function of the sum of i.n.i.d. Fisher-Snedecor F variates are derived, which are subsequently employed in the analysis of multiple branch maximal-ratio combining (MRC). Specifically, we investigate the impact of multipath and shadowed fading on the outage probability and outage capacity of MRC based receivers. In addition, we derive exact closed-form expressions for the average bit error rate of coherent binary modulation schemes followed by an asymptotic analysis which provides further insights into the effect of the system parameters on the overall performance.

Original languageBritish English
Article number8359199
Pages (from-to)966-969
Number of pages4
JournalIEEE Wireless Communications Letters
Issue number6
StatePublished - Dec 2018


  • Fisher-Snedecor F distribution
  • maximal-ratio combining (MRC)
  • sum of random variables


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