## Abstract

A versatile envelope distribution which generalizes many commonly used models for multipath and shadow fading is the so-called generalized Gamma (GG) distribution. By considering the product of N GG random variables (RV)s, novel expressions for its moments-generating, probability density, and cumulative distribution functions are obtained in closed form. These expressions are used to derive a closed-form union upper bound for the distribution of the sum of GG distributed RVs. The proposed bound turns out to be an extremely convenient analytical tool for studying the performance of N-branch equal-gain combining receivers operating over GG fading channels. For such receivers, first the moments of the signal-to-noise (SNR) at the output, including average SNR and amount of fading, are obtained in closed form. Furthermore, novel union upper bounds for the outage and the average bit error probability are derived and evaluated in terms of Meijer's G-functions. The tightness of the proposed bounds is verified by performing comparisons between numerical evaluation and computer simulations results.

Original language | English |
---|---|

Article number | 1705958 |

Pages (from-to) | 2967-2974 |

Number of pages | 8 |

Journal | IEEE Transactions on Wireless Communications |

Volume | 5 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1 2006 |

## Keywords

- Equal-gain combining (EGC)
- Generalized Gamma
- Generalized fading channels
- Lognormal
- Nakagami-m
- Outage probability
- Sum of random variables
- Weibull

## ASJC Scopus subject areas

- Computer Science Applications
- Electrical and Electronic Engineering
- Applied Mathematics