### Abstract

This paper proposes to unify fading distributions by modeling the instantaneous SNR as an infinitely divisible random variable, which is a known class of random variables from the probability theory literature. A random variable is said to be infinitely divisible, if it can be written as a sum of <formula><tex>${n}$</tex></formula> ≥ 1 independent and identically distributed random variables, for each <formula><tex>${n}$</tex></formula>. The proposed unification subsumes several classes of multipath and shadowing fading distributions previously proposed in the wireless communications literature. We show that infinitely divisible random variables have many useful mathematical properties, that are applied in the performance analysis of wireless systems. Specific applications include diversity analysis and partial ordering of fading distributions.

Original language | English (US) |
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Journal | IEEE Transactions on Vehicular Technology |

DOIs | |

State | Accepted/In press - Sep 28 2017 |

### Keywords

- infinitely divisible
- Measurement
- Random variables
- Rayleigh channels
- Shadow mapping
- Signal to noise ratio
- stochastic ordering
- unification of fading models
- Wireless communication

### ASJC Scopus subject areas

- Automotive Engineering
- Aerospace Engineering
- Applied Mathematics
- Electrical and Electronic Engineering