### 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 |

### Fingerprint

### 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

### Cite this

**A Unified Approach for Modeling Fading Channels Using Infinitely Divisible Distributions.** / Rajan, Adithya; Tepedelenlioglu, Cihan; Zeng, Ruochen.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A Unified Approach for Modeling Fading Channels Using Infinitely Divisible Distributions

AU - Rajan, Adithya

AU - Tepedelenlioglu, Cihan

AU - Zeng, Ruochen

PY - 2017/9/28

Y1 - 2017/9/28

N2 - 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 ${n}$ ≥ 1 independent and identically distributed random variables, for each ${n}$. 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.

AB - 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 ${n}$ ≥ 1 independent and identically distributed random variables, for each ${n}$. 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.

KW - infinitely divisible

KW - Measurement

KW - Random variables

KW - Rayleigh channels

KW - Shadow mapping

KW - Signal to noise ratio

KW - stochastic ordering

KW - unification of fading models

KW - Wireless communication

UR - http://www.scopus.com/inward/record.url?scp=85030768054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030768054&partnerID=8YFLogxK

U2 - 10.1109/TVT.2017.2758261

DO - 10.1109/TVT.2017.2758261

M3 - Article

AN - SCOPUS:85030768054

JO - IEEE Transactions on Vehicular Technology

JF - IEEE Transactions on Vehicular Technology

SN - 0018-9545

ER -