TY - GEN

T1 - New Results On the Sum of Two Generalized Gaussian Random Variables

AU - Soury, Hamza

AU - Alouini, Mohamed-Slim

N1 - KAUST Repository Item: Exported on 2020-04-23

PY - 2015

Y1 - 2015

N2 - We propose in this paper a new method to compute
the characteristic function (CF) of generalized Gaussian (GG)
random variable in terms of the Fox H function. The CF
of the sum of two independent GG random variables is then
deduced. Based on this results, the probability density function
(PDF) and the cumulative distribution function (CDF) of the
sum distribution are obtained. These functions are expressed in
terms of the bivariate Fox H function. Next, the statistics of the
distribution of the sum, such as the moments, the cumulant, and
the kurtosis, are analyzed and computed. Due to the complexity
of bivariate Fox H function, a solution to reduce such complexity
is to approximate the sum of two independent GG random
variables by one GG random variable with suitable shape factor.
The approximation method depends on the utility of the system
so three methods of estimate the shape factor are studied and
presented.

AB - We propose in this paper a new method to compute
the characteristic function (CF) of generalized Gaussian (GG)
random variable in terms of the Fox H function. The CF
of the sum of two independent GG random variables is then
deduced. Based on this results, the probability density function
(PDF) and the cumulative distribution function (CDF) of the
sum distribution are obtained. These functions are expressed in
terms of the bivariate Fox H function. Next, the statistics of the
distribution of the sum, such as the moments, the cumulant, and
the kurtosis, are analyzed and computed. Due to the complexity
of bivariate Fox H function, a solution to reduce such complexity
is to approximate the sum of two independent GG random
variables by one GG random variable with suitable shape factor.
The approximation method depends on the utility of the system
so three methods of estimate the shape factor are studied and
presented.

UR - http://hdl.handle.net/10754/556078

UR - http://ieeexplore.ieee.org/document/7418351/

U2 - 10.1109/GlobalSIP.2015.7418351

DO - 10.1109/GlobalSIP.2015.7418351

M3 - Conference contribution

AN - SCOPUS:84964734996

SN - 978-1-4799-7591-4

BT - 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

PB - Institute of Electrical and Electronics Engineers Inc.

ER -