Title :
An efficient series for the computation of the distribution function of a sum of random variables and its application to the sum of Rayleigh random variables
Author :
Beaulieu, Norman C.
Author_Institution :
Dept. of Electr. Eng., Queen´´s Univ., Kingston, Ont., Canada
Abstract :
An infinite series is derived for the computation of the distribution function of a sum of independent random variables. The general result is applied to derive efficient expansions for the distributions of uniform and Rayleigh variables. Truncation errors and numerical issues are considered. A useful form of the characteristic function of a Rayleigh random variable (RV), together with an efficient computational procedure, are presented. The inversion of characteristic functions, a trapezoidal rule for numerical integration, and the sampling theorem in the frequency domain are related to, and interpreted in terms of, the results. The theory is particularly applicable to studies of Rayleigh fading channels
Keywords :
fading; random processes; roundoff errors; series (mathematics); statistics; telecommunication channels; telecommunications computing; Rayleigh fading channels; characteristic functions; computational procedure; distribution function; frequency domain; infinite series; inversion; numerical integration; sampling theorem; sum of Rayleigh random variables; sum of independent random variables; trapezoidal rule; truncation errors; Distributed computing; Distribution functions; Diversity reception; Fading; Interpolation; Probability distribution; Random variables; Upper bound;
Conference_Titel :
Global Telecommunications Conference, 1990, and Exhibition. 'Communications: Connecting the Future', GLOBECOM '90., IEEE
Conference_Location :
San Diego, CA
Print_ISBN :
0-87942-632-2
DOI :
10.1109/GLOCOM.1990.116640
