On the η – κ Distribution

Authors

Saralees Nadarajah, University of Nebraska-LincolnFollow
Samuel Kotz, George Washington University

Date of this Version

9-2006

Comments

Published in IEEE TRANSACTIONS ON BROADCASTING, VOL. 52, NO. 3, SEPTEMBER 2006. Copyright © 2006 IEEE. Used by permission.

Abstract

The recent paper byYacoub et al. [1] introduces what is referred to as the η – κ distribution to describe the statistical variation of the envelope in a fast fading environment. The paper discusses several properties of the distribution. Two of the properties discussed are the nth moment, E(Pⁿ), and the cumulative probability function (cpf), F_P (•), where P is a random variable representing the normalized envelope. The expression given for E(Pⁿ) (see equation (10) in Yacoub et al. [1]) is a doubly infinite sum of the Gauss hypergeometric function (which, itself, is an infinite sum). That given for F_P (•) (see equation (11) in Yacoub et al. [1]) is a triple sum of the incomplete gamma function.