Abstract

The non-central chi-square distribution plays an important role in
communications, for example in the analysis of mobile and wireless
communication systems. It not only includes the important cases of a
squared Rayleigh distribution and a squared Rice distribution, but
also the generalizations to a sum of independent squared Gaussian
random variables of identical variance with or without mean,
i.e., a "squared MIMO Rayleigh" and "squared MIMO Rice"
distribution.

In this paper closed-form expressions are derived for the expectation
of the logarithm and for the expectation of the n-th power of the
reciprocal value of a non-central chi-square random variable. It is
shown that these expectations can be expressed by a family of
continuous functions g_m(.) and that these families have nice
properties (monotonicity, convexity, etc.). Moreover, some
tight upper and lower bounds are derived that are helpful in
situations where the closed-form expression of g_m(.) is too
complex for further analysis.

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Scientist, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan
/ \     []  \|    |_|   / \/    Web: https://moser-isi.ethz.ch/

Last modified: Fri Sep 7 13:31:04 UTC+8 2007