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,

"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

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

properties (monotonicity, convexity, etc.). Moreover, some tight upper

and lower bounds are derived that are helpful in situations where the

closed-form expression of

logarithm, expected reciprocal value.

-||- _|_ _|_ / __|__ 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 Apr 27 10:29:57 UTC+8 2007