Title: Some expectations of a non-central chi-square distribution with an even number of degrees of freedom
Authors: Moser, Stefan M.
電信工程研究所
Institute of Communications Engineering
Issue Date: 2007
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.
URI: http://hdl.handle.net/11536/6590
ISBN: 978-1-4244-1271-6
ISSN: 0886-1420
Journal: TENCON 2007 - 2007 IEEE REGION 10 CONFERENCE, VOLS 1-3
Begin Page: 1059
End Page: 1062
Appears in Collections:Conferences Paper