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 (inverse moments) of a noncentral chi-square
random variable of even degree of freedom. 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

As an example of the applicability of these results, in the second
part of this paper an independent and identically distributed (IID)
Gaussian multiple-input–multiple-output (MIMO) fading channel
with a scalar line-of-sight component is analyzed. Some new
expressions are derived for the fading number that describes the
asymptotic channel capacity at high signal-to-noise ratios (SNR).

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Researcher & Lecturer, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adj. Professor, National Chiao Tung University (NCTU), Taiwan
/ \     []  \|    |_|   / \/    Web: http://moser-isi.ethz.ch/

Last modified: Fri Apr 27 10:30:44 UTC+8 2007