The capacity of regular noncoherent fading channels grows like
log(log(SNR)) + χ at high signal-to-noise ratios (SNR). Here, χ,
denoted fading number, is a constant independent of the
SNR, but dependent on the distribution of the fading process.
Recently, an expression of the fading number has been derived for the
situation of general memoryless multiple-input multiple-output (MIMO)
fading channels. In this paper, this expression is evaluated in the
special situation of an independent and identically distributed MIMO
Gaussian fading channel with a scalar line-of-sight component
d. It is shown that, for large |d|, the fading number grows like
min{n_r, n_t}log(|d|^2) where n_r and n_t denote the number of
antennas at the receiver and transmitter, respectively.

As a side-product along the way, 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 noncentral 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, concavity, 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 Researcher & Lecturer, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adj. Professor, National Chiao Tung University (NCTU), Taiwan
/ \     []  \|    |_|   / \/    Web: http://moser-isi.ethz.ch/

Last modified: Thu Sep 20 16:15:45 UTC+8 2007