We derive the fading number of stationary and ergodic (not necessarily
Gaussian) single-input multiple-output (SIMO) fading channels with
memory. This is the second term, after the double logarithmic term, of
the high signal-to-noise ratio (SNR) expansion of channel
capacity. The transmitter and receiver are assumed to be cognizant of
the probability law governing the fading but not of its realization.

It is demonstrated that the fading number is achieved by IID
circularly symmetric inputs of squared-magnitude whose logarithm is
uniformly distributed over an SNR dependent interval. The upper limit
of the interval is the logarithm of the allowed transmit power, and
the lower limit tends to infinity sub-logarithmically in the SNR. The
converse relies inter alia on a new observation regarding input
distributions that escape to infinity.

Lower and upper bounds on the fading number for Gaussian fading are
also presented. These are related to the mean squared-errors of the
one-step predictor and the one-gap interpolator of the fading process
respectively. The bounds are computed explicitly for stationary m-th
order auto-regressive AR(m) Gaussian fading processes.


Auto-regressive process, channel capacity, fading, fading number, high
SNR, memory, multiple-antenna, SIMO.

-||-   _|_ _|_     /    __|__   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: Wed Sep 12 06:54:12 UTC+8 2007