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

It is demonstrated that the fading number is achieved by independent
and identically distributed (i.i.d.) 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 sublogarithmically in the SNR. The converse relies inter
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
mth-order autoregressive 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 May 10 13:04:17 2006