We derive the fading number of a general (not necessarily Gaussian)
single-input multiple-output (SIMO) fading channel with memory,
where the transmitter and receiver-while fully cognizant of the
probability law governing the fading process-have no access to
the fading realization.

It is demonstrated that the fading number is achieved by IID
circularly-symmetric inputs of log squared-magnitude that is uniformly
distributed over a signal-to-noise (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. Among the new ingredients in the proof is a new theorem
regarding input distributions that escape to infinity.

Upper and lower bounds on the fading number for SIMO Gaussian fading
are also presented. Those 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 May 10 13:01:03 2006