The fading number of a general (not necessarily Gaussian) regular
multiple-input multiple-output (MIMO) fading channel with arbitrary
temporal and spatial memory is derived. The channel is assumed to be
noncoherent, i.e., neither receiver nor transmitter have knowledge
about the channel state, but they only know the probability law of the
fading process. The fading number is the second term in the asymptotic
expansion of channel capacity when the signal-to-noise ratio (SNR)
tends to infinity. It is related to the border of the high-SNR region
with double-logarithmic capacity growth.

It is shown that the fading number can be achieved by an input that is
the product of two independent processes: a stationary and circularly
symmetric direction- (or unit-) vector process whose distribution is
chosen such that the fading number is maximized, and a nonnegative
magnitude process that is independent and identically distributed
(i.i.d.) and escapes to infinity. Additionally, in the more general
context of an arbitrary stationary channel model satisfying some weak
conditions on the channel law, it is shown that there exists an
optimal input distribution that is stationary apart from some edge


Channel capacity, circular symmetry, escaping to infinity, fading
number, flat fading, high signal-to-noise ratio (SNR), memory,
multiple-input multiple-output (MIMO), noncoherent detection,
stationary input distribution.

-||-   _|_ _|_     /    __|__   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: Mon May 25 09:25:14 UTC+8 2009