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
non-coherent, 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 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
needs to be chosen such that it maximizes the fading number, and a
non-negative magnitude process that is independent and identically
distributed (IID) and that 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 the optimal input distribution is stationary apart from
some edge effects.

-||-   _|_ _|_     /    __|__   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: Fri Apr 6 20:41:02 UTC+8 2007