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

effects.

number, flat fading, high signal-to-noise ratio (SNR), memory,

multiple-input multiple-output (MIMO), noncoherent detection,

stationary input distribution.

-||- _|_ _|_ / __|__ Stefan M. Moser

[-] --__|__ /__\ /__ Senior Scientist, ETH Zurich, Switzerland

_|_ -- --|- _ / / Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan

/ \ [] \| |_| / \/ Web: https://moser-isi.ethz.ch/

Last modified: Mon May 25 09:25:14 UTC+8 2009