Abstract

It has recently been shown that at high signal-to-noise ratios (SNR)
the capacity of multi-antenna systems over flat fading channels
(without receiver or transmitter side-information) typically grows
only double-logarithmically in the SNR. Here we further refine the
analysis and study the "fading number" chi, which we define as the
limit of the difference between channel capacity and
log(1+log(1+SNR)).

It is suggested that at high SNR, i.e., at rates that significantly
exceed the fading number, a capacity increase of one bit per channel
use requires the squaring of the SNR, or equivalently, the doubling
of the SNR as expressed in decibels. In this loose sense, the fading
number can be viewed as the channel limiting rate for power-efficient
communication. Note, however, that the fading number may be negative.

While the use of multiple antennae does not typically change the
double-logarithmic asymptotic dependence of channel capacity on the
SNR, multiple antennae do typically increase the fading number, albeit
at times (e.g., in the Rayleigh fading case) only in an additive way
that grows only logarithmically with the number of antennae.

-||-   _|_ _|_     /    __|__   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: Wed May 10 13:01:03 2006