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 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