log(log(SNR)) + χ at high signal-to-noise ratios (SNR). Here, χ,

denoted

SNR, but dependent on the distribution of the fading process.

Recently, an expression of the fading number has been derived for the

situation of general memoryless multiple-input multiple-output (MIMO)

fading channels. In this paper, this expression is evaluated in the

special situation of an independent and identically distributed MIMO

Gaussian fading channel with a scalar line-of-sight component

min{

antennas at the receiver and transmitter, respectively.

As a side-product along the way, closed-form expressions are derived

for the expectation of the logarithm and for the expectation of the

variable. It is shown that these expectations can be expressed by a

family of continuous functions

have nice properties (monotonicity, concavity,

Moreover, some tight upper and lower bounds are derived that are

helpful in situations where the closed-form expression of

is too complex for further analysis.

-||- _|_ _|_ / __|__ 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: Thu Sep 20 16:15:45 UTC+8 2007