multiple-access general fading channel is investigated, where each

user has an arbitrary number of antennas and the receiver has only one

antenna. The transmitted signal is subject to additive Gaussian noise

and fading. The fading process is assumed to be general and

memoryless, i.e., it is not restricted to a specific distribution like

Rayleigh or Rician fading. While it is memoryless (i.e., independent

and identically distributed IID) over time, spacial memory is allowed,

i.e., the fading affecting different antennas may be dependent. On

the transmitter side cooperation between users is not allowed, i.e.,

the users are assumed to be statistically independent.

Based on known results about the capacity of a single-user fading

channel, we derive the exact expression for the asymptotic

multiple-user sum-rate capacity. It is shown that the capacity grows

only double-logarithmically in the available power. Futhermore, the

second term of the high-SNR asymptotic expansion of the sum-rate

capacity, the so-called

shown to be identical to the fading number of the single-user channel

when all users apart from one is switched off at all times.

The result holds for three different power constraints. In a first

scenario, each user must satisfy its own strict peak-power constraint;

in a second case, each user's power is limited by an average-power

constarint; and in a third situation — somewhat unrealistically —

it is assumed that the users have a common power supply and can share

power (even though they still cannot cooperate on a signal basis).

The proof is based on a duality-based upper bound on mutual

information and on the concept of input distributions that escape to

infinity, meaning that when the available power tends to infinity, the

input must use symbols that also tend to infinity.

-||- _|_ _|_ / __|__ 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 Aug 19 11:34:52 UTC+8 2013