rates that allow,

connections inspires a quick advance in wireless transmission

technology. So far most systems rely on an approach where the channel

state is measured with the help of regularly transmitted training

sequences. The detection of the transmitted data is then done under

the assumption of

approach will not be sufficient anymore for very high data rate

systems since the loss of bandwidth due to the training sequences is

too large. Therefore, the research interest on joint estimation and

detection schemes has been increased considerably.

Apart from potentially higher data rates a further advantage of such a

system is that it allows for a fair analysis of the theoretical upper

limit, the so-called

the sense that the capacity analysis does not ignore the estimation

part of the system,

receiver to gain some knowledge about the channel state without

restricting it to assume some particular form (particularly, this

approach does also include the approach with training sequences!). The

capacity of such a joint estimation and detection scheme is often also

known as

Recent studies investigating the non-coherent capacity of fading

channels have shown very unexpected results. In stark contrast to the

capacity with perfect channel knowledge at the receiver, it has been

shown that non-coherent fading channels become very power-inefficient

at high signal-to-noise ratios (SNR) in the sense that increasing the

transmission rate by an additional bit requires

necessary SNR (or

depending on the channel in use, "high SNR" typically starts somewhere

between 30 to 80 dB. Since transmission in such a regime will be

highly inefficient, it is crucial to avoid a system operating at such

a rate. Hence we need to better understand this behavior and to be

able to give an estimation as to where the inefficient regime

starts. One parameter that provides a good approximation to such a

threshold between the power-efficient low-SNR and the

power-inefficient high-SNR regime is the so-called

number

asymptotic expansion of channel capacity.

The results of this report concern this fading number. We investigate

a channel model based on a flat fading assumption without inter-symbol

interference, which is a typical situation encountered when using a

system based on orthogonal frequency division multiplexing (OFDM) or

on orthogonal frequency division multiple-access (OFDMA). We assume

several users at the transmitter side, but only one receiver (typical

setup of a several mobile users communicating with one base-station),

where all users and the receiver might have multiple antennas

available. In the most general setup we do not restrict the fading to

have a particular distribution (

but we only ask it to be a stationary, ergodic, finite-energy, and

regular random process, possibly with memory both over time and

space. For the sake of simplicity, however, we will introduce further

restrictions or simplifying assumptions on the way.

The results can be grouped into two main chapters: firstly we

investigate a single-user setup where we allow multiple-antennas both

at transmitter and receiver. The fading is assumed to have no temporal

memory, but the different antennas are allowed to have arbitrary

correlation. The distribution of the fading is not restricted to be

Gaussian, and not specified apart from the stationarity, ergodicity

and regularity assumptions. In this setup we are able to derive the

fading number precisely,

asymptotic channel capacity in the limit when the available power

tends to infinity, and we can give a good estimation of the threshold

between the efficient low- to medium-SNR regime and the highly

power-inefficient high-SNR regime.

This result is then specialized to the already known cases of

single-input multiple-output (SIMO), multiple-input single-output

(MISO), and single-input single-output (SISO) fading channels, as well

as to the situation of Gaussian fading. As a byproduct a new upper

bound is derived on g_m(.), the expected value of a logarithm of a

non-central chi-square random variable.

In a second chapter we investigate a simple two-user single-antenna

setup assuming no memory and Gaussian fading. We prove that under the

additional constraint that the users use circularly symmetric

signaling, the sum-rate capacity of this multiple-access channel

equals to the single-user capacity of the user with the better

channel.

fading, general fading, high signal-to-noise ratio, high SNR, joint

estimation and detection, MAC, memory, MIMO, multiple-access channel,

multiple-antenna, multiple-input multiple-output, multiple-user,

non-central chi-square, non-coherent.

-||- _|_ _|_ / __|__ 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: Fri Oct 27 08:47:07 2006