The demand of new wireless communication systems with much higher
data rates that allow, e.g., mobile wireless broadband
Internet 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 perfect knowledge
of the channel state. This 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 channel capacity. "Fair" is used
here in the sense that the capacity analysis does not ignore the
estimation part of the system, i.e., it takes into account
the need of the 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 non-coherent capacity.

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
squaring the necessary SNR. Since transmission in such a regime will
be highly inefficient, it is crucial 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 border between the power-efficient low-SNR
and the power-inefficient high-SNR regime is the so-called
fading number which is defined as the second term in the
high-SNR asymptotic expansion of channel capacity. The results of
this report concern this fading number.
New detection schemes, however, will not be sufficient for future
mobile transmission systems in order to achieve the aimed high data
rates. Another promising development step is to incorporate multiple
antennas, both at transmitter and receiver. It therefore becomes
important to evaluate the channel capacity of such a multiple-input
multiple-output (MIMO) system.

In this report, both innovations---joint estimation and detection
and multiple antennas---are studied together. The main result is an
exact expression of the fading number of a MIMO fading channel
without temporal memory. While we restrict ourselves to fading
processes that are temporally independent and identically
distributed (IID), we do allow dependencies between the fading of
the different paths corresponding to the different antennas (spatial
memory). Furthermore, the fading law is not restricted to be
Gaussian, but is assumed to be a general regular law with spatial
(but without temporal) memory. This result can be seen as a further
step towards the final goal of the fading number of general MIMO
fading channels with memory.

The result is also specialized to the 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.


Channel capacity, fading, fading number, flat fading, high SNR, joint
estimation and detection, memory, MIMO, multiple-antenna, non-
coherent detection.

-||-   _|_ _|_     /    __|__   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: Fri Oct 19 18:08:59 UTC+8 2007