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 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

term in the high-SNR asymptotic expansion of channel capacity.

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

ourselves to fading channels with multiple antennas at the

transmitter, but only one antenna at the receiver (a multiple-input

single-output (MISO) situation), however, we do allow memory.

Furthermore, the fading laws are not restricted to be Gaussian, but is

assumed to be a general regular law with spatial and temporal

memory. The main result of this report are a new upper bound and a new

lower bound on the fading number of this MISO fading channel with

memory. It can be seen as a further step towards the final goal of the

fading number of general multiple-inputs multiple-outputs (MIMO)

fading channels with memory.

In case of an isotropically distributed fading vector it is proven

that the upper and lower bound coincide,

fading number with memory is known precisely.

The upper and lower bounds show that a type of beam-forming is

asymptotically optimal.

channel, high SNR, joint estimation and detection, memory, MISO,

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 27 08:47:07 2006