Abstract
In this thesis we study the capacity of Gaussian fading channels with
memory where neither transmitter nor receiver has access to the
realization of the fading process, though both are fully cognizant of
the fading laws. The emphasis is on the high signal-to-noise ratio
(SNR) regime.
For regular fading processes, i.e., the "present" fading cannot be
predicted precisely from its "past", we derive an upper bound on the
fading number of multiple-input single-output (MISO) fading channels,
where the fading number is the second-order term in the high SNR
expansion of capacity. We show that this bound is tight (i.e., it
coincides with a lower bound) if the channels are uncorrelated and the
fading process is either zero-mean or its spectral density matrix
contains identical entries. In the former case, the fading number can
be achieved by transmitting from only one antenna, i.e., the one that
yields the smallest prediction error in predicting the "present"
fading from its "past". In the latter case, the fading number can be
achieved by beam forming.
For non-regular fading processes, i.e., the "present" fading can be
predicted precisely from its "past", we derive upper bounds on the
capacity of MISO and multiple-input multiple-output (MIMO) fading
channels. For cases where the channels are uncorrelated the bound on
the MISO capacity is tight and we provide an expression for the
pre-log, i.e., the limiting ratio of the capacity to the logarithm of
the SNR. Moreover, we show that this pre-log can be achieved by
transmitting from only one antenna, i.e., the one that yields the
smallest prediction error in predicting the "present" fading from its
"past". In addition, we present an improved lower bound on the
capacity of single-input single-output (SISO) fading channels if
channel capacity only grows double-logarithmically in the SNR. This
allows for an expression of the pre-log-log, i.e., the limiting ratio
of the capacity to the logarithm of the logarithm of the SNR.
Keywords
Channel capacity, fading channels, fading number, high SNR,
multiplexing gain, non-coherent, pre-log, pre-log-log, regular and
non-regular fading processes.
-||- _|_ _|_ / __|__ 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 May 11 08:18:58 2006