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.

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