In this report, we study the non-coherent capacity of SISO zero-mean
Gaussian fading channels with memory. Because the non-coherent
capacity in asymptotic form (in the SNR) is already well understood
and so far there is not yet an exact expression for the non-asymptotic
capacity, we focus on deriving upper and lower bounds on the
non-asymptotic capacity.

First, we use a prediction technique on the fading channel to get rid
of the channel memory and finally derive a lower bound on the
non-asymptotic capacity. Second, we implement the Blahut-Arimoto
algorithm to perform the optimization in the expression of the derived
lower bound. Third, we present a numerically computed lower bound, and
compare the new numerical lower bound with analytical results.

On the other hand, we also derive an upper bound on the non-asymptotic
capacity, and then implement the cutting-plane algorithm to perform
the optimization in the expression of the derived upper bound.
Therefore, we also present a numerically computed upper bound, and
finally compare the new numerical upper bound with analytical results.

By comparison, the two new numerical bounds are found to be better
(closer) than the known analytical results. The characteristics of the
input distributions that achieve the new numerical bounds are
presented as well.

Unfortunately, we observe numerical problems which result from the
limitation of numerical methods. The new numerical bounds, especially
the new upper bound, stop growing in the SNR at high SNR regime. We
believe this is because we use a finite alphabet size for the channel
inputs and outputs to simulate the infinite alphabet size of the
channel inputs and outputs.

-||-   _|_ _|_     /    __|__   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 May 18 11:05:12 UTC+8 2007