🚀 go-pugleaf

The following statistical problem arises in data communications, esp in
analysis of equalisation adaptation. So far I have been unable to find any
joy with this problem and there appears to be absolutely no work in the 
literature but I may not be looking in the right places. I am convinced that
there is very little residual correlation but this is only an impression.

Problem :

 At intervals of T seconds a signal (assume white gaussian noise) is
 sampled - call this r(k) at the k'th sampling instant.

 This is then corrected as follows    y(k) = r(k) - f(k)

 and an estimate of received data formed    ae(k) = sign ( y(k) )

 Coming back to the correction signal f(k), this is formed by the use of prior
 ae(k) 
             f(k) = ( ae(k-1) * d(1) + ae(k-2) * d(2) + ...

                              + ae(k-N) * d(N) )

 where the d's are constant.

 Problem is to determine the correlation between ae(k)'s ie. to
 what extent to new ae depend on the prior ae. It sure is HARD.


-- 
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ACSNET: andrew@trlvlsi.oz     UUCP: seismo!munnari!trlvlsi.oz!andrew
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Andrew Jennings  ,  Telecom Australia Research Laboratories,  P.O. Box 249 
                    Clayton,  Victoria 3168,  AUSTRALIA.
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