estimating maximum performance of a filter, adaptive filtering, Wiener filtering

Hi everyone,

currently I try to understand adaptive filtering a little deeper, and
on this way stumbled over a problem. Surely someone could comment my
thoughts, wheather I'm right or wrong...and provide some advice which
way to think further?

Imagine some filtering problem where you have a distorted signal d(n)
(say distorted speech) and a reference signal x(n) (say some signal
which is the cause for the noise within d) which is correlated to the
distortion within d(n).
Using an adaptive filter, one can estimate the distortion within d(n):
by feeding the filter with x(n) and subtract the output from d(n) to
get some clean ("error") signal e(n). The adaptive filter is
approaching the Wiener Filter solution for the filtering problem.

Heres the question:
For the Wiener filter, there exist some formulae to calculate the
minimum error (which include the filter coefficients, the
autocorrelation and cross correlation values of the signals x(n) and
d(n)).

My idea is that, for a given record of x(n) and d(n), I could measure
the auto- and cross-correlation values. Having these I should be able
to calculate the maximum possible attenuation of the ideal converged
adaptive filter as a function of the filter length (since the maximum
attenuation is the Wiener filter's minimum error in comparison to
d(n)).

Furthermore, there exist formulae to calculate the excess error, e.g.
for a LMS filter, as a function of filter length, input signal's energy
and step width of the filter, which is giving me the "real" attenuation
of the adaptive filter.

Therefore I think that it could be possible to estimate the
theoretically possible attenuation of an adaptive filter, by
calculating the energy of the input signals, auto- and
cross-correlation-matrices etc., as above. From the results, it should
be possible to choose the ideal suited algorithm and the ideal
parameters for an adaptive filter problem as mine before doing any
experiments, just from the signal's characteristics. This just sound
too simple, and I'm really thinking that I miss something
fundamental...

If you could bring some light into this, it would be very helpful. Any
comments appreciated...

Sincerely

stereo