Opinion - Adaptive Filtering of Uncorrelated Sequences

Hello,

I have several questions to ask regarding the expected behaviour of a linear
adaptive filter applied in a system identification arrangement using two
uncorrelated sequences for both the reference and desired signals.

I'll describe the experiment, the observed results, and then put forward my
questions.

In Matlab I create two uncorrelated sequences using the following code:

SIZE = 4096;
randn('seed', 0);
desired=randn(1,SIZE);
randn('seed', 4);
reference=randn(1,SIZE);

These two sequences form the desired and reference sequences for a
FIR-based, linear adaptive filter configured in a system identification
arrangement with the weights updated using both the conventional RLS and
QR-decomposition RLS algorithms.

In this case, the adaptive filter's estimate of the desired sequence should
theoretical be zero due to the uncorrelated relationship between the desired
and reference sequences; the weights should go to zero.

This behaviour is roughly observed when the forgetting-factor is larger than
0.9; significantly greater than zero and less than unity, as stated in all
standard references.

However, if the forgetting factor is mid-range, for example, say 0.5, the
adaptive filter's estimate becomes significant and the resulting error tends
to zero.

Why is this occurring?

Are there strict limits for the forgetting-factor?  Should it always be
larger than 0.9?  Is there a working ballpark range for sequences like
speech?

Any insights would be greatly appreciated.


Thank you,

Michael.