In this paper stands:
The derivation and analysis of NLMS rest upon the usual independence assumptions.
It has a footnote:
The independence assumptions used in the analysis of adaptive filters are:
- sequences $x(k)$ and $w(k)$ are zero mean, stationary, jointly normal, and with finite moments
- the successive increments of tap weights are independent of one another; and
- the error and $x(k)$ sequences are statistically independent of one another
I have several problems with that:
Who and when choose this assumptions? Is it something general or it just appears in the first publication on this topic?
I think in practice it is not possible to work just with stationary inputs $x(k)$. And also input and the adaptive weights also will never be zero mean (especially during online usage when it is impossible to normalize the input data). Also the error and input are strongly correlated, so how it can be statistically independent?
Is there some other theory dealing with analyzing those more real-life applications where those assumptions cannot be fulfiled?
If is it possible to answer, than please answer. If my questions are too stupid, please correct me. Thanks in advance.