April 2008
Intermediate
832 pages
26h 2m
English
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CHAPTER 17 Performance of NLMS
We now illustrate the use of the variance relation (15.40) in evaluating the steady-state performance of the ∈NLMS algorithm,
for which
(17.2) 
The data {d(i),ui, v(i)} are assumed to satisfy model (15.16). The variance relation (15.40) in this case becomes
Again, several terms in this equality get cancelled. Since the arguments are similar to what we did for the LMS case in the previous chapter, we shall be brief and only highlight the main steps.
17.1 SEPARATION PRINCIPLE
Note first that by expanding both sides of (17.3) we get
In order to simplify this equation, we resort to the same separation principle (16.7) that we used in the LMS case, namely, that at steady-state, ||ui||2 is independent of |ea(i)|2. Under this condition, equality (17.4)becomes
If we define the quantities (which are solely dependent on the statistics of the regression data):
(17.5)
then the above equality can be written more compactly as
so that
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