April 2008
Intermediate
832 pages
26h 2m
English
Content preview from Adaptive Filters
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CHAPTER 21 Tracking Performance
The reader will soon realize that the arguments that are used in the sequel in order to arrive at the nonstationary EMSE, starting from the variance relation (20.32), are almost identical to the arguments used before in Chapters 16–19 while studying the stationary EMSE of several adaptive filters. For this reason, the derivations here are brief.
21.1 PERFORMANCE OF LMS
We start with the simplest of algorithms, namely, LMS. Thus, assume that {d(i), ui} satisfy model (20.16) and consider the LMS recursion
for which
(21.2) 
Relation (20.32) then becomes
Except for the term
on the left-hand side, we note that the identity (21.3) has the same form as the identity (16.3) that appeared in our study of the mean-square performance of LMS in Chapter 16. Therefore, performing the same expansions that we did in that section following (16.3), we can readily verify that (21.3) leads to
This expression extends the result (16.5) to the nonstationary ...
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