Theory of Affine Projection Algorithms for Adaptive Filtering by Kazuhiko Ozeki

Author:Kazuhiko Ozeki
Language: eng
Format: epub
Publisher: Springer Japan, Tokyo

(5.54)

Now let us assume that the adaptive filter is in the steady state. Then, for large k, we have from (5.54)

(5.55)

Substitution of (5.52) into the right-hand side of (5.55) yields

(5.56)

where

and

Thus, at steady state, we have

(5.57)

5.5.1.2 Evaluation of

Using (5.50) together with the assumptions (A-3) and (A-4), we get from (5.57)

(5.58)

In order to derive an expression for , we first note

(5.59)

In the same way, we have

(5.60)

and

(5.61)

To simplify (5.60) and (5.61), we assume the following:(D-1)The random vector is statistically independent of at steady state.

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