April 2008
Intermediate
832 pages
26h 2m
English
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CHAPTER 24 LMS with non-Gaussian Regressors
We now drop the Gaussian assumption on the regressors and show how the variance relation of Thm. 22.3 can be used to study the performance of LMS in this case as well. Although we are using the words non-Gaussian regressors in the title of this chapter, the results herein include the Gaussian case as a special case as well.
24.1 MEAN AND VARIANCE RELATIONS
Thus, refer again to the transformed recursion (23.7), which characterizes the transient performance of LMS. When the regressors ui were Gaussian, we were able to evaluate the three moments below (see (23.9)–(23.11)):
In particular, we found that 
and 
were simultaneously diagonal and that the weighting matrices 
themselves could be made diagonal as well — see (23.13).
However, when the regressors ui are non-Gaussian, it is generally not possible to express the last moment in (24.1) in closed-form any longer (as we did in (23.11); see though Prob. V.ll). In addition, and more importantly perhaps, the moments and need not be simultaneously diagonal anymore. In this way, the weighting ...
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