Question
For the model X=+W , and under the usual independence and normality assumptions for and W , the mean squared error of the LMS estimator
For the modelX=+W, and under the usual independence and normality assumptions forandW, the mean squared error of the LMS estimator is
1(1/02)+(1/12),
where02and12are the variances ofandW, respectively.Suppose now that we change the observation model toY=3+W. In some sense the "signal"has a stronger presence, relative to the noise termW, and we should expect to obtain a smaller mean squared error. Suppose02=12=1. The mean squared error of the original modelX=+Wis then1/2. In contrast, the mean squared error of the new modelY=3+Wis _____?
Hint:Do not solve the problem from scratch. Think of an alternative observation model in which you observeY=+(W/3)
.
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