For the model X W , and under the usual independence and normality assumptions for and W , the mean squared error of the LMS estimator is 1(1 0 2 ) (1 1 2 ), where 0 2 and 1 2 are the variances of and W , respectively Suppose now that we change the observation model to Y 3 W In some sense the signal has a stronger presence, relative to the noise term W , and we should expect to obtain a smaller mean squared error Suppose 0 2 1 2 1 The mean squared error of the original model X W is then 1 2 In contrast, the mean squared error of the new model Y 3 W i s Hint Do not solve the problem from scratch Think of an alternative observation model in which you observe Y (W 3)

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 is 1(1  0 2 ) (1  1 2 ), where 0 2 and 1 2 are the variances of and W , respectively Suppose now that we change the observation model to Y 3 W   In some sense the  signal  has a stronger presence, relative to the noise term W , and we should expect to obtain a smaller mean squared error  Suppose 0 2   1 2  1   The mean squared error of the original model X  W is then 1 2   In contrast, the mean squared error of the new model Y 3 W i s        Hint  Do not solve the problem from scratch  Think of an alternative observation model in which you observe Y  (W 3)

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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

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