1. Show that as the estimator

1. Show that as  the estimator of Prob. 3 becomes efficient. Hint: note that the estimate  is Gaussian with mean A and variance  known results for the moments of a Gaussian RV.

Problem 3

Use the CRLB for transformed parameters (see App. A) and Eq. (7.15) to determine the CRLB for the signal power A2. Additive WGN, it seems plausible that an efficient estimator for A2 might be the square of the sample mean  Show that this estimator is not efficient even though the estimator for  was efficient. Hint: consider the estimator bias.

Eq. (7.15)

2. Determine whether an alternative power estimator for the real-valued constant-in-AWGN problem that forms the sample mean of 2,  is efficient. If not, is it asymptotically efficient?

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