09hw11 - 2(a What is the(non-linear MMSE estimate of Θ...

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EE 464, Mitra Spring 2009 Homework 11 Due FRIDAY, April 17, 2009, 5pm This problem set investigates minimum-mean squared-error estimation, both linear and non-linear and begins the examination of the convergence of random sequences. Since we are back to the old schedule, to keep things short, there is no computer exercise this week. 1. Consider a binary phase-shift keying system in additive noise: Y = Θ+ N . Where N ∼ N ( 0 2 ) and Θ is equal to ± 1 with probability 1
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Unformatted text preview: 2 . (a) What is the (non-linear) MMSE estimate of Θ given Y ? (b) What happens to your estimator as σ 2 → ? 2. L-G 6.73 (a) and (b) and compute the mean-squared error for the estimators of parts (a) and (b). 3. L-G 6.75 (b), compute the associated mean-squared error for your estimator in part (b). 4. L-G 7.41: Determine whether the sequences converge surely or almost surely (only consider these two forms of convergence)....
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