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Unformatted text preview: Stochastic Processes nctuee07f Homework 3 Due on 11/26/2007 , Monday, 1 p.m. at EC 713 Reading assignments: Chapter 3, Gallager’s note, except Sec. 3.5. Problem assignments: 1. Exercise 3.10 in Gallager’s note. 2. Exercise 3.11 in Gallager’s note. 3. Consider the problem of detecting a known signal s , with dimension m × 1, in the presence of additive noise n . Assume the noise has a Gaussian distribution with n ∼ N ( , K n ) where K n is nonsingular. The detector is to determine whether the received signal y consists of signal plus noise or noise alone. That is, the two hypotheses to be tested for are H 1 : y = s + n H 2 : y = n . (a) Conduct the maximum likelihood detection, and show that the corresponding likelihood ratio test is equivalent to the test w H ML y ≶ η, where w ML = K- 1 n s . Determine η and indicate which hypothesis is true in the inequality. (b) Suppose the received signal y is passed through a filter w with output w H y . Show that the vector w MR that maximizes the signal to noise ratio (SNR), defined by SNR , E [ | w H s | 2 ] E [ | w H n | 2 ]...
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This note was uploaded on 11/28/2010 for the course EE 301 taught by Professor Gfung during the Winter '10 term at National Chiao Tung University.
- Winter '10