midterm2007

midterm2007 - Principles of Digital Communications EPFL...

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Unformatted text preview: Principles of Digital Communications EPFL Summer Semester 2007 April 26, 2007 Midterm This is a closed-book exam, but a single page of hand-written notes is allowed. Cal- culators and cell-phones are not allowed. You have 1 hour 45 minutes to solve the problems. Try to do side calculations on a separate sheet and report well organized solutions. If we cant read it we cant grade it. If you need additional pages, do not forget to write your name! Good Luck!! Name: Problem 1 / 13 Problem 2 / 5 Problem 3 / 6 Problem 4 / 11 Total / 35 1 1. Bhattacharyya Bound (13 points) When Y R is an continuous random variable, the Bhattacharyya bound states that Pr { Y B i,j | H = i } radicalBigg P H ( j ) P H ( i ) integraldisplay y R radicalBig f Y | H ( y | i ) f Y | H ( y | j ) dy, where i, j are two possible hypotheses and B i,j = { y R : P H ( i ) f Y | H ( y | i ) P H ( j ) f Y | H ( y | j ) } . In this problem H = { , 1 } and P H (0) = P H (1) = 0 . 5....
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midterm2007 - Principles of Digital Communications EPFL...

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