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Unformatted text preview: Z =  XY  . 3. (20 points) Multiplicative noise channel. The signal X and the noise Z are independent random variables and each is uniform in the interval (0 , 1). We observe the output Y = XZ . a. (10 points) Find the joint pdf of the random variables X and Y . b. (10 points) Find the MMSE estimate of X given Y . 4. (20 points) Fading channel. Let the signal X = b 1 with probability 1 / 2 2 with probability 1 / 2 and the channel gain A with pdf f A ( a ) = b λeλa a ≥ otherwise be independent random variables. The channel output Y = AX is observed. a. (10 points) Find the optimal decoding rule D ( y ) for deciding whether X = 1 or 2, i.e., the rule that minimizes the probability of decoding error. b. (10 points) Find the probability of error for the decoding rule in part (a). Page 2 of 2 EE 278, Spring 2009...
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This note was uploaded on 05/20/2011 for the course EE 278 taught by Professor Balajiprabhakar during the Winter '09 term at Stanford.
 Winter '09
 BalajiPrabhakar
 Signal Processing

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