hw2 - n has a normal distribution with a mean of 3V and a...

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COSC4214: Digital Communications Instructor: Amir Asif Quiz for Assignment # 2 Time Allowed: 15 minutes Name: __________________________________________________________________________________ Student ID Number: ____________________________Email: _____________________________________ A binary communication system transmits signals s i ( t ), for i = 1, 2. The receiver test statistics are given by 0 ) ( n a T z i + = , where the signal component a i is either a 1 = +5V when bit 1 (represented by s 1 (t)) is transmitted or a 2 = - 5V when bit 0 (represented by s 2 (t)) is transmitted. The noise component
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Unformatted text preview: n has a normal distribution with a mean of 3V and a variance of 5V 2 . Assume that the prior probability for transmitting s 1 is given by P 1 = 0.25 and for s 1 is given by P 2 = 0.75. (a) [5 points] Starting with the maximum likelihood (ML) ratio test 1 2 2 1 2 1 ) ( ) ( P P s z p s z p s s z z < > where p z ( z | s 1 ) and p z ( z | s 2 ) are the conditions pdfs on s 1 and s 2 respectively, derive the ML detector for the receiver. (b) [5 points] Determine the probability of error for the detector designed in part (a)....
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