## (solution) We now consider the influence of AWGN and polarity reversals on the bit error probability for NRZI.

We now consider the influence of AWGN and polarity reversals on the bit error probability for NRZI. Consider the information bit sequence of Problem 6.1, assume that they are equally likely and that V 2 T b = 1 joule. Draw the signal space diagram for the two signals used in NRZI. √ The sampled output of the matched filter r k = s k + w k , where s k =± E b , in general is due to the signal transmitted and w k is AWGN. What is the output sequence { s k } for the given information bit sequence? Now assume that the noise sample sequence, { w k }, is: {−0.4, −1.2, 0.2, 0.2, −0.4, −0.2, −0.8, 1.2, 0.2, 0.0}. Determine the complete sampled output sequence { r k }. Based on these { r k }, what are the detected bit estimates { d ˆ k } and the corresponding { b ˆ k }? Note, particularly, the errors in { d ˆ k } and { b ˆ k }. Based on this can you make a general statement about the bit error probability? Now assume that a polarity reversal has occurred at t = 4 T b . What is the { s k } sequence now? Given the noise samples of (c) what is the { r k } sequence and then what are the { d ˆ k }, { b ˆ k } sequences?

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Sep 13, 2020

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