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EE_564_F09_HW4_Updated

EE_564_F09_HW4_Updated - ௣் Assume equal prior...

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EE‐564 Fall 2009 Homework #4 Due Wednesday, October 7, 2009 1. “Digital Communications”, 5 th Edition, Proakis & Salehi, Problem 4.15 2. “Digital Communications”, 5 th Edition, Proakis & Salehi, Problem 4.34 3. “Digital Communications”, 5 th Edition, Proakis & Salehi, Problem 4.52 4. Assume in a binary PSK demodulator and detector there is a synchronization error in form of a time bias ݌ܶ, where ܶ is the bit duration and ݌ א ሾ0,1ሿ is a relative time offset with respect to ܶ. This synchronization error results in a shift in the integral, i.e., instead of ׬ ሺ. ሻ , there will be ׬ ሺ. ሻ
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Unformatted text preview: ௣் . Assume equal prior probabilities and perfect phase and frequency synchronization in the coherent detection. a) Find the general form of error probability ܲ ௘ as a function of ݌. Assume the noise variance is ܰ ଴ /2 and signal energy is ܧ. b) For ݌ ൌ 1/5 and ܧ/ܰ ଴ ൌ 10 ݀ܤ, find ܲ ௘ and compare it to the case when ݌ ൌ 0. c) When ݌ ൌ 1/5, how much in dB should you increase the signal energy (ܧ) to achieve the same error probability as when ݌ ൌ 0 and ܧ/ܰ ଴ ൌ 10 ݀ܤ? (You may need a computer to find the answer.)...
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