EE_564_F09_HW8_v2

EE_564_F09_HW8_v2 - −௝2గ௟௙/ௐ ௅−1 ௟=0 3...

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EE-564 Fall 2009 Homework #8 Due Wednesday, November 25, 2009 1. “Digital Communications”, 5 th Edition, Proakis & Salehi, Problem 11.3 2. Consider the following communication channel ݕሾ݊ሿ = ߙ 0 ݔሾ݊ሿ + ߙ 1 ݔሾ݊ − 1ሿ + ߙ 2 ݔሾ݊ − 2ሿ + ݖ[݊] In which z[n] is a white Gaussian noise, ߙ 0 = 1, ߙ 1 = 0.5 and ߙ 2 = −0.25. Consider OFDM modulation format. a) What is the minimum length of the cyclic prefix required for the above channel? b) Assuming that there are N symbols for OFDM, find the channel coefficients H[k] for ܰ = 3. c) Plot |ܪ[݇]| 2 at points ݇ and for the following cases 1. ܰ = 16, sampling interval = 2ߤݏ. 2. ܰ = 128, sampling interval = 2ߤݏ. d) Using the following description for Fourier transform, plot |ܪ(݂)| 2 and compare it to the results from part c. ܪሺ݂ሻ = ෍ ℎሾ݈ሿ݁
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Unformatted text preview: −௝2గ௟௙/ௐ ௅−1 ௟=0 3. Consider an OFDM transmission system with 8 tones and cyclic prefix of length 2 over the following communication channel. ݕሾ݊ሿ = ݔሾ݊ሿ + 0.5 ݔሾ݊ − 1ሿ − 0.25 ݔሾ݊ − 2ሿ + ݖ[݊] In which z[n] is a zero mean white Gaussian noise with variance N ଴ . Assume 1ܯܪݖ available bandwidth. Find the average SER for ܴܵܰ ± ܧ ௌ /ܰ ଴ ± 10݀ܤ, 15݀ܤ, 20݀ܤ in each of the following cases and plot SER versus SNR for each signaling format in (a) to (c). a) BPSK signaling on each tone and constant transmit power. b) QPSK signaling on each tone and constant transmit power. c) BPSK signaling and power is transmitted only on half of the tones that have higher SNR. (A form of adaptive modulation.)...
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