HW10Solutions

# HW10Solutions - ECEN 661 - Modulation Theory Homework #10...

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ECEN 661 - Modulation Theory Homework #10 Solutions 1. (a) Assuming a root-raised cosine transmitted pulse shape. The occupied bandwidth will be , where is the constellation size. Since we have, . In this problem, , hence we choose . This leads to a symbol rate of . (b) The rolloff factor is chosen to satisfy . This leads to . 2. (a) The equivalent channel response (as specified in class) for a raised cosine channel is The magnitude response of the transmitter filter should be , where . (b) The loss relative to the non-bandlimited channel is given by . This is plotted in the figure below. (c) 0.5dB loss is achieved when . 1.0dB loss is achieved when B 1 β + () R s 1 β + R b log 2 M ----------------------- == M 0 β 1 << R b B ----- l o g 2 M 2 R b B --------- R b B 14400 2700 -------------- 5.33 log 2 M 6 = M 64 = R s R b 6 2400bps B 1 β + R s = β 0.125 = Xf 1 f 1 β 2 ----------- R s < , 1 2 --1 π β R s -------- f 1 β 2 R s   cos +    1 β 2 R s f 1 β + 2 ------------ R s , 0 f 1 β + 2 R s > . = Gf Cf ------------- = 1 1 f f o --- 2 2 2 f f o 2 + ------------------------------------------------------- = loss 20log 10 f d f d -------------------------------------- = R s 1.75 f o 1.75MHz

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. 3. We can approach this problem in two manners. First we could treat the channel as a lowpass channel and proceed as in the previous problem. Otherwise we could treat the channel as a band-
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## This note was uploaded on 02/21/2012 for the course ECEN 661 taught by Professor Miller during the Spring '11 term at Texas A&M.

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HW10Solutions - ECEN 661 - Modulation Theory Homework #10...

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