sm10_31

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Problem 10.31 In this experiment, we simulate the performance of bipolar signalling in 
additive white Gaussian noise but with root-raised-cosine pulse shaping. A Matlab script 
is included in Appendix 7 for doing this. With this simulation: 
(a) Compute the spectrum of the transmitted signal and compare to the theoretical. Also 
compare to the transmit spectrum with rectangular pulse shaping 
(b) Plot the eye diagram of the received signal under no noise conditions. Explain the 
relationship of the eye opening to bit error rate performance. 
(c) Confirm the theoretically predicted bit error rate for Eb/N0 from 0 to 10 dB. 
 
Solution 
(a) We compare the spectra by inserting the following statements prior to noise being 
added to the signal 
[P,F] = spectrum(S,256,0,Hanning(256),Fs); 
plot(F,P(:,1)); 
midpt = floor(length(F)/2); 
hold on, plot(F, abs([(1+cos(pi*F(1:midpt)))/2; 0*F(midpt+1:end)]),'g'), hold off 
xlabel('Frequency'), ylabel('Spectrum') 
 
The comparison plot is shown below. 
 
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency
S
pe
ct
ru
m
 
 
(b) To plot the eye diagram we eliminate the noise by setting Eb/N0 to a high value 
Eb_N0 = 2000; 
 
Then running the Matlab script produces the following eye diagram. 
 
Continued on next slide 
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Problem 10.31 continued 
 
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1.5
-1
-0.5
0
0.5
1
1.5
Symbol periods
A
m
pl
itu
de
 
 
 
(c) We simulate the bit error rate by commenting out the plotting statements and adding a 
set of statements similar to those used in Problem 10.30. 
 
0 1 2 3 4 5 6 7 8 9 10
10-6
10-5
10-4
10-3
10-2
10-1
Eb/No (dB)
B
E
R
Theory 
Simulation 
 
 
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only 
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that 
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.