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Modeling of QPSK transmitter and receiverusing MATLABy
Chang�Gene Woo�� Sung�Wook Jung� � and Hwan�Mok Jung�
Abstract� This report describes fundamentals of QPSKand its implementation� And functional model of the blockhas developed using MATLAB�
Keywords�Digital Communications� QAM� QPSK� Mod�
eling�
I� Introduction
THE increasing demand for digital transmission chan�nels has led to the investigation of spectrally e�cient
modulation techniques which is to maximize bandwidth ef��ciency and thus help ameliorate the spectral congestionproblem�Quadrature phase shift keying�QPSK� modulation is a
well�known technique for achieving bandwidth reduction�And this report focused on designing� and modeling of aQPSK transmitter and receiver� Design speci�cations aregiven as follows�
� Symbol rate� Msps� Given channel bandwidth� MHz� Pulse shaping �lter� root raised cosine �lter� Sample rate� fs � ��ts � MHz
II� Transmitter Design
Trasmitter parts of the MATLAB script are consists of�White random binary source generator�� �Serial to Parallelconverter�� �Zero Insertion� and �Pulse Shaping Filter��
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000−40
−20
0
20
40
60
80
100Spectrum of Input binary data
Fig� �� Spectrum of Input random binary data
Spectrum of random input binay data is shown as �gure
y MATLAB is a registered trademark of The MathWorks� Inc�
Report submitted May �� ���� �LATEX�� used��� Chang�Gene Woo �������� Sung�Wook Jung ���� �� and
Hwan�Mok Jung ���� � are the members of the ASIC Lab��Kyungpook National University�
�� And Spectrum of I�� Q�channel data with data after zeroinsertion is plotted in �gure �
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0
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100
Spectrum of I−channel data
0 1000 2000 3000 4000 5000
0
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Spectrum of Q−channel data
0 0.5 1 1.5 2 2.5
x 104
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140Spectrum of I−channel data after zero insertion
0 0.5 1 1.5 2 2.5
x 104
−20
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140Spectrum of Q−channel data after zero insertion
Fig� �� Spectrum of I�� Q�channel data�
The design of raised cosine �lter is mainly focused on�� the roll�o� factor also known as the normalized excessbandwidth which is given by � � �f
fxand can take any
value between � and �� According to the speci�cationgiven� the � is �� But we de�ne the roll�o� factor�rf�� as ��� for the su�cient margin� After the �Mapping� and�Filtering�� the data are IF modulated by I� Q mixer respec�tively� I�channel data are in�phase mixed with IF carrierand Q�channel data are quadrature mixed�
200 220 240 260 280 300−0.2
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0.4
0.5
Time domain response of pulse shaping filter
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0
50Transfer function of pulse shaping filter
0 0.5 1 1.5 2 2.5
x 104
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150Spectrum of I−channel after pulse shaping filter
0 0.5 1 1.5 2 2.5
x 104
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−150
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−50
0
50
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150Spectrum of Q−channel after pulse shaping filter
Fig� �� Time domain response of pulse shaping �lter�
III� Receiver Design
Since QPSK systems require a fully coherent or di�eren�tially coherent detection scheme� assuming that the amount
0 0.5 1 1.5 2 2.5
x 104
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150Spectrum of I−channel after modulation
0 0.5 1 1.5 2 2.5
x 104
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0
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150Spectrum of Q−channel after modulation
Fig� �� Spectrum of I�� Q�channel data after modulation
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−1
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0
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1
I channel after pulse shaping filter
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Q channel after pulse shaping filter
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−1
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I channel after modulation
400 500 600 700 800
−1
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0
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1
Q channel after modulation
Fig� � Waveform data after pulse shaping �lter and modulator
of phase shift at the carrier and the exact sampling timeare known�
IV� Conclusions
In this report� QPSK transmitter and receiver model hasdeveloped using MATLAB� Full script �le is attached inSupplement section�
References
��� Bernard Sklar� Digital Communications� Fundamentals and Ap�plications� Prentice Hall� �����
��� John G� Proakis� Digital Communications� McGraw�Hill� ������� Ian A� Glover and Peter M� Grant� Digital Communications�
Prentice�Hall� �����
0 0.5 1 1.5 2 2.5
x 104
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0
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150Spectrum of I−channel after demodulation
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x 104
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150Spectrum of Q−channel after demodulation
0 0.5 1 1.5 2 2.5
x 104
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200Spectrum of I−channel after matched filter
0 0.5 1 1.5 2 2.5
x 104
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−300
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0
100
200Spectrum of Q−channel after matched filter
Fig� �� Spectrum of I�� Q�channel data after demodulation�
0 1000 2000 3000 4000 5000
0
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150Spectrum of I−channel after sampler
0 1000 2000 3000 4000 5000
0
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150Spectrum of Q−channel after sampler
0 1000 2000 3000 4000 5000
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150Spectrum of I−channel after Decision threshold
0 1000 2000 3000 4000 5000
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150Spectrum of Q−channel after Decision threshold
Fig� � Spectrum of I�� Q�channel data after sampler�
Supplement
� MATLAB script for System Simulation Homework ��
clear
� Carrier frequency for modulation and
� demodulation
Fc � �e��
�
� QPSK transmitter
�
data � ����� � Input binary data of �MHz
randdata � randn�� data �
for i ���data
if randdatai �� ���
inputi � ��
else
inputi � ��
end
end
−1.5 −1 −0.5 0 0.5 1 1.5
−1.5
−1
−0.5
0
0.5
1
1.5
Constellation of matched filter output
Fig� �� Constellation of matched �lter output
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Constellation of sampler
Fig� �� Constellation of sampler
� Series to Parallel
for i � ��data
if remi� � �� �
if inputi �� �
Ii � ��
Ii � � � ��
else
Ii � ���
Ii � � � ���
end
else
if inputi �� �
Qi � � � ��
Qi � ��
else
Qi � � � ���
Qi � ���
end
end
end
� Zero insertion
zero � �� � Sampling rate is ��MHz
for i � ��zero�data
if remi� zero �� �
0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000
20
40
60
80
100
120Spectrum of final received binary data
Fig� �� Spectrum of received binary data
Izeroi � Ifixi � � � zero � � �
Qzeroi � Qfixi � � � zero � � �
else
Izeroi � ��
Qzeroi � ��
end
end
� Pulse shaping filter
NT � ���
N � ��zero�NT�
Fs � ��e��
rf � ����
psf � rcosfirrf� NT� zero� Fs� �sqrt� �
Ipulse � convIzero� psf �
Qpulse � convQzero� psf �
� Modulation
for i � ��zero�data�N
ti � i � � � Fc � zero �
Imodi �Ipulsei ��sqrt� �cos��pi�Fc�ti �
Qmodi �Qpulsei ���sqrt� �sin��pi�Fc�ti �
end
sum � Imod � Qmod�
�
� QPSK Receiver
�
� Demodulation
for i � ��zero�data�N
Idemi �sumi ��sqrt� �cos��pi�Fc�ti �
Qdemi �sumi ���sqrt� �sin��pi�Fc�ti �
end
� Matched filter
mtf � rcosfirrf� NT� zero� Fs� �sqrt� �
Imat � convIdem� mtf �
Qmat � convQdem� mtf �
� Data selection
for i � ��zero�data
Iseli � Imati�N �
Qseli � Qmati�N �
end
� Sampler
for i � ��data
Isami � Iseli�� �zero�� �
Qsami � Qseli�� �zero�� �
end
� Decision threshold
threshold � ����
for i � ��data
if Isami �� threshold
Ifinali � ��
else
Ifinali � ���
end
if Qsami �� threshold
Qfinali � ��
else
Qfinali � ���
end
end
� Parallel to Series
for i � ��data
if remi� � �� �
if Ifinali �� �
finali � ��
else
finali � ��
end
else
if Qfinali �� �
finali � ��
else
finali � ��
end
end
end
figure�
plot���logabsfftinput
axis�� data ��� ����
grid
title�Spectrum of Input binary data�
figure�
subplot���
plot���logabsfftI
axis�� data ��� ����
grid
title�Spectrum of I�channel data�
subplot���
plot���logabsfftQ
axis�� data ��� ����
grid
title�Spectrum of Q�channel data�
subplot���
plot���logabsfftIzero
axis�� zero�data ��� ����
grid
title�Spectrum of I�channel data after
zero insertion�
subplot���
plot���logabsfftQzero
axis�� zero�data ��� ����
grid
title�Spectrum of Q�channel data after
zero insertion�
figure�
subplot���
plotpsf
axis���� ��� ���� ����
grid
title�Time domain response of
pulse shaping filter�
subplot���
plot���logabsfftpsf
axis�� N ���� ���
grid
title�Transfer function of
pulse shaping filter�
subplot���
plot���logabsfftIpulse
axis�� zero�data�N ���� ����
grid
title�Spectrum of I�channel after
pulse shaping filter�
subplot���
plot���logabsfftQpulse
axis�� zero�data�N ���� ����
grid
title�Spectrum of Q�channel after
pulse shaping filter�
figure�
subplot���
plot���logabsfftImod
axis�� zero�data�N ���� ����
grid
title�Spectrum of I�channel after modulation�
subplot���
plot���logabsfftQmod
axis�� zero�data�N ���� ����
grid
title�Spectrum of Q�channel after modulation�
figure�
subplot���
plot���logabsfftIdem
axis�� zero�data�N ���� ����
grid
title�Spectrum of I�channel after demodulation�
subplot���
plot���logabsfftQdem
axis�� zero�data�N ���� ����
grid
title�Spectrum of Q�channel after demodulation�
subplot���
plot���logabsfftImat
axis�� zero�data ���� ����
grid
title�Spectrum of I�channel after
matched filter�
subplot���
plot���logabsfftQmat
axis�� zero�data ���� ����
grid
title�Spectrum of Q�channel after
matched filter�
figure�
subplot���
plot���logabsfftIsam
axis�� data ��� ����
grid
title�Spectrum of I�channel after sampler�
subplot���
plot���logabsfftQsam
axis�� data ��� ����
grid
title�Spectrum of Q�channel after sampler�
subplot���
plot���logabsfftIfinal
axis�� data ��� ����
grid
title�Spectrum of I�channel after
Decision threshold�
subplot���
plot���logabsfftQfinal
axis�� data ��� ����
grid
title�Spectrum of Q�channel after
Decision threshold�
figure�
plotIsel� Qsel
axis����� ��� ���� ����
grid
title�Constellation of matched filter output�
figure�
plotIsam� Qsam� �X�
axis����� ��� ���� ����
grid
title�Constellation of sampler�
figure�
plot���logabsfftfinal
axis�� data � ����
grid
title�Spectrum of final received binary data�