To generate the waveform for Quadrate Phase Shift Keying (QPSK) signal using MATLAB

Objective:

To generate the waveform for Quadrate Phase Shift Keying (QPSK) signal using MATLAB

Software required:

1. MATLAB
2. Computer installed with Windows XP or higher Version

Theory

Generation of Quadrature phase shift keyed (QPSK) signal:

QPSK is also known as quaternary PSK, quadriphase PSK, 4-PSK, or 4-QAM. It is a phase modulation technique that transmits two bits in four modulation states.

Phase of the carrier takes on one of four equally spaced values such as π/4, 3π/4, 5π/4 and7π/4.

Si(t) = √2E/T cos {2 πƒct + (2i – 1) π/4} , 0≤ t ≤T

0, elsewhere

where i = 1,2,3,4, E = transmitted signal energy per symbol and T== symbol duration

Each of the possible value of phase corresponds to a pair of bits called dibits

Thus the gray encoded set of dibits: 10,00,01,11

Si (t) = √2E/T*cos [(2i – 1)π/4] cos (2πfc t) - √2E/T*sin [(2i –1) π/4] sin (2πfc t) , 0≤ t ≤Tb

0 , else where

There are two orthononormal basis functions

c1 (t) = √2/T cos 2πƒct, 0≤ t ≤Tb

c2 (t) = √2/T sin 2πƒct, 0≤ t ≤Tb

There are four message points

The I/p binary sequence b(t) is represented in polar from with symbols 1 & 0 represented as +√E/2 and -√E/2. This binary wave is demutiplexed into two separate binary waves consisting of odd & even numbered I/P bits denoted by b₁(t) & b₂(t). b₁(t) & b₂(t) are used to modulate a pair of quadrature carrier. This results two PSK waves .These two binary PSK waves are added to produce the desired QPSK signal as shown in figure 9.1.

QPSK modulation:

1. Generate quadrature carriers.
2. Start for loop
3. Generate binary data, message signal(bipolar form)
4. Multiply carrier 1 with odd bits of message signal and carrier 2 with even bits of message signal
5. Perform addition of odd and even modulated signals to get the QPSK modulated signal
6. Plot QPSK modulated signal.
7. End for loop.
8. Plot the binary data and carriers

Program:

% QPSK Modulation

clc;

clear all;

close all;

%Generate Quadrature Carrier Signal

Tb=1;

t=0:(Tb/100):Tb;

fc=1;

c1=sqrt(2/Tb)*cos(2*pi*fc*t);

c2=sqrt(2/Tb)*sin(2*pi*fc*t);

%generate message signal

N=8;

m=rand(1,N);

t1=0;t2=Tb

for i=1:2:(N-1)

t=[t1:(Tb/100):t2]

if m(i)>0.5

m(i)=1;

m_s=ones(1,length(t));

else

m(i)=0;

m_s=-1*ones(1,length(t));

end

%odd bits modulated signal

odd_sig(i,:)=c1.*m_s;

if m(i+1)>0.5

m(i+1)=1;

m_s=ones(1,length(t));

else

m(i+1)=0;

m_s=-1*ones(1,length(t));

end

%even bits modulated signal

even_sig(i,:)=c2.*m_s;

%qpsk signal

qpsk=odd_sig+even_sig;

%Plot the QPSK modulated signal

subplot(3,2,4);

plot(t,qpsk(i,:));

title('QPSK signal');

xlabel('t--->');

ylabel('s(t)');

grid on;

hold on;

t1=t1+(Tb+.01);

t2=t2+(Tb+.01);

end

hold off

%Plot the binary data bits and carrier signal

subplot(3,2,1);

stem(m);

title('binary data bits');

xlabel('n--->');

ylabel('b(n)');

grid on;

subplot(3,2,2);

plot(t,c1);

title('carrier signal-1');

xlabel('n--->');

ylabel('cl(t)');

grid on;

subplot(3,2,3);

plot(t,c2);

title('carrier signal-2');

xlabel('t--->');

ylabel('c2(t)');

subplot(3,2,3);

grid on;

Observation:The desired BFSK waveforms i.e. binary data, message signal, carrier signal 1&2 and output waveforms are shown in figure 8.2.

Conclusion:The program for QPSK modulation has been simulated in MATLAB and observed the desired waveforms.

Questions:

1. Write a MATLAB program to sample a message signal m(t) and reconstruct it
2. Draw the constellation diagram of QPSK.
3. Write the applications of QPSK.