To generate the waveform of Phase Shift Keying (PSK) signal using MATLAB
Generation of PSK:Generation of PSK signal PSK is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). PSK uses a finite number of phases, each assigned a unique pattern of binary digits. Usually, each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular phase. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. In a coherent binary PSK system, the pair of signal S_{1}(t) and S_{2}(t) used to represent binary symbols 1 & 0 are defined by
S_{1}(t) = √2Eb/ Tb Cos 2πfct
S_{2}(t) =√2Eb/Tb (2πfct+π) = - √ 2Eb/Tb Cos 2πfct where 0 ≤ t< T _{b} and
E_{b}=Transmitted signed energy for bit
The carrier frequency f _{c}= n/T _{b} for some fixed integer n.
Antipodal Signal:The pair of sinusoidal waves that differ only in a relative phase shift of 180° are called antipodal signals.
BPSK Transmitter:The input binary symbols are represented in polar form with symbols 1 & 0 represented by constant amplitude levels √Eb & -√Eb. This binary wave is multiplied by a sinusoidal carrier in a product modulator. The result is a BSPK signal as shown in figure 7.1.
PSK modulation:
%ASK Modulation
clc;
clear all;
close all;
%Generate Carrier Signal
Tb=1;
t=0:Tb/100:Tb;
fc=2;
c=sqrt(2/Tb)*sin(2*pi*fc*t);
%generate message signal
N=8;
m=rand(1,N);
t1=0;t2=Tb
for i=1:N
t=[t1:.01:t2]
if m(i)>0.5
m_s=zeros(1,length(t));
m(i)=1;
m_s=ones(1,length(t));
else
m(i)=0;
m_s=-1*ones(1,length(t));
end
message(i,:)=m_s;
%product of carrier and message signal bpsk
sig(i,:)=c.*m_s;
%Plot the message and BPSK modulated signal
subplot(5,1,2);
axis([0 N -2 2]);
plot(t,message(i,:),'r');
title('message signal(POLAR form)');
xlabel('t--->');
ylabel('m(t)');
grid on;
hold on;
subplot(5,1,4);
plot(t,bpsk_sig(i,:));
title('BPSK signal');
xlabel('t--->);
title('BPSK signal');
ylabel('s(t)');
grid on;
hold on;
t1=t1+1.01;
t2=t2+1.01;
end
hold off
%plot the input binary data and carrier signal
subplot(5,1,1);
stem(m);
title('binary data bits');
xlabel('n--->');
ylabel('b(n)');
grid on;
subplot(5,1,3);
plot(t,c);
title('carrier signal');
xlabel('t--->');
ylabel('c(t)');
grid on;
Observation:The desired BPSK waveforms i.e. binary data, message signal, carrier signal and output waveforms are shown in figure 6.1.
Conclusion:The program for binary PSK modulation has been simulated in MATLAB and observed the desired waveforms.
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