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##### Introduction

BPSK stands for Binary Phase Shift Keying. It is a type of digital modulation technique used in digital communications. In BPSK, the phase of a carrier signal is changed to represent two different binary digits or symbols (0 or 1). The phase of the carrier signal is shifted 180 degrees to represent a binary “1”, and is not shifted to represent a binary “0”. BPSK is a simple and robust modulation technique that is widely used in wireless communication systems due to its low complexity and ease of implementation. It is also known to be a very resilient to noise, thus making it a popular choice for long-distance wireless communications.

Matlab Software

##### Explanation

BPSK (Binary Phase Shift Keying) is a digital modulation technique that uses a carrier signal with two different phase states, 0 and 180 degrees, to represent binary data (0 or 1).

In MATLAB, one way to implement BPSK modulation is by first generating a binary data sequence of 0s and 1s. Then, using a carrier signal at a specific frequency, the phase of the carrier is shifted by 180 degrees to represent a binary “1”, and is not shifted to represent a binary “0”. The modulated signal can be created by multiplying the binary data sequence with the carrier signal.

##### Matlab Code
``````clc;
clear all;
close all;
%fine Transmitted Signal=
N=10;
x_inp=round(rand(1,N)); % Message Signal
Tb=0.0001; % Bit Period

%Represent Input Signal as Digital Signal
x_bit=[];
nb=100;

for n=1:1:N
if x_inp(n)==1
x_bitt=ones(1,nb);
else
x_bitt=zeros(1,nb);
end
x_bit=[x_bit x_bitt];
end
t1=Tb/nb:Tb/nb:nb*N*(Tb/nb);
f1=figure(1);
set(f1,'color',[1 1 1]);
subplot(3,1,1);
plot(t1,x_bit,'LineWidth',2);
grid on;
axis([0 Tb*N -0.5 1.5]);
ylabel('Amplitude(volt)');
xlabel('Time(sec)');
title('Input Signal as Digital Signal');

%fine BPSK Modulation
Ac=10;
mc=4;
fc=mc*(1/Tb);
fi1=0;
fi2=pi;
t2=Tb/nb:Tb/nb:Tb;
t2L=length(t2);
x_mod=[];
for i=1:1:N
if x_inp(i)==1
x_mod0=Ac*cos(2*pi*fc*t2+fi1);
else
x_mod0=Ac*cos(2*pi*fc*t2+fi2);
end
x_mod=[x_mod x_mod0];
end

t3=Tb/nb:Tb/nb:Tb*N;
subplot(3,1,2);
plot(t3,x_mod);
xlabel('Time(sec)');
ylabel('Amplitude(volt)');
title('Signal of BPSK modulation');

%Transmitted Signal x
x=x_mod;
h=1;
w=0;

y=h.*x+w;

%BPSK Demodulation
y_dem=[];
for n=t2L:t2L:length(y)
t=Tb/nb:Tb/nb:Tb;
c=cos(2*pi*fc*t);
y_dem0=c.*y((n-(t2L-1)):n);
t4=Tb/nb:Tb/nb:Tb;
z=trapz(t4,y_dem0);
A_dem=round((2*z/Tb));
if(A_dem>Ac/2)
A=1;
else
A=0;
end
y_dem=[y_dem A];
end
x_out=y_dem;

%Represent output signal as Digital Signal

xx_bit=[];
for n=1:length(x_out)
if x_out(n)==1
xx_bitt=ones(1,nb);
else
xx_bitt=zeros(1,nb);
end
xx_bit=[xx_bit xx_bitt];
end
t4=Tb/nb:Tb/nb:nb*length(x_out)*(Tb/nb);
subplot(3,1,3)
plot(t4,xx_bit,'LineWidth',2);
grid on;
axis([0 Tb*length(x_out) -0.5 1.5]);
ylabel('Amplitude(volt)');
xlabel('Time(sec)');
title('Output Signal as Digital Signal');
``````
##### Output

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