Write a MATLAB program to Simulate(modulate) BPSK signals for the data {10000111} and demodulate it using MATLAB. Plot all waveforms. Obtain a bit error rate graph.

% This is for the modulation and Demodulation of BPSK for the data [ 1 0 0 0 0 1 1 1]

% If you obtain the Bit error rate for the given data please post it in the comments

% ********************* BPSK modulation and de-modulation ****************%

clc;

clear all;

close all;

% ********************* Define transmitted signal *************************

x_inp = [1 0 0 0 0 1 1 1]; % Binary information as stream of bits (binary signal 0 or 1)

N = length(x_inp);

Tb = 0.0001; %Data rate = 1MHz i.e., bit period (second)

disp('Binary Input Information at Transmitter: ');

disp(x_inp);

% ********************* Represent input signal as digital signal ****

x_bit=[];

nb=100; % Digital signal per bit

for n=1:1:N

if x_inp(n)==1;

x_bitt=ones(1,nb);

else x_inp(n)==0;

x_bitt=zeros(1,nb);

end

x_bit=[x_bit x_bitt];

end

t1=Tb/nb:Tb/nb:nb*N*(Tb/nb); % time of the signal

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');

% ********************* Define BPSK Modulation ****************************

Ac=5; % Amplitude of carrier signal

mc=4; % fc>>fs fc=mc*fs fs=1/Tb

fc=mc*(1/Tb); % carrier frequency for bit 1

fi1=0; % carrier phase for bit 1

fi2=pi; % carrier phase for bit 0

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);%modulation signal with carrier signal 1

else

x_mod0=Ac*cos(2*pi*fc*t2+fi2);%modulation signal with carrier signal 2

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;

% ********************* Channel model h and w *****************************

h=1; % Fading

w=0; % Noise

% ********************* Received signal y *********************************

y=h.*x+w;

% ********************* Define BPSK Demodulation **************************

y_dem=[];

for n=t2L:t2L:length(y)

t=Tb/nb:Tb/nb:Tb;

c=cos(2*pi*fc*t); % carrier siignal

y_dem0=c.*y((n-(t2L-1)):n);

t4=Tb/nb:Tb/nb:Tb;

z=trapz(t4,y_dem0); % intregation

A_dem=round((2*z/Tb));

if(A_dem>Ac/2) % logic level = Ac/2

A=1;

else

A=0;

end

y_dem=[y_dem A];

end

x_out=y_dem; % output signal;

% *************** 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 x_out(n)==0;

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');

[John D'Errico]

And your question is????

Answer 1

[Nikshith Shetty]

% This is for the modulation and Demodulation of BPSK for the data [ 1 0 0 0 0 1 1 1]

% If you obtain the Bit error rate for the given data please post it in the comments

% ********************* BPSK modulation and de-modulation ****************%

clc;

clear all;

close all;

% ********************* Define transmitted signal *************************

x_inp = [1 0 0 0 0 1 1 1]; % Binary information as stream of bits (binary signal 0 or 1)

N = length(x_inp);

Tb = 0.0001; %Data rate = 1MHz i.e., bit period (second)

disp('Binary Input Information at Transmitter: ');

disp(x_inp);

% ********************* Represent input signal as digital signal ****

x_bit=[];

nb=100; % Digital signal per bit

for n=1:1:N

if x_inp(n)==1;

x_bitt=ones(1,nb);

else x_inp(n)==0;

x_bitt=zeros(1,nb);

end

x_bit=[x_bit x_bitt];

end

t1=Tb/nb:Tb/nb:nb*N*(Tb/nb); % time of the signal

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');

% ********************* Define BPSK Modulation ****************************

Ac=5; % Amplitude of carrier signal

mc=4; % fc>>fs fc=mc*fs fs=1/Tb

fc=mc*(1/Tb); % carrier frequency for bit 1

fi1=0; % carrier phase for bit 1

fi2=pi; % carrier phase for bit 0

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);%modulation signal with carrier signal 1

else

x_mod0=Ac*cos(2*pi*fc*t2+fi2);%modulation signal with carrier signal 2

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;

% ********************* Channel model h and w *****************************

h=1; % Fading

w=0; % Noise

% ********************* Received signal y *********************************

y=h.*x+w;

% ********************* Define BPSK Demodulation **************************

y_dem=[];

for n=t2L:t2L:length(y)

t=Tb/nb:Tb/nb:Tb;

c=cos(2*pi*fc*t); % carrier siignal

y_dem0=c.*y((n-(t2L-1)):n);

t4=Tb/nb:Tb/nb:Tb;

z=trapz(t4,y_dem0); % intregation

A_dem=round((2*z/Tb));

if(A_dem>Ac/2) % logic level = Ac/2

A=1;

else

A=0;

end

y_dem=[y_dem A];

end

x_out=y_dem; % output signal;

% *************** 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 x_out(n)==0;

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');

[Tien Bui]

do you know how to rewrite this code with Python? Thank you.

Answer 2

[Idin Motedayen-Aval]

The question, as stated, doesn't seem to be specific enough.

The given code plots 100 points for each bit of data, and shows the BPSK modulation on a carrier signal. That all seems to be fine.

Bit since this page is getting a fair number of views, it seems BPSK mod/demod is a popular topic. I am going to give some answers to the question in the title (ignoring the MATLAB code given above).

Modulating/demodulating a BPSK signal using Communications Toolbox is almost trivial:

x =  [1 0 0 0 0 1 1 1]; % data
x_mod = pskmod(x,2); % BPSK Modulation
x_hat = pskdemod(x_mod,2); % BPSK Demodulation

% Plots (use "stairs" to give the stair-step shape)
subplot(3,1,1)
stairs(x)
subplot(3,1,2)
stairs(real(mod_x))
subplot(3,1,3)
stairs(x_hat)

To generate a bit error rate (BER) graph (as the last part of the title says), it is not enough to simulate 8 bits! One must simulate many more bits. Below is a very simple version of such a code (there are many more elaborate examples given in MATLAB Answers).

% To get bit error rate curve
% one needs many more bits (generated at random)
N = 1e6;  % number of bits to simulate
x = randi([0,1],[N,1]); % generate N bits (1 million in this case)
x_mod = pskmod(x,2);      % BPSK modulate

snr_vec = 0:9;
ber = zeros(size(snr_vec)); % pre-allocate BER vector
for idx = 1:length(snr_vec)
    y = awgn(x_mod,snr_vec(idx));  % Add noise
    x_hat = pskdemod(y,2);    % demod received signal
    errs = sum(x_hat~=x);     % count errors
    ber(idx) = errs/N;
end

figure % create new figure window
semilogy(snr_vec,ber,'-*')

Hope this helps someone.