Simulating Communication Systems with MATLAB

Simulating Communication Systems
with MATLAB : An Introduction

Aniruddha Chandra
ECE Department, NIT Durgapur, WB, India.
aniruddha.chandra@ieee.org

September 23, 2010

NIT DGP Student
Branch

Presentation Outline Sep. 23, 2010

 Objective of the Lecture

 Expected Background

 Simulating Analog Communication Systems
Amplitude Modulation (AM)

 Simulating Digital Communication Systems
Binary Phase Shift Keying (BPSK)

A. Chandra, ECE Deptt., NITD Simulating Communication Systems with MATLAB 2

Objective of the Lecture Sep. 23, 2010

After the Lecture … You’ll be able to

 Write your own Matlab Script

 Make a Analog/ Digital Communication Link

 Compare your Results with Theoretical Values


Expected Background Sep. 23, 2010

I assume that …You understand

 Basic MATLAB Operations (function, matrix)

 Basics of Communication (modulation)

 Performance Metrics (BER)


Analog Communication Systems Sep. 23, 2010

Source Modulator

Channel

Destination Demodulator


Simulate a Source Sep. 23, 2010

Source Modulator

Channel


 Produces message signal … e.g. a simple Sine wave



Generate message signal (simple sine wave)
m( t ) = Vm sin ( 2πf mt )

 Define time instants (1000 sample points)
tmin = 0; tmax = 10^(-3); step = (tmax-tmin)/1000;
t = tmin:step:tmax;

 Define amplitude and frequency (initial phase is zero)
Vm = 1; % Amplitude
fm = 2*10^3; % Frequency

 Construct the Signal
m = Vm*sin(2*pi*fm*t);

 View the Signal
plot(t,m,'r');



Complete MATLAB Script [Prog1.m]

t = tmin:step:tmax;
fm = 2*10^3;
Vm = 1;
plot(t,m,'r');



Assignment #1 [Prog2.m], [Prog3.m]

 What happens if there is an initial phase?
phi_deg = 45;
phi_rad = phi_deg*pi/180;
m = Vm*sin(2*pi*fm*t+phi_rad);

 What happens if the message is not sinusoidal?
tmin = 0; tmax = 1; step = (tmax-tmin)/1000;
t = tmin:step:tmax;
f = 2;
m = sawtooth(2*pi*f*t);
plot(t,m,'r');


Simulate Modulation Sep. 23, 2010

Source Modulator

Channel


 Built-in functions are available (ammod, amdemod etc.)
 WYSIWYG?? No


Amplitude Modulation Sep. 23, 2010

Simulate with built-in functions [Prog4.m]
fs = 8000; % Sampling rate is 8000 samples per second
fc = 300; % Carrier frequency in Hz
t = [0:0.1*fs]'/fs; % Sampling times for 0.1 second
m = sin(20*pi*t); % Representation of the signal
v = ammod(m,fc,fs); % Modulate m to produce v

figure(1)
subplot(2,1,1); plot(t,m); % Plot m on top
subplot(2,1,2); plot(t,v); % Plot v below

mr = amdemod(v,fc,fs); % Demodulate v to produce m

figure(2);
subplot(2,1,1); plot(t,m); % Plot m on top
subplot(2,1,2); plot(t,mr); % Plot mr below

Source: Introduction to Communications Toolbox in MATLAB 7.6.0 (R2008) by Amit Degada
Available: http://amitdegada.weebly.com/download.html



Don’t have the feel??? …. Try this

 Define message signal, m( t ) = Vm sin ( 2πf m t ) (as done earlier)

t = tmin:step:tmax;
Vm = 1;
fm = 2*10^3;

 Define carrier, c( t ) = Vc sin ( 2πf c t )

Vc = 2; % Amplitude
fc = 10^4; % Frequency
c = Vc*sin(2*pi*fc*t); % Carrier signal



Continued ….
 Vm 
 Modulate the Signal, v( t ) = Vc 1 + sin ( 2πf mt )  sin ( 2πf c t )
 Vc 
v = (1+m/Vc).*c; % DSB-FC modulation

 View Modulated Wave

plot(t,v); % Modulated Wave
hold on;
plot(t,Vc*(1+m/Vc),'r:'); % Upper Envelope
hold on;
plot(t,-Vc*(1+m/Vc),'r:'); % Lower Envelope
hold off ;



Complete MATLAB Script [Prog5.m]

clear all; close all; clc;
t = tmin:step:tmax; % Time
Vm = 1; Vc = 2; % Amplitude
fm = 2*10^3; fc = 10^4; % Frequency

m = Vm*sin(2*pi*fm*t); % Message
c = Vc*sin(2*pi*fc*t); % Carrier
v = (1+m/Vc).*c; % Modulated Wave

plot(t,v); hold on;
plot(t,Vc*(1+m/Vc),'r:'); hold on; % Upper Envelope
plot(t,-Vc*(1+m/Vc),'r:'); hold off % Lower Envelope



Assignment #2 [Prog6.m]

 How to view effect of changing modulation index?
t = tmin:step:tmax;
Vm = 1; mu = 1.5; Vc = Vm/mu;
fm = 2*10^3; fc = 10^4;

c = Vc*sin(2*pi*fc*t);
v = (1+m/Vc).*c;

plot(t,v); hold on;
plot(t,Vc*(1+m/Vc),'r:'); hold on;
plot(t,-Vc*(1+m/Vc),'r:'); hold off



Assignment #2 (Contd…) [Prog7.m]

 How to simulate DSB-SC modulation?
t = tmin:step:tmax;
Vm = 2; Vc = 1;
fm = 2*10^3; fc = 10^4;

v = m.*c;

plot(t,v); hold on;
plot(t,m,'r:'); hold on;
plot(t,-m,'r:'); hold off


Demodulation Sep. 23, 2010

Demodulate DSB-SC with filter [Prog8.m]
tmin = 0; tmax = 1; step = (tmax-tmin)/(10^3);
t = tmin:step:tmax;
Vm = 2; Vc = 1;
fm = 2; fc = 10^2;

v = m.*c;

r = v.*c;

[b a] = butter(1,0.01);
mr = filter(b,a,r);

figure(1)
subplot(2,1,1); plot(t,m);
subplot(2,1,2); plot(t,mr);



Ideal Demodulation of DSB-SC [Prog9.m]
fs = 10^5; N = 10^5;
t = 1/fs:1/fs:N/fs;
fm = 2; fc = 10^3;
m = sin(2*pi*fm*t);
c = sin(2*pi*fc*t);
v = m.*c;

r = zeros(1,N); n =f s/fc;
for k = 1:fc
mr((k-1)*n+1:k*n) = 2*v((k-1)*n+1:k*n)*c((k-1)*n+1:k*n)'/n;
end

figure(1)
subplot(2,1,2); plot(t,mr);


Analog Communication Systems Sep. 23, 2010

Source Modulator

Channel


 Introduces noise … Additive White Gaussian Noise


Simulate Channel Sep. 23, 2010

Introducing AWGN [Prog10.m]
fs = 10^5; N = 10^5;
t = 1/fs:1/fs:N/fs;
fm = 2; fc = 10^3;
m = sin(2*pi*fm*t);
c = sin(2*pi*fc*t);
v = m.*c;

SNRdB = 10; SNR = 10^(SNRdB/10);
vn = var(v)/SNR;
n = sqrt(vn)*randn(1,N);
v = v + n;

r=zeros(1,N); n=fs/fc;
for k=1:fc
mr((k-1)*n+1:k*n)=2*v((k-1)*n+1:k*n)*c((k-1)*n+1:k*n)'/n;
end

figure(1)
subplot(2,1,2); plot(t,mr); axis([0 1 -1 1])


Simulate Channel Sep. 23, 2010


Digital Communication Systems Sep. 23, 2010

Source Modulator

Channel



Simulate BPSK Sep. 23, 2010

Simulation [Prog11.m]

%This program simulates BER of BPSK in AWGN channel%
num_bit=100000; %Signal length
max_run=20; %Maximum number of iterations for a single SNR
Eb=1; %Bit energy
SNRdB=0:1:9; %Signal to Noise Ratio (in dB)
SNR=10.^(SNRdB/10);

hand=waitbar(0,'Please Wait....');
for count=1:length(SNR) %Beginning of loop for different SNR
avgError=0;
No=Eb/SNR(count); %Calculate noise power from SNR



Simulation (Contd.) [Prog11.m]
for run_time=1:max_run %Beginning of loop for different runs
waitbar((((count-1)*max_run)+run_time-1)/(length(SNRdB)*max_run));
Error=0;

data=randint(1,num_bit); %Generate binary data source
s=2*data-1; %Baseband BPSK modulation

N=sqrt(No/2)*randn(1,num_bit); %Generate AWGN

Y=s+N; %Received Signal

for k=1:num_bit %Decision device taking hard decision and deciding error
if ((Y(k)>0 && data(k)==0)||(Y(k)<0 && data(k)==1))
Error=Error+1;
end
end

Error=Error/num_bit; %Calculate error/bit
avgError=avgError+Error; %Calculate error/bit for different runs
end %Termination of loop for different runs



Simulation (Contd.) [Prog11.m]
BER_sim(count)=avgError/max_run; %Calculate BER for a particular SNR

end %Termination of loop for different SNR
BER_th=(1/2)*erfc(sqrt(SNR)); %Calculate analytical BER
close(hand);

semilogy(SNRdB,BER_th,'k'); %Plot BER
hold on
semilogy(SNRdB,BER_sim,'k*');
legend('Theoretical','Simulation',3);
axis([min(SNRdB) max(SNRdB) 10^(-5) 1]);
hold off


References Sep. 23, 2010

[1] http://www.mathworks.com/matlabcentral/

[2] http://www.freewebs.com/acwebpage/teaching.htm

[3] B.P. Lathi and Z. Ding, Modern Digital and Analog
Communication Systems, Oxford University Press,
International 4th edition, 2010.

[4] J.G. Proakis, M. Salehi, and G. Bauch, Contemporary
Communication Systems using MATLAB, Thomson/ CL-
Engineering, 2nd edition, 2003.


Sep. 23, 2010

Thank You!

Questions???
aniruddha.chandra@ieee.org


Simulating Communication Systems with MATLAB

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