Matlab Communication

Simulating Communication Systems with MATLAB : An Introduction I ntroduction Anirud dha Chandra Chandra ECE Department, NIT Durgapur, WB, India. [email protected]

September 23, 2010

Presentation Outline 

Objective of the Lecture

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Expected Background

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Sep. 23, 2010

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

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Expected Background

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Sep. 23, 2010




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Expected Background

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Sep. 23, 2010




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Sep. 23, 2010

After the Lecture … You’ll be able to

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Write your own Matlab Script

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Make a Analog/ Digital Communication Link

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Compare your Results with Theoretical Values



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Expected Background

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Sep. 23, 2010




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Expected Background

Sep. 23, 2010

I assume that …You understand

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Basic MATLAB Operations (function, matrix)

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Basics of Communication (modulation)

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Performance Metrics (BER)



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Expected Background

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Sep. 23, 2010




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Analog Communication Systems

Source

Sep. 23, 2010

Modulator Channel

Destination


Demodulator


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Simulate a Source

Source

Sep. 23, 2010

Modulator Channel

Destination

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Demodulator

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



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Simulate a Source

Sep. 23, 2010

Generate message signal (simple sine wave) m(t ) = V m sin (2π f mt ) 

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

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

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% Amplitude % Frequency

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

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View the Signal plot(t,m,'r');



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Simulate a Source Complete MATLAB Script

Sep. 23, 2010

[Prog1.m]

tmin = 0; tmax = 10^(-3); step = (tmax-tmin)/1000; t = tmin:step:tmax; fm = 2*10^3; Vm = 1; m = Vm*sin(2*pi*fm*t); plot(t,m,'r');



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Simulate a Source



Sep. 23, 2010

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Simulate a Source Assignment #1 

Sep. 23, 2010

[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);

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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');



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Simulate Modulation

Source

Sep. 23, 2010

Modulator Channel

Destination

Demodulator

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Built-in functions are available (ammod, amdemod etc.)

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WYSIWYG?? No



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Amplitude Modulation Simulate with built-in functions fs = 8000; fc = 300; t = [0:0.1*fs]'/fs; m = sin(20*pi*t); v = ammod(m,fc,fs);

% % % % %

[Prog4.m]

Sampling rate is 8000 samples per second Carrier frequency in Hz Sampling times for 0.1 second Representation of the signal Modulate m to produce v

figure(1) subplot(2,1,1); plot(t,m); subplot(2,1,2); plot(t,v); mr = amdemod(v,fc,fs);

Sep. 23, 2010

% Plot m on top % Plot v below

% Demodulate v to produce m

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

% Plot m on top % Plot mr below

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



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Amplitude Modulation



Sep. 23, 2010

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Sep. 23, 2010

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Sep. 23, 2010

Don’t have the feel??? …. Try this 

Define message signal, m(t ) = V m sin (2π f m t ) (as done earlier) tmin = 0; tmax = 10^(-3); step = (tmax-tmin)/1000; t = tmin:step:tmax; Vm = 1; fm = 2*10^3; m = Vm*sin(2*pi*fm*t);

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Define carrier, c(t ) = V c sin (2π f c t ) Vc = 2; % Amplitude fc = 10^4; % Frequency c = Vc*sin(2*pi*fc*t); % Carrier signal



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Sep. 23, 2010

Continued …. 

v = (1+m/Vc).*c;

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⎡

V m

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V c

Modulate the Signal, v(t ) = V c ⎢1 +

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sin (2π f mt )⎥ sin (2π f ct )

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% 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 ;



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Amplitude Modulation Complete MATLAB Script

Sep. 23, 2010

[Prog5.m]

clear all; close all; clc; tmin = 0; tmax = 10^(-3); step = (tmax-tmin)/1000; 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); c = Vc*sin(2*pi*fc*t); v = (1+m/Vc).*c;

% Message % Carrier % 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



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Sep. 23, 2010

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Amplitude Modulation Assignment #2 

Sep. 23, 2010

[Prog6.m]

How to view effect of changing modulation index? tmin = 0; tmax = 10^(-3); step = (tmax-tmin)/1000; t = tmin:step:tmax; Vm = 1; mu = 1.5; Vc = Vm/mu; fm = 2*10^3; fc = 10^4; m = Vm*sin(2*pi*fm*t); 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



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Amplitude Modulation Assignment #2 (Contd…) 

Sep. 23, 2010

[Prog7.m]

How to simulate DSB-SC modulation? tmin = 0; tmax = 10^(-3); step = (tmax-tmin)/1000; t = tmin:step:tmax; Vm = 2; Vc = 1; fm = 2*10^3; fc = 10^4; m = Vm*sin(2*pi*fm*t); c = Vc*sin(2*pi*fc*t); v = m.*c; plot(t,v); hold on; plot(t,m,'r:'); hold on; plot(t,-m,'r:'); hold off



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Demodulation Demodulate DSB-SC with filter

Sep. 23, 2010

[Prog8.m]

clear all; close all; clc; tmin = 0; tmax = 1; step = (tmax-tmin)/(10^3); t = tmin:step:tmax; Vm = 2; Vc = 1; fm = 2; fc = 10^2; m = Vm*sin(2*pi*fm*t); c = Vc*sin(2*pi*fc*t); 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);



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Demodulation



Sep. 23, 2010

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Demodulation Ideal Demodulation of DSB-SC

Sep. 23, 2010

[Prog9.m]

clear all; close all; clc; 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(2,1,1); plot(t,m); subplot(2,1,2); plot(t,mr);



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Demodulation



Sep. 23, 2010

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Analog Communication Systems

Source

Sep. 23, 2010

Modulator Channel

Destination

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Demodulator

Introduces noise … Additive White Gaussian Noise



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Simulate Channel Introducing AWGN

Sep. 23, 2010

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



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Simulate Channel



Sep. 23, 2010

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Expected Background

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Sep. 23, 2010




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Digital Communication Systems

Source

Sep. 23, 2010

Modulator Channel

Destination


Demodulator


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Simulate BPSK Simulation %This program simulates BER clear all; close all; clc; num_bit=100000; max_run=20; Eb=1; SNRdB=0:1:9; SNR=10.^(SNRdB/10);

Sep. 23, 2010

[Prog11.m] of BPSK in AWGN channel% %Signal length %Maximum number of iterations for a single SNR %Bit energy %Signal to Noise Ratio (in dB)

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



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Simulate BPSK Simulation (Contd.)

Sep. 23, 2010

[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); s=2*data-1;

%Generate binary data source %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; avgError=avgError+Error; end


%Calculate error/bit %Calculate error/bit for different runs %Termination of loop for different runs


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Simulate BPSK Simulation (Contd.)

Sep. 23, 2010

[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



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Simulate BPSK



Sep. 23, 2010

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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/ CLEngineering, 2nd edition, 2003.



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Matlab Communication

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