simulating communication systems with matlab: an introduction

September 23, 2010

NIT DGP Student Branch

Aniruddha ChandraECE Department, NIT Durgapur, WB, India.

aniruddha.chandra@ieee.org

Simulating Communication Systems Simulating Communication Systems with MATLAB : An Introductionwith MATLAB : An Introduction

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

Sep. 23, 2010Presentation OutlinePresentation Outline

Objective of the Lecture

Expected Background

Simulating Analog Communication Systems Amplitude Modulation (AM)

Simulating Digital Communication SystemsBinary Phase Shift Keying (BPSK)

Expected Background

Sep. 23, 2010Objective of the LectureObjective of the Lecture

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, 2010Expected BackgroundExpected Background

I assume that …You understand

Basic MATLAB Operations (function, matrix)

Basics of Communication (modulation)

Performance Metrics (BER)

Expected Background

Sep. 23, 2010Analog Communication SystemsAnalog Communication Systems

Source

Channel

Destination Demodulator

Modulator

Sep. 23, 2010Simulate a SourceSimulate a Source

Source

Channel

Modulator

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

Sep. 23, 2010

Generate message signal (simple sine wave)

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; % Amplitudefm = 2*10^3; % Frequency

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

View the Signalplot(t,m,'r');

Simulate a SourceSimulate a Source

tfVtm mm 2sin

Sep. 23, 2010

Complete MATLAB Script [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');

Simulate a SourceSimulate a Source

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');

Sep. 23, 2010Simulate ModulationSimulate Modulation

Source

Channel

Modulator

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

WYSIWYG?? No

Sep. 23, 2010Amplitude ModulationAmplitude Modulation

Simulate with built-in functions [Prog4.m]

fs = 8000; % Sampling rate is 8000 samples per secondfc = 300; % Carrier frequency in Hzt = [0:0.1*fs]'/fs; % Sampling times for 0.1 secondm = sin(20*pi*t); % Representation of the signalv = ammod(m,fc,fs); % Modulate m to produce v

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

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

Don’t have the feel??? …. Try this

Define message signal, (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);

Define carrier,

Vc = 2; % Amplitudefc = 10^4; % Frequencyc = Vc*sin(2*pi*fc*t); % Carrier signal

tfVtm mm 2sin

tfVtc cc 2sin

Continued ….

Modulate the Signal,

v = (1+m/Vc).*c; % DSB-FC modulation

View Modulated Wave

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

VVtv cm

2sin2sin1

Sep. 23, 2010

Complete MATLAB Script [Prog5.m]

clear all; close all; clc;tmin = 0; tmax = 10^(-3); step = (tmax-tmin)/1000;t = tmin:step:tmax; % TimeVm = 1; Vc = 2; % Amplitude fm = 2*10^3; fc = 10^4; % Frequency

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

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

Amplitude ModulationAmplitude Modulation

Sep. 23, 2010

Assignment #2 [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

Sep. 23, 2010

Assignment #2 (Contd…) [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

Sep. 23, 2010DemodulationDemodulation

Demodulate DSB-SC with filter [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);

Sep. 23, 2010

Ideal Demodulation of DSB-SC [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);

DemodulationDemodulation

Sep. 23, 2010Analog Communication SystemsAnalog Communication Systems

Source

Channel

Modulator

Introduces noise … Additive White Gaussian Noise

Sep. 23, 2010Simulate ChannelSimulate Channel

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

Sep. 23, 2010Simulate ChannelSimulate Channel

Expected Background

Sep. 23, 2010Digital Communication SystemsDigital Communication Systems

Source

Channel

Modulator

Sep. 23, 2010Simulate BPSKSimulate BPSK

Simulation [Prog11.m]

%This program simulates BER of BPSK in AWGN channel% clear all; close all; clc; 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

Sep. 23, 2010ReferencesReferences

[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: an introduction

ece deptt

tmax vm

tmaxtmin1000 t

vm sin

f c t vc v

amplitude fc

amplitude modulationsep

vc sin

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