Question

Use the Matlab code discussed in class to build a simulator for the digital modulation scheme PPM Coherent. Once finished, run the simulations required to plot BER curves with a minimum probability of bit-error of 10.

1. Plots:

a. ??? vs ??? (??) plot – in the same graph, plot at least 4 BER curves corresponding to different values of symbol periods and pulse widths.

b. Transmitted signal plot – plot the transmitted signal corresponding to 3 bits.

c. Received signal plots – for the transmitted signal (3 bits), plot the received noisy signal for at least 4 values of ??? (e.g. 0 ??, 10 ??, 20 ??, 30 ??) .

Code in Matlab:

% Description: Simple simulator for digital (binary) communications

%% Main Function
function runComm_code()
clear;clc;
  
SNRdB = 0:0.5:26;
nBits = 1e6;
SNRdBLength = length(SNRdB);
Pe = ones(1,SNRdBLength);
clc; disp('Simulation running: 0.0% completed.');
for i = 1:SNRdBLength
Pe(i) = transmitReceive(nBits,SNRdB(i));
clc;fprintf('%s: %.1f%% completed','Simulation running',i/SNRdBLength*100);
end
hold on; semilogy(SNRdB,Pe); grid on;
clc; disp('Simulation finished.');
return

%% Bit Transmission Function
function [Perror,nErrors,TxBits,RxBits] = transmitReceive(nBits,SNRdB)
% TxBits = [0 1 1 0 1 0 0 1 1 1];
nBitsMax = 100000;
nBitsOrig = nBits;
TxBits = [];
RxBits =[];
if(nBits > nBitsMax)
n = ceil(nBits/nBitsMax);
nErrorsArr = zeros(1,n);
for i = 1:n
if(nBits < nBitsMax)
[~,nErrorsArr(i),TxBitsTmp,RxBitsTmp] = transmitReceive(nBits,SNRdB);
TxBits = [TxBits,TxBitsTmp];
RxBits = [RxBits,RxBitsTmp];
break;
else
[~,nErrorsArr(i),TxBitsTmp,RxBitsTmp] = transmitReceive(nBitsMax,SNRdB);
TxBits = [TxBits,TxBitsTmp];
RxBits = [RxBits,RxBitsTmp];
nBits = nBits - nBitsMax;
end
end
nErrors = sum(nErrorsArr);
Perror = nErrors/nBitsOrig;
return;
end
  
TxBits = round(rand(1,nBits));
TxSignals = modulation(TxBits);
[RxSignals] = addAWGNoise(TxSignals,SNRdB);
RxBits = demodulation(RxSignals);
errorBits = TxBits ~= RxBits;
nErrors = sum(errorBits);
Perror = nErrors/nBits;
  

return

%% Modulation and Demodulation Functions
function [outSignals,time] = modulation(inBits)

% This code is for On-Off Keying (OOK) modulation
% You need to substitute this with your own Matlab code according
% to your assigned modulation scheme.

pulseWidth = 1e-9;
timeWindow = 10.5e-9;
carrierFreq = 4e9;
  
signalBW = 1.5/pulseWidth;
osFactor = 1 + carrierFreq/signalBW;
  
[signal1,time] = pulseSignal(pulseWidth,timeWindow,osFactor);
signal1 = signal1.*squareSignal(time,carrierFreq);
signalLength = length(signal1);
signal0 = zeros(signalLength,1);
  
inBits = inBits(:)';
nBits = length(inBits);
outSignals = zeros(signalLength,nBits);
col0 = inBits == 0;
col1 = inBits == 1;
outSignals(:,col0) = repmat(signal0,1,sum(col0));
outSignals(:,col1) = repmat(signal1,1,sum(col1));

return
function [outBits] = demodulation(inSignals)
  
% This code is for On-Off Keying (OOK) modulation
% You need to substitute this with your own Matlab code according
% to your assigned modulation scheme.

SNRmin = 10^(12/10);
Ps = sum(modulation(1).^2);
Po = Ps./SNRmin;
  
Psignals = sum(inSignals.^2);
outBits = Psignals > Po;
return

%% Noise Adding Function
function [outSignals,noiseSignals] = addAWGNoise(signals,SNRdB)
signalsSize = size(signals);
SNR = 10^(SNRdB/10);
Ps = max(sum(signals.^2));
Po = Ps./SNR;
noiseSignals = sqrt(Po/2).*randn(signalsSize(1),signalsSize(2));
outSignals = signals+noiseSignals;
return

%% Signal Creation Functions
function [outSignal,time] = pulseSignal(Tp,Tw,osFactor)
if(nargin == 2), osFactor = 1; end
if(osFactor < 1), osFactor = 1; end
B = 1.5/Tp;
fs = osFactor*2*B;
Nw = ceil(fs*Tw);
Np = ceil(fs*Tp);
outSignal = [0; ones(Np,1); zeros(Nw-Np-1,1)];
outSignal(end)=0;
time = (0:length(outSignal)-1)'/fs;
return
function [outSignal] = squareSignal(time,freq)
tsample = time(2)-time(1);
tperiod = 1/freq;
n = ceil(tperiod/tsample);
npos = ceil(n/2);
nneg = n - npos;
Nperiods = ceil(time(end)*freq);
signalTmp = [ones(npos,1); -1*ones(nneg,1)];
outSignal = repmat(signalTmp,Nperiods+1,1);
outSignal = [ 0; outSignal(1:length(time)-1) ];
return

Answer 1

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Answer:

Explanation:

CODE:

Answer for 1-a

clc;          //it clears the data

clear all; //clears all the pervious data

close all; //closes all the pervious data

b=101;    //bit rate

data=randint(1,b);%random bit generation (1 or 0)

s=2*data-1

SNRdB=0:9;         //signal to noise ratio I db

SNR=10.^(SNRdB/10);

for(k=1:length(SNRdB))

y=s+awgn(s,SNRdB(k));      //y signal representation

error=0;

for(c=1:1:b)

    if (y(c)>0&&data(c)==0)||(y(c)<0&&data(c)==1)

        error=error+1;               //increment the error value

    end

end

error=error/b; %Calculate error/bit

m(k)=error;            //mk signal wil end here

end

figure(1)

semilogy(SNRdB,m,'r','linewidth',2),grid on,hold on;

BER_th=(1/2)*erfc(sqrt(SNR));          //square of the bit rate

semilogy(SNRdB,BER_th,'k','linewidth',2);

title(' curve for Bit Error Rate verses SNR for Binary PSK modulation');

xlabel(' SNR(dB)');

ylabel('BER');        //y labei reperesentation

legend('simulation','theorytical')

Answr for 1-b:

clear all; //clears all the pervious data

close all; closes all the pervious data

T=1;     /t value representation

b=[1 0 1];        //bit rate

NRZ_out=[];

Vp=1;

for index=1:size(b,2)

if b(index)==1

NRZ_out=[NRZ_out ones(1,200)*Vp]; //non return zero value

elseif b(index)==0

NRZ_out=[NRZ_out ones(1,200)*(-Vp)];

end

end//some the prog end herev

figure(1);

stem(b);

xlabel('Time (seconds)-->')

ylabel('Amplitude (volts)-->')

title('Impulses of bits to be transmitted');

figure(2);

plot(NRZ_out);//ploting th nrz plot

xlabel('Time (seconds)-->');

ylabel('Amplitude (volts)-->');

title('Generated NRZ signal');

t=0.005:0.005:5;

f=5;

s=NRZ_out.*(sqrt(2/T)*cos(2*pi*f*t));

figure;

plot(s);

xlabel('Time (seconds)-->');

ylabel('Amplitude (volts)-->');

title('BPSK Modulated signal'); //representing of the title

answer for 1- c

y=[];

demodulated=Modulated.*(sqrt(2/T)*cos(2*pi*f*t));

for i=1:200:size(demodulated,2)

y=[y trapz(t(i:i+199),demodulated(i:i+199))];

end

received=y>0;

figure;

stem(received)

title('Impulses of Received bits');

xlabel('Time (seconds)-->');     //xlabel representation

ylabel('Amplitude (volts)')

Eb_N0_dB = 0 ;

Eb_N0=10^(Eb_N0_dB/10);

M=2;//representing the m-value

fs=1000;

T=1;

Ts=T/log2(M); //ts value

R=1/Ts;

A=5;

E=A^2*T;

ts=1/fs;

t=0:ts:1

noiseVariance=E*fs/(2*log2(M)*Eb_N0);

sigma_n=sqrt(noiseVariance);

n = sigma_n*randn(1,length(s));

r = s+n ;% received noisy signal array

subplot(4,1,4);

plot(t,r);           //plot the t,r signals

axis([0 MaxPlotTime min(r) max(r)]);

grid on;//it will terminate here

xlabel('time');

ylabel('r(t)');

title('Received Bandpass BPSK signal r(t)'); //representing the title

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