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

1. Plots:

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

b. Transmitted signal plot – plot the transmitted signalcorresponding 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','Simulationrunning',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 codeaccording
% 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 codeaccording
% 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