OFDMwFading.m

%% OFDM with a Fading Channel
%% Housekeeping and Constant Assignment
close all
clc  

for L=[16 64 256]  %size of IFFT/FFT
    if L==16
        m=4;  %m = log2(M) is the number bits per symbol or M = 2^m
        M=2^m;    %number of symbols in M-ary modulation
    elseif L==64
        m=6;    %m = log2(M) is the number bits per symbol or M = 2^m
        M=2^m;    %number of symbols in M-ary modulation
    else
        m=8;    %m = log2(M) is the number bits per symbol or M = 2^m
        M=2^m;    %number of symbols in M-ary modulation
    end
    
N=200;  %number of OFDM symbols

%% (a) Generate Input Bit Sequence
% Generate a random sequence bk of 1s and 0s with equal probability of 
% length m×L×N. Suggested values are: m = 2; L = 16 (64 and 256 are 
% optional); and N = 200 or more.
bits_bk =randi([0 1],[N*L*m 1]);    %Input Bit Sequence

%% (b) Convert Bit Sequence to Bit Group Sequence
%  Let us consider QPSK, i.e., m = 2 or M = 4. A higher order modulation is 
%  an option. Convert groups of m bits mk into a sequence of unsigned 
%  decimal values.
bitsTo_M_Vectors_mk = reshape(bits_bk,length(bits_bk)/m,m);     %Bit Group
DecimalVector = bi2de(bitsTo_M_Vectors_mk);

%% (c) Convert Bit Group Sequence into Constellation Symbol Group
%  Use the constellation diagram below to map mk into constellation symbol 
% sequence Xk. These are complex values (I-Q data).
Symbols_Xk = qammod(DecimalVector,L,0,'gray');  %Constellation Symbol Group

%% (d) Apply Constellation Symbol Groups to IFFT
%  Take a block of size L constellation symbols and apply the IFFT 
% algorithm. Repeat this N times. These are complex valued too. 
SymbolsIFFT = ifft(Symbols_Xk); 

%% (e) Calculate Gaussian Noise and Rayleigh Fading for Signal
%  Simulate the channel as appropriate for each scenario. For AWGN, add 
% (I-Q) white Gaussian noise with zero mean; suggested standard deviation 
% values are ? = 0, 0.02, 0.08. The fading cannel can be realized in a 
% number of ways with Rayleigh being the simplest. Here are two models 
% to consider (the second is optional).  
sigmaValues = [0.0, 0.02, 0.08];    %Standard Deviation 
randQ=randn(length(Symbols_Xk),1)*i;    %Creates random variations of Q
randI=randn(length(Symbols_Xk),1);      %Creates random variations of I
Noise=(randQ+randI)*sigmaValues;        %Imposes Noise to the signal vector
% Add Stanford University Interium Model Fading to 
%SUI channel   y(n)=x(n)+0.5x(n-1)+0.25x(n-2)


%% (ea) Fading Scenario 1 SingleCarrier Modulation,fading Channel
SymbolsOut_rk_SingleCarrier(1)=Symbols_Xk(1);
SymbolsOut_rk_SingleCarrier(2)=Symbols_Xk(2)+0.5* ...
    SymbolsOut_rk_SingleCarrier(1);
for i=3:N*L
    SymbolsOut_rk_SingleCarrier(i)=Symbols_Xk(i)+0.5*Symbols_Xk(i-1)+ ...
        0.25*Symbols_Xk(i-2);
end

%% (eb) Fading Scenario 2 Multicarrier Modulation, fading channel
SymbolsOut_rk_woNoise(1)=SymbolsIFFT(1);
SymbolsOut_rk_woNoise(2)=SymbolsIFFT(2)+0.5*SymbolsIFFT(1);
for i=3:N*L
    SymbolsOut_rk_woNoise(i)=SymbolsIFFT(i)+0.5*SymbolsIFFT(i-1)+ ...
        0.25*Symbols_Xk(i-2);
end

%% (ec) Noise Scenario 3 MultiCarrier Modulation, AWGN channel
SymbolsOut_rk(:,1)=SymbolsIFFT+Noise(:,1);
SymbolsOut_rk(:,2)=SymbolsIFFT+Noise(:,2);
SymbolsOut_rk(:,3)=SymbolsIFFT+Noise(:,3);

%% (f) Use FFT to Recover Constellation Symbol
% (fa) N/A
% (fb) FFT Scenario 2 Multicarrier Modulation, fading channel
SymbolsInFFT_Rayleigh = fft(SymbolsOut_rk_woNoise);

% (fc) FFT Scenario 3 MultiCarrier Modulation, AWGN channel
SymbolsInFFT_AWGM(:,1) = fft(SymbolsOut_rk(:,1));
SymbolsInFFT_AWGM(:,2) = fft(SymbolsOut_rk(:,2));
SymbolsInFFT_AWGM(:,3) = fft(SymbolsOut_rk(:,3));

%% (g) Implement Demapping to Return Received Symbols to Bit Stream 
% (ga) Demap Scenario 1 SingleCarrier Modulation,fading Channel
SymbolsIn_dk_Single(1,:) = qamdemod(SymbolsOut_rk_SingleCarrier,L,0,...
    'gray');

% (gb) Demap Scenario 2 Multicarrier Modulation,Raleigh fading channel 
SymbolsIn_dk_Rayleigh(1,:) = qamdemod(SymbolsInFFT_Rayleigh,L,0,...
    'gray');

% (gc) Demap Scenario 3 MultiCarrier Modulation, AWGN channel
SymbolsIn_dk(:,1) = qamdemod(SymbolsInFFT_AWGM(:,1),L,0,'gray');
SymbolsIn_dk(:,2) = qamdemod(SymbolsInFFT_AWGM(:,2),L,0,'gray');
SymbolsIn_dk(:,3) = qamdemod(SymbolsInFFT_AWGM(:,3),L,0,'gray');

%% (h) Convert From Integer Symbols to Binary
%Rayleigh-Single Carrier
DecimalVector_To_Binary_ck_Single = de2bi(SymbolsIn_dk_Single(:),m);
bitsIn_ck_Single=reshape(DecimalVector_To_Binary_ck_Single,[N*L*m 1]);

%Rayleigh-MultiCarrier
DecimalVector_To_Binary_ck_Rayleigh = de2bi(SymbolsIn_dk_Rayleigh,m);
bitsIn_ck_Rayleigh=reshape(DecimalVector_To_Binary_ck_Rayleigh,[N*L*m 1]);

%AWGM-MultiCarrier
DecimalVector_To_Binary_ck(:,1:m) = de2bi(SymbolsIn_dk(:,1),m);
DecimalVector_To_Binary_ck(:,m+1:2*m) = de2bi(SymbolsIn_dk(:,2),m);
DecimalVector_To_Binary_ck(:,2*m+1:3*m) = de2bi(SymbolsIn_dk(:,3),m);

bitsIn_ck(:,1)=reshape(DecimalVector_To_Binary_ck(:,1:m),[N*L*m 1]);
bitsIn_ck(:,2)=reshape(DecimalVector_To_Binary_ck(:,m+1:2*m),[N*L*m 1]);
bitsIn_ck(:,3)=reshape(DecimalVector_To_Binary_ck(:,2*m+1:3*m),[N*L*m 1]);

%% (i) Calculate Bit Error Rates and display
fprintf('\n%d Bits Per Symbol over %d samples resulted in:\n',L,N)
[numErrors,ber]=biterr(bits_bk,bitsIn_ck_Single);
fprintf('Single Carrier Stanford Model had a bit error rate of:\n')
fprintf('%5.2e(%d errors).\n', ber,numErrors)
[numErrors,ber]=biterr(bits_bk,bitsIn_ck_Rayleigh);
fprintf('Multiple Carrier Stanford Model had a bit error rate of:\n')
fprintf('%5.2e(%d errors).\n', ber,numErrors)
[numErrors,ber]=biterr(bits_bk,bitsIn_ck(:,1));
fprintf('Multiple Carrier AWGN had a bit error rate of:\n')
fprintf('%5.2e(%d errors) with Sigma=0.\n', ber,numErrors)
[numErrors,ber]=biterr(bits_bk,bitsIn_ck(:,2));
fprintf('Multiple Carrier AWGN had a bit error rate of:\n')
fprintf('%5.2e(%d errors) with Sigma=0.02.\n' , ber,numErrors)
[numErrors,ber]=biterr(bits_bk,bitsIn_ck(:,3));
fprintf('Multiple Carrier AWGN had a bit error rate of:\n')
fprintf('%5.2e(%d errors) with Sigma=0.08.\n', ber,numErrors)

%% (j) Graphs
splotfig1=scatterplot(SymbolsOut_rk_SingleCarrier,1,0,'g.');
hold on
scatterplot(Symbols_Xk,1,0,'k*',splotfig1);
title(strcat('Single Carrier: L = ', {' '},num2str(L)))
axis([-m m -m m])

splotfig4=scatterplot(SymbolsInFFT_Rayleigh,1,0,'g.');
hold on
scatterplot(Symbols_Xk,1,0,'k*',splotfig4);
title(strcat('Multiple Carrier: L = ', {' '},num2str(L)))
axis([-m m -m m])

splotfig7=scatterplot(SymbolsInFFT_AWGM(:,1),1,0,'g.');
hold on
scatterplot(Symbols_Xk,1,0,'k*',splotfig7);
title(strcat('Multiple Carrier AWGN: L = ', {' '},num2str(L), ...
    ' sigma = 0.0'))
axis([-m m -m m])

splotfig8=scatterplot(SymbolsInFFT_AWGM(:,2),1,0,'g.');
hold on
scatterplot(Symbols_Xk,1,0,'k*',splotfig8);
title(strcat('Multiple Carrier AWGN: L = ', {' '},num2str(L), ...
    ' sigma = 0.02'))
axis([-m-1 m+1 -m-1 m+1])

splotfig9=scatterplot(SymbolsInFFT_AWGM(:,3),1,0,'g.');
hold on
scatterplot(Symbols_Xk,1,0,'k*',splotfig9);
title(strcat('Multiple Carrier AWGN: L =  ', {' '},num2str(L), ...
    ', sigma = 0.08'))
axis([-m m -m m])

%% Clean Up for next run
clear all
end