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OFDM in MATLAB

 

MATLAB Script

% The code is written by SalimWireless.Com

1. Initialization

clc;
clear all;
close all;


2. Generate Random Bits

% Generate random bits
numBits = 100;
bits = randi([0, 1], 1, numBits);


3. Define Parameters

% Define parameters
numSubcarriers = 4; % Number of subcarriers
numPilotSymbols = 3; % Number of pilot symbols
cpLength = ceil(numBits / 4); % Length of cyclic prefix (one-fourth of the data length)


4. Add Cyclic Prefix

% Add cyclic prefix
dataWithCP = [bits(end - cpLength + 1:end), bits];


5. Insert Pilot Symbols

% Insert pilot symbols
pilotSymbols = ones(1, numPilotSymbols); % Example pilot symbols (could be any pattern)
dataWithPilots = [pilotSymbols, dataWithCP];

 

6. Perform OFDM Modulation (IFFT)

% Perform OFDM modulation (IFFT)
dataMatrix = reshape(dataWithPilots, numSubcarriers, []);
ofdmSignal = ifft(dataMatrix, numSubcarriers);
ofdmSignal = reshape(ofdmSignal, 1, []);


7. Display the Generated Data

% Display the generated data
disp("Original Bits:");
disp(bits);
disp("Data with Cyclic Prefix and Pilots:");
disp(dataWithPilots);
disp("OFDM Signal:");
disp(ofdmSignal);

%%%%%%%%%%%%%%%%%%%%%%%%%%% Demodulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


8. Demodulation

% Perform FFT on the received signal
%ofdmSignal = awgn(ofdmSignal, 1000);
ofdmSignal = reshape(ofdmSignal, numSubcarriers, []);
rxSignal = fft(ofdmSignal, numSubcarriers);
%rxSignal = [rxSignal(1,:) rxSignal(2,:) rxSignal(3,:) rxSignal(4,:)];


9. Remove Cyclic Prefix

% Remove cyclic prefix
rxSignalNoCP = rxSignal(cpLength + 1:end);


10. Extract Data Symbols and Discard Pilot Symbols

% Extract data symbols and discard pilot symbols
dataSymbols = rxSignalNoCP(numPilotSymbols + 1:end);


11. Demodulate the Symbols Using Thresholding

% Demodulate the symbols using thresholding
threshold = 0;
demodulatedBits = (real(dataSymbols) > threshold);


12. Plot the Original and Received Bits

figure(1)
stem(bits);
legend("Original Information Bits")

figure(2)
stem(demodulatedBits);
legend("Received Bits")

Output

 

 
 
Fig 1: Original Information Bits
 
 
 
 
 
Fig 2: OFDM Signal
 
 
 
 
 
Fig 3: Received Demodulated Bits

 

Copy the MATLAB Code above from here

 

 

Another Example

clc;
clear;
close all;

% Main script
bitsLength = 128;
subcarriers = 64;
cpLength = 8;

bits = generateRandomBits(bitsLength);
txSignal = OFDMTransmitter(bits, subcarriers, cpLength);
rxSignal = OFDMReceiver(txSignal, subcarriers, cpLength);

Fs = 100; % Sampling frequency
[transmittedSignal, transmittedTime] = representDigitalSignal(bits, Fs);
[receivedSignal, receivedTime] = representDigitalSignal(rxSignal, Fs);

plotSignal(transmittedTime, transmittedSignal, 'Transmitted Bits');
plotSignal(receivedTime, receivedSignal, 'Received Bits');

% Plot OFDM Modulated Signal
figure;
subplot(2,1,1);
plot(real(txSignal));
title('OFDM Modulated Signal - Real Part');
xlabel('Sample');
ylabel('Amplitude');

subplot(2,1,2);
plot(imag(txSignal));
title('OFDM Modulated Signal - Imaginary Part');
xlabel('Sample');
ylabel('Amplitude');

% Function to generate random bits
function bits = generateRandomBits(length)
    bits = randi([0 1], 1, length);
end

% Function to perform FFT
function spectrum = myfft(signal)
    N = length(signal);
    if N <= 1
        spectrum = signal;
        return;
    end

    even = signal(1:2:end);
    odd = signal(2:2:end);

    evenFFT = myfft(even);
    oddFFT = myfft(odd);

    spectrum = zeros(1, N);
    for k = 1:N/2
        angle = -2 * pi * (k-1) / N;
        cosAngle = cos(angle);
        sinAngle = sin(angle);

        oddPart = oddFFT(k) * (cosAngle - 1i * sinAngle);
        spectrum(k) = evenFFT(k) + oddPart;
        spectrum(k + N/2) = evenFFT(k) - oddPart;
    end
end

% Function to perform IFFT
function signal = myifft(spectrum)
    conjugateSignal = conj(spectrum);
    fftResult = myfft(conjugateSignal);
    signal = conj(fftResult) / length(conjugateSignal);
end

% Function for OFDM Transmitter
function txSignal = OFDMTransmitter(bits, N, cpLength)
    symbols = zeros(1, length(bits)/2);
    for i = 1:2:length(bits)
        realPart = bits(i) * 2 - 1;
        imagPart = bits(i+1) * 2 - 1;
        symbols((i+1)/2) = realPart + 1i * imagPart;
    end

    parallelSymbols = reshape(symbols, N, []);
    timeDomainSignal = zeros(size(parallelSymbols));

    for i = 1:size(parallelSymbols, 2)
        timeDomainSignal(:, i) = myifft(parallelSymbols(:, i));
    end

    txSignal = [];
    for i = 1:size(timeDomainSignal, 2)
        cp = timeDomainSignal(end-cpLength+1:end, i);
        txSignal = [txSignal; cp; timeDomainSignal(:, i)];
    end
end

% Function for OFDM Receiver
function receivedBits = OFDMReceiver(rxSignal, N, cpLength)
    numSymbols = floor(length(rxSignal) / (N + cpLength));
    removedCP = zeros(N, numSymbols);

    for i = 1:numSymbols
        symbolStart = (i-1) * (N + cpLength) + cpLength + 1;
        removedCP(:, i) = rxSignal(symbolStart:symbolStart + N - 1);
    end

    frequencyDomainSignal = zeros(size(removedCP));
    for i = 1:size(removedCP, 2)
        frequencyDomainSignal(:, i) = myfft(removedCP(:, i));
    end

    receivedBits = zeros(1, numel(frequencyDomainSignal) * 2);
    index = 1;
    for i = 1:numel(frequencyDomainSignal)
        realPart = real(frequencyDomainSignal(i));
        imagPart = imag(frequencyDomainSignal(i));
        receivedBits(index) = realPart >= 0;
        receivedBits(index + 1) = imagPart >= 0;
        index = index + 2;
    end
end

% Function to represent digital signal for plotting
function [bitRepresentation, timeInstances] = representDigitalSignal(bits, Fs)
    bitRepresentation = zeros(1, Fs * length(bits));
    for n = 1:length(bits)
        if bits(n) == 1
            bitRepresentation((n-1)*Fs+1:n*Fs) = 1;
        else
            bitRepresentation((n-1)*Fs+1:n*Fs) = 0;
        end
    end
    timeInstances = (0:Fs*length(bits)-1) / Fs;
end

% Function to plot the signal
function plotSignal(timeInstances, signal, label)
    figure;
    plot(timeInstances, signal);
    title(label);
    xlabel('Time');
    ylabel('Amplitude');
end


Output


 
 
 
 
 
 
 
  
 
 
 
 

Copy the MATLAB Code above from here

 

 

MATLAB Code for OFDM Subcarriers (using 16-QAM)

clc;
clear;
close all;

% OFDM System with 16-QAM and Cooley-Tukey FFT/IFFT

% Parameters
N = 64; % Number of OFDM subcarriers
M = 16; % Modulation order (16-QAM -> M = 16)
nSymbols = 100;% Number of OFDM symbols
Ncp = 16; % Length of cyclic prefix

% Generate random data for transmission (0 to M-1 for 16-QAM)
data = randi([0 M-1], nSymbols, N);

% 16-QAM modulation of the data using custom function
modData = zeros(nSymbols, N);
for i = 1:nSymbols
modData(i, :) = qammod(data(i, :), M);
end

% Perform IFFT using Cooley-Tukey to generate the time domain OFDM signal
ofdmTimeSignal = zeros(size(modData));
for i = 1:nSymbols
ofdmTimeSignal(i, :) = ifft(modData(i, :));
end

% Add cyclic prefix
cyclicPrefix = ofdmTimeSignal(:, end-Ncp+1:end); % Extract cyclic prefix
ofdmWithCP = [cyclicPrefix ofdmTimeSignal]; % Add cyclic prefix to the signal

%% Plot Subcarriers in Frequency Domain (before IFFT)
figure;
stem(0:N-1, abs(modData(100, :))); % Plot absolute value of the subcarriers for the first symbol
title('Subcarriers in Frequency Domain for 1st OFDM Symbol (Before IFFT)');
xlabel('Subcarrier Index');
ylabel('Magnitude');

%% Plot Time Domain OFDM Signal (after IFFT)
figure;
plot(real(ofdmTimeSignal(1, :))); % Plot real part of the OFDM time signal for the first symbol
title('OFDM Signal in Time Domain for 1st OFDM Symbol (Without CP)');
xlabel('Time Sample Index');
ylabel('Amplitude');

%% Plot Time Domain OFDM Signal with Cyclic Prefix
figure;
plot(real(ofdmWithCP(1, :))); % Plot real part of the OFDM time signal with CP for the first symbol
title('OFDM Signal in Time Domain for 1st OFDM Symbol (With Cyclic Prefix)');
xlabel('Time Sample Index');
ylabel('Amplitude');

%% Receiver Side - Remove Cyclic Prefix and Demodulate
% Remove cyclic prefix
receivedSignal = ofdmWithCP(:, Ncp+1:end); % Remove cyclic prefix

% Apply FFT using Cooley-Tukey to recover the received subcarriers (back to frequency domain)
receivedSubcarriers = zeros(size(receivedSignal));
for i = 1:nSymbols
receivedSubcarriers(i, :) = fft(receivedSignal(i, :));
end

% 16-QAM Demodulation of the received subcarriers using custom function
receivedData = zeros(nSymbols, N);
for i = 1:nSymbols
receivedData(i, :) = qamdemod(receivedSubcarriers(i, :), M);
end

% Calculate symbol errors
numErrors = sum(data(:) ~= receivedData(:));
fprintf('Number of symbol errors: %d\n', numErrors);

%% Plot Received Subcarriers in Frequency Domain (after FFT at the receiver)
figure;
stem(0:N-1, abs(receivedSubcarriers(100, :))); % Plot absolute value of received subcarriers for the first symbol
title('Received Subcarriers in Frequency Domain for 1st OFDM Symbol (After FFT)');
xlabel('Subcarrier Index');
ylabel('Magnitude');

%% Plot Transmitted Data Constellation (Before IFFT)
figure;
scatterplot(modData(1, :)); % Plot for the first OFDM symbol
title('Transmitted 16-QAM Symbols for 1st OFDM Symbol');
xlabel('In-phase');
ylabel('Quadrature');

%% Plot Received Data Constellation (After Demodulation)
receivedModData = qammod(receivedData(1, :), M); % Map back for plotting
figure;
scatterplot(receivedModData);
title('Received 16-QAM Symbols for 1st OFDM Symbol');
xlabel('In-phase');
ylabel('Quadrature');

 Output

 












Copy the MATLAB code above from here

 

Read more about

[1] OFDM in details

[2] Structure of an OFDM packet

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