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OFDM in MATLAB


๐Ÿ“˜ Overview ๐Ÿงฎ Simple OFDM Code ๐Ÿ“ก Using QPSK Code ๐Ÿ“Š Using 16-QAM Code ๐Ÿ“š Reading

MATLAB Script: Simple OFDM System

The following code provides a fundamental implementation of an OFDM system including initialization, data generation, pilot insertion, and modulation.

1. Initialization

Clearing the workspace and command window to ensure a clean run.

MATLAB 
clc;
clear all;
close all;

% 2. Generate Random Bits
numBits = 100;
bits = randi([0, 1], 1, numBits);

% 3. Define Parameters
numSubcarriers = 4; 
numPilotSymbols = 3; 
cpLength = ceil(numBits / 4); 

% 4. Add Cyclic Prefix
dataWithCP = [bits(end - cpLength + 1:end), bits];

% 5. Insert Pilot Symbols
pilotSymbols = ones(1, numPilotSymbols); 
dataWithPilots = [pilotSymbols, dataWithCP];

% 6. Perform OFDM Modulation (IFFT)
dataMatrix = reshape(dataWithPilots, numSubcarriers, []);
ofdmSignal = ifft(dataMatrix, numSubcarriers);
ofdmSignal1 = reshape(ofdmSignal, 1, []);

% 7. Display the Generated Data
disp("Original Bits:");
disp(bits);
disp("Data with Cyclic Prefix and Pilots:");
disp(dataWithPilots);
disp("OFDM Signal:");
disp(ofdmSignal1);

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

% 8. Demodulation
ofdmSignal = reshape(ofdmSignal1, numSubcarriers, []);
rxSignal = fft(ofdmSignal, numSubcarriers);

% 9. Remove Cyclic Prefix
rxSignalNoCP = rxSignal(cpLength + 1:end);

% 10. Extract Data Symbols
dataSymbols = rxSignalNoCP(numPilotSymbols + 1:end);

% 11. Demodulate using Thresholding
threshold = 0;
demodulatedBits = (real(dataSymbols) > threshold);

% 12. Plotting
figure(1)
stem(bits);
legend("Original Information Bits")

figure(2)
hReal = stem(real(ofdmSignal1), 'r', 'DisplayName', 'Real Part');
hold on;
hImag = stem(imag(ofdmSignal1), 'b', 'DisplayName', 'Imaginary Part');
grid on;
title('Real and Imaginary Parts of OFDM Signal');
xlabel('Index');
ylabel('Amplitude');
legend;
hold off;

figure(3)
stem(demodulatedBits);
legend("Received Bits")
Original Bits
Fig 1: Original Information Bits
OFDM Signal
Fig 2: OFDM Signal (Time Domain)
Received Bits
Fig 3: Received Demodulated Bits

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MATLAB Code for OFDM using QPSK

This script demonstrates OFDM implementation using Quadrature Phase Shift Keying (QPSK) modulation.

MATLAB (QPSK) 
% The code is written by SalimWireless.Com
clc;
clear all;
close all;

% Generate random bits (must be even for QPSK)
numBits = 20;
if mod(numBits, 2) ~= 0
numBits = numBits + 1; % Make even
end
bits = randi([0, 1], 1, numBits);

% QPSK Modulation (2 bits per symbol)
bitPairs = reshape(bits, 2, []).';
qpskSymbols = (1/sqrt(2)) * ((2*bitPairs(:,1)-1) + 1j*(2*bitPairs(:,2)-1)); % Gray-coded

% Parameters
numSubcarriers = 4; % Number of OFDM subcarriers
numPilotSymbols = 3; % Number of pilot symbols
cpLength = ceil(length(qpskSymbols) / 4); % Cyclic prefix length

% Insert pilot symbols
pilotSymbols = ones(1, numPilotSymbols); % Example pilot symbols (BPSK pilots)
dataWithPilots = [pilotSymbols, qpskSymbols.'];

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

% Reshape and perform IFFT (OFDM modulation)
dataMatrix = reshape(dataWithCP, numSubcarriers, []);
ofdmSignal = ifft(dataMatrix, numSubcarriers);
ofdmSignal1 = reshape(ofdmSignal, 1, []);

% Display
disp("Original Bits:");
disp(bits);
disp("QPSK Symbols:");
disp(qpskSymbols.');
disp("Data with CP and Pilots:");
disp(dataWithCP);
disp("OFDM Signal:");
disp(ofdmSignal1);

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

% Reshape back to subcarrier-wise blocks and FFT
ofdmRxMatrix = reshape(ofdmSignal1, numSubcarriers, []);
rxSignal = fft(ofdmRxMatrix, numSubcarriers);

% Remove cyclic prefix
rxSignal1D = reshape(rxSignal, 1, []);
rxSignalNoCP = rxSignal1D(cpLength + 1:end);

% Remove pilots
rxDataSymbols = rxSignalNoCP(numPilotSymbols + 1:end);

% QPSK Demodulation
demodBits = zeros(1, 2*length(rxDataSymbols));
demodBits(1:2:end) = real(rxDataSymbols) > 0;
demodBits(2:2:end) = imag(rxDataSymbols) > 0;

%%%%%%%%%%%%%%%%%%%%%%%%%%% Plotting %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(1)
stem(bits);
title("Original Bits");
xlabel("Bit Index"); ylabel("Bit Value");
legend("Original Bits");

figure(2)
hReal = stem(real(ofdmSignal1), 'r', 'DisplayName', 'Real Part');
hold on;
hImag = stem(imag(ofdmSignal1), 'b', 'DisplayName', 'Imaginary Part');
set(hReal, 'Marker', 'o', 'LineWidth', 1.5);
set(hImag, 'Marker', 'x', 'LineWidth', 1.5);
grid on;
title('OFDM Signal (Time Domain)');
xlabel('Sample Index');
ylabel('Amplitude');
legend;
hold off;

figure(3)
stem(demodBits);
title("Demodulated Bits");
xlabel("Bit Index"); ylabel("Bit Value");
legend("Demodulated Bits");

% Optional: Calculate BER
numErrors = sum(bits ~= demodBits);
ber = numErrors / numBits;
fprintf("Bit Error Rate (BER): %.4f\n", ber);

MATLAB Code for OFDM (using 16-QAM)

Implementation using 16-QAM modulation and the Cooley-Tukey algorithm logic for FFT/IFFT.

MATLAB (16-QAM) 
% The code is written by SalimWireless.Com 
  clc;
clear all;
close all;

% OFDM System with 16-QAM

% 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 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 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');
OFDM Subcarriers
Constellation
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Read more about

[1] OFDM in details

[2] Structure of an OFDM packet

[3] OFDM Symbols & Subcarriers Explained

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