Skip to main content

OFDM in MATLAB


📘 Overview 🧮 Simple OFDM Code 📡 Using QPSK Code 📊 Using 16-QAM Code 📚 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

Ready to Learn More?

Explore our comprehensive guide on OFDM implementation and wireless communication systems.

View OFDM Simulator →

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
Return to Home →

Read more about

[1] OFDM in details

[2] Structure of an OFDM packet

[3] OFDM Symbols & Subcarriers Explained

📊 MATLAB & ONLINE SIMULATIONS (Web-Based)
🎓 GATE & UGC - NET SOLUTIONS
📡 WIRELESS & SIGNAL PROCESSING


Contact Us

Name

Email *

Message *

Popular Posts

UGC NET Electronic Science Previous Year Question Papers with Solutions

Download Papers and Solutions Exam Pattern Preparation Tips FAQs More Home / Engineering & Other Exams / UGC NET 2026 PYQ 📊 Exam Highlights: Electronic Science (88) Feature Details Junior Research Fellowship (JRF) ₹37,000 + HRA per month Eligibility M.Sc/M.Tech in Electronics (55%) Validity of Certificate JRF (3 Years) | Lectureship (Lifetime) 📥 Download UGC NET Electronics PDFs Complete collection of previous year question papers, answer keys and explanations for Subject Code 88. Start Downloading 📂 View All Question Papers June 2026 - Question Paper Download PDF June 202...
Read more

The output voltage V0 (in Volt) for the network given in the Figure is ___

  Find the Output Voltage V o Solve the given circuit using Kirchhoff's Current Law (KCL), Ohm's law, and the supernode method. 1. Given Circuit Parameters Current source 1 mA Resistors 1 kΩ Each resistor Voltage source 6 V Required V o 2. Understand the Circuit The circuit contains a 1 mA current source, four 1 kΩ resistors, and a 6 V source connected between the two midpoint nodes. The output voltage is measured between the top and bottom rails. Reference node Take the bottom rail as ground: 0 V . Let the top rail voltage be V T , and...
Read more

GMSK BER vs SNR (with Simulation)

  GMSK Performance: Why the BER vs. SNR Curve Matters If you’ve ever wondered why GMSK (Gaussian Minimum Shift Keying) became the backbone of the global GSM revolution, the answer lies in its unique balance of spectral efficiency and power performance. But there is no free lunch in engineering. To get that sleek, narrow spectrum, you have to pay a price in Bit Error Rate (BER) . In this guide, we break down the theoretical BER vs. SNR performance of GMSK, the "magic" of the BT product, and how to optimize your link budget for real-world conditions. What is GMSK and Why Should You Care? GMSK is a derivative of MSK (Minimum Shift Keying) that uses a Gaussian pre-modulation filter. This filter "smooths" the phase transitions, significantly reducing sideband power. The result? A constant envelope signal that allows you to use high-efficiency Class-C amplifiers without distorting the signal. This is the secr...
Read more

What is a Supernode?

  Circuit Analysis What Is a Supernode? A supernode is formed when an ideal voltage source connects two non-reference nodes. It allows us to apply Kirchhoff's Current Law (KCL) to the combined circuit boundary. 1. Understanding a Supernode In nodal analysis, a voltage source between two unknown-voltage nodes makes the current through that source difficult to express directly using Ohm's law. We combine the two nodes and the voltage source into one extended region called a supernode. Key idea Apply KCL around the outer boundary of the supernode, then use the voltage source to write an additional voltage equation. 2. Supernode Circuit Diagram The voltage source connects nodes V L an...
Read more

Parametric Down-Conversion of Photons

  Nonlinear Optics One incoming photon is converted into two lower-energy photons, typically in a nonlinear optical medium. Energy is conserved: E in = E 1 + E 2 E in ​ = E 1 ​ + E 2 ​ . Parametric Down-Conversion A nonlinear optical process in which one pump photon is converted into two lower-energy photons, known as the signal and idler photons. 1 Energy Conservation The energy of the pump photon equals the sum of the energies of the signal and idler photons. \[ \boxed{\hbar\omega_p=\hbar\omega_s+\hbar\omega_i} \] \[ \boxed{\omega_p=\omega_s+\omega_i} \] ωₚ Pump angular frequency ...
Read more

A binary ripple counter is designed to count (0)₁₀ to (64)₁₀. Which of the following is/are the number of flip-flops required ...

  Q. A binary ripple counter is designed to count  (0)₁₀ to (64)₁₀ . Which of the following is/are the number of flip-flops required to design the counter?   (A) 6 (B) 7 (C) 4 (D) 5 Solution A binary ripple counter must count from (0)₁₀ to (64)₁₀ , including both endpoints. Step 1: Calculate the total number of states Since both 0 and 64 are included, add 1 to the difference: N = Last value − First value + 1 N = 64 − 0 + 1 = 65 states The counter visits every integer from 0 through 64: 0, 1, 2, 3, ..., 63, 64 There are 65 distinct states in total. Step 2: Calculate the number of flip-flops Each flip-flop stores one bit. With n flip-flops, the counter can represent 2ⁿ distinct states. 2⁶ = 64 states (not enough) 2⁷ = 128 states (eno...
Read more

SRAM, DRAM, EPROM, MRAM, and DDRAM Explained

Computer Fundamentals Types of Memory and Their Technologies Understand the fundamental relationship between different types of computer memory and the technologies used to implement them. Fundamental Matching Memory type, technology, and key characteristics Memory Type Technology Key Characteristic Cache Memory SRAM Very fast; stores frequently accessed data Main Memory DRAM Holds programs and data currently in use Au...
Read more

The cutoff frequency (in GHz) for the dominant TE10 mode of an air-filled rectangular waveguide of ...

  Q. The cutoff frequency (in GHz) for the dominant TE10 mode of an air-filled rectangular waveguide of inner dimension 0.28 inch×0.14 inch is __. (rounded off to two decimal places). Given Information Waveguide dimensions = 0.28 inch × 0.14 inch Wider dimension (a) = 0.28 inch Smaller dimension (b) = 0.14 inch Medium = Air Dominant mode = TE 10 Speed of light (c) = 3 × 10 8 m/s Step 1: Cutoff Frequency Formula The cutoff frequency of a rectangular waveguide is: f c = (c / 2) √[(m/a) 2 + (n/b) 2 ] For the dominant TE 10 mode: m = 1, n = 0 f c = c / 2a Step 2: Convert Inch into Meter We know that 1 inch = 0.0254 meter. a = 0.28 × 0.0254 a = 0.007112 m ...
Read more