Skip to main content

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

 

 

MATLAB Code for OFDM using 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);



Output


 

 
 
 
 

 
 
  
 

 
 
 

 

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

People are good at skipping over material they already know!

View Related Topics to







Contact Us

Name

Email *

Message *

Popular Posts

Simulation of ASK, FSK, and PSK using MATLAB Simulink (with Online Simulator)

📘 Overview 🧮 How to use MATLAB Simulink 🧮 Simulation of ASK using MATLAB Simulink 🧮 Simulation of FSK using MATLAB Simulink 🧮 Simulation of PSK using MATLAB Simulink 🧮 Simulator for ASK, FSK, and PSK 🧮 Digital Signal Processing Simulator 📚 Further Reading ASK, FSK & PSK HomePage MATLAB Simulation Simulation of Amplitude Shift Keying (ASK) using MATLAB Simulink In Simulink, we pick different components/elements from MATLAB Simulink Library. Then we connect the components and perform a particular operation. Result A sine wave source, a pulse generator, a product block, a mux, and a scope are shown in the diagram above. The pulse generator generates the '1' and '0' bit sequences. Sine wave sources produce a specific amplitude and frequency. The scope displays the modulated signal as well as the original bit sequence created by the pulse generator. Mux i...
Read more

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

Bit Error Rate (BER) & SNR Guide Analyze communication system performance with our interactive simulators and MATLAB tools. 📘 Theory 🧮 Simulators 💻 MATLAB Code 📚 Resources BER Definition SNR Formula BER Calculator MATLAB Comparison 📂 Explore M-ary QAM, PSK, and QPSK Topics ▼ 🧮 Constellation Simulator: M-ary QAM 🧮 Constellation Simulator: M-ary PSK 🧮 BER calculation for ASK, FSK, and PSK 🧮 Approaches to BER vs SNR What is Bit Error Rate (BER)? The BER indicates how many corrupted bits are received compared to the total number of bits sent. It is the primary figure of merit for a...
Read more

Antenna Gain-Combining Methods - EGC, MRC, SC, and RMSGC

📘 Overview 🧮 Equal gain combining (EGC) 🧮 Maximum ratio combining (MRC) 🧮 Selective combining (SC) 🧮 Root mean square gain combining (RMSGC) 🧮 Zero-Forcing (ZF) Combining 🧮 MATLAB Code 📚 Further Reading  There are different antenna gain-combining methods. They are as follows. 1. Equal gain combining (EGC) 2. Maximum ratio combining (MRC) 3. Selective combining (SC) 4. Root mean square gain combining (RMSGC) 5. Zero-Forcing (ZF) Combining  1. Equal gain combining method Equal Gain Combining (EGC) is a diversity combining technique in which the receiver aligns the phase of the received signals from multiple antennas (or channels) but gives them equal amplitude weight before summing. This means each received signal is phase-corrected to be coherent with others, but no scaling is applied based on signal strength or channel quality (unlike MRC). Mathematically, for received signa...
Read more

MATLAB Codes for Various types of beamforming | Beam Steering, Digital...

📘 How Beamforming Improves SNR 🧮 MATLAB Code 📚 Further Reading 📂 Other Topics on Beamforming in MATLAB ... MIMO / Massive MIMO Beamforming Techniques Beamforming Techniques MATLAB Codes for Beamforming... How Beamforming Improves SNR The mathematical [↗] and theoretical aspects of beamforming [↗] have already been covered. We'll talk about coding in MATLAB in this tutorial so that you may generate results for different beamforming approaches. Let's go right to the content of the article. In analog beamforming, certain codebooks are employed on the TX and RX sides to select the best beam pairs. Because of their beamforming gains, communication created through the strongest beams from both the TX and RX side enhances spectrum efficiency. Additionally, beamforming gain directly impacts SNR improvement. Wireless communication system capacity = bandwidth*log2(1+SNR)...
Read more

Constellation Diagrams of ASK, PSK, and FSK (with MATLAB Code + Simulator)

Constellation Diagrams: ASK, FSK, and PSK Comprehensive guide to signal space representation, including interactive simulators and MATLAB implementations. 📘 Overview 🧮 Simulator ⚖️ Theory 📚 Resources Definitions Constellation Tool Key Points MATLAB Code 📂 Other Topics: M-ary PSK & QAM Diagrams ▼ 🧮 Simulator for M-ary PSK Constellation 🧮 Simulator for M-ary QAM Constellation BASK (Binary ASK) Modulation Transmits one of two signals: 0 or -√Eb, where Eb​ is the energy per bit. These signals represent binary 0 and 1. BFSK (Binary FSK) Modulation Transmits one ...
Read more

Online Simulator for ASK, FSK, and PSK

Try our new Digital Signal Processing Simulator!   •   Interactive ASK, FSK, and BPSK tools updated for 2025. Start Now Interactive Modulation Simulators Visualize binary modulation techniques (ASK, FSK, BPSK) in real-time with adjustable carrier and sampling parameters. 📡 ASK Simulator 📶 FSK Simulator 🎚️ BPSK Simulator 📚 More Topics ASK Modulator FSK Modulator BPSK Modulator More Topics Simulator for Binary ASK Modulation Digital Message Bits Carrier Freq (Hz) Sampling Rate (...
Read more

BER performance of QPSK with BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc (MATLAB + Simulator)

📘 Overview 📚 QPSK vs BPSK and QAM: A Comparison of Modulation Schemes in Wireless Communication 📚 Real-World Example 🧮 MATLAB Code 📚 Further Reading   QPSK provides twice the data rate compared to BPSK. However, the bit error rate (BER) is approximately the same as BPSK at low SNR values when gray coding is used. On the other hand, QPSK exhibits similar spectral efficiency to 4-QAM and 16-QAM under low SNR conditions. In very noisy channels, QPSK can sometimes achieve better spectral efficiency than 4-QAM or 16-QAM. In practical wireless communication scenarios, QPSK is commonly used along with QAM techniques, especially where adaptive modulation is applied. Modulation Bits/Symbol Points in Constellation Usage Notes BPSK 1 2 Very robust, used in weak signals QPSK 2 4 Balanced speed & reliability 4-QAM ...
Read more

OFDM Symbols and Subcarriers Explained

This article explains how OFDM (Orthogonal Frequency Division Multiplexing) symbols and subcarriers work. It covers modulation, mapping symbols to subcarriers, subcarrier frequency spacing, IFFT synthesis, cyclic prefix, and transmission. Step 1: Modulation First, modulate the input bitstream. For example, with 16-QAM , each group of 4 bits maps to one QAM symbol. Suppose we generate a sequence of QAM symbols: s0, s1, s2, s3, s4, s5, …, s63 Step 2: Mapping Symbols to Subcarriers Assume N sub = 8 subcarriers. Each OFDM symbol in the frequency domain contains 8 QAM symbols (one per subcarrier): Mapping (example) OFDM symbol 1 → s0, s1, s2, s3, s4, s5, s6, s7 OFDM symbol 2 → s8, s9, s10, s11, s12, s13, s14, s15 … OFDM sym...
Read more