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

Shannon Limit Explained: Negative SNR, Eb/No and Channel Capacity

Understanding Negative SNR and the Shannon Limit Understanding Negative SNR and the Shannon Limit An explanation of Signal-to-Noise Ratio (SNR), its behavior in decibels, and how Shannon's theorem defines the ultimate communication limit. Signal-to-Noise Ratio in Shannon’s Equation In Shannon's equation, the Signal-to-Noise Ratio (SNR) is defined as the signal power divided by the noise power: SNR = S / N Since both signal power and noise power are physical quantities, neither can be negative. Therefore, the SNR itself is always a positive number. However, engineers often express SNR in decibels: SNR(dB) When SNR = 1, the logarithmic value becomes: SNR(dB) = 0 When the noise power exceeds the signal power (SNR < 1), the decibel representation becomes negative. Behavior of Shannon's Capacity Equation Shannon’s channel capacity formula is: C = B log₂(1 + SNR) For SNR = 0: log₂(1 + SNR) = 0 When SNR becomes smaller (in...
Read more

Analog vs Digital Modulation Techniques | Advantages of Digital ...

Modulation Techniques Analog vs Digital Modulation Techniques... In the previous article, we've talked about the need for modulation and we've also talked about analog & digital modulations briefly. In this article, we'll discuss the main difference between analog and digital modulation in the case of digital modulation it takes a digital signal for modulation whereas analog modulator takes an analog signal.  Advantages of Digital Modulation over Analog Modulation Digital Modulation Techniques are Bandwidth efficient Its have good resistance against noise It can easily multiple various types of audio, voice signal As it is good noise resistant so we can expect good signal strength So, it leads high signal-to-noise ratio (SNR) Alternatively, it provides a high data rate or throughput Digital Modulation Techniques have better swathing capability as compared to Analog Modulation Techniques  The digital system provides better security than the a...
Read more

Amplitude, Frequency, and Phase Modulation Techniques (AM, FM, and PM)

📘 Overview 🧮 Amplitude Modulation (AM) 🧮 Online Amplitude Modulation Simulator 🧮 MATLAB Code for AM 🧮 Q & A and Summary 📚 Further Reading Amplitude Modulation (AM): The carrier signal's amplitude varies linearly with the amplitude of the message signal. An AM wave may thus be described, in the most general form, as a function of time as follows .                       When performing amplitude modulation (AM) with a carrier frequency of 100 Hz and a message frequency of 10 Hz, the resulting peak frequencies are as follows: 90 Hz (100 - 10 Hz), 100 Hz, and 110 Hz (100 + 10 Hz). Figure: Frequency Spectrums of AM Signal (Lower Sideband, Carrier, and Upper Sideband) A low-frequency message signal is modulated with a high-frequency carrier wave using a local oscillator to make communication possible. DSB, SSB, and VSB are common amplitude modulation techniques. We find a lot of bandwi...
Read more

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

📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 📚 Further Reading 📂 View Other Topics on M-ary QAM, M-ary PSK, QPSK ... 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR What is Bit Error Rate (BER)? The abbreviation BER stands for Bit Error Rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. BER = (number of bits received in error) / (total number of tran...
Read more

Comparing Baseband and Passband Implementations of m-ary QAM

  Let's assume your original message signal is: 1, 0, 1, 1, 1, 0, 1, 1, 0, 1. If you want to modulate it using 4-QAM, then your baseband signal will be: 4-QAM Symbols (Real + jImag) Symbol 0: -1.00 + j-1.00 Symbol 1: 1.00 + j-1.00 Symbol 2: -1.00 + j-1.00 Symbol 3: 1.00 + j-1.00 Symbol 4: 1.00 + j1.00   Now, if you want to transmit them through a typical wireless medium, you need to modulate the baseband signal with a carrier frequency (in our case, 50 Hz). The resulting passband signal looks like this               In the above code, the symbol rate is 5 symbols per second.   Detailed explanation 4-QAM Constellation Points In typical normalized 4-QAM, each symbol is mapped to a complex number: Bits Symbol (I + jQ) 00 -1 - 1j 01 -1 + 1j 11 +1 + 1j 10 +1 - 1j Each point lies on a square centered at the origin with I and Q values either +1 or -1. ...
Read more

Comparing Baseband and Passband Implementations of ASK, FSK, and PSK

📘 Overview 🧮 Baseband and Passband Implementations of ASK, FSK, and PSK 🧮 Difference betwen baseband and passband 📚 Further Reading 📂 Other Topics on Baseband and Passband ... 🧮 Baseband modulation techniques 🧮 Passband modulation techniques   Baseband modulation techniques are methods used to encode information signals onto a baseband signal (a signal with frequencies close to zero), allowing for efficient transmission over a communication channel. These techniques are fundamental in various communication systems, including wired and wireless communication. Here are some common baseband modulation techniques: Amplitude Shift Keying (ASK) [↗] : In ASK, the amplitude of the baseband signal is varied to represent different symbols. Binary ASK (BASK) is a common implementation where two different amplitudes represent binary values (0 and 1). ASK is simple but susceptible to noise...
Read more

Online Simulator for ASK, FSK, and PSK

Try our new Digital Signal Processing Simulator!   Start Simulator for binary ASK Modulation Message Bits (e.g. 1,0,1,0) Carrier Frequency (Hz) Sampling Frequency (Hz) Run Simulation Simulator for binary FSK Modulation Input Bits (e.g. 1,0,1,0) Freq for '1' (Hz) Freq for '0' (Hz) Sampling Rate (Hz) Visualize FSK Signal Simulator for BPSK Modulation ...
Read more

Theoretical vs. simulated BER vs. SNR for ASK, FSK, and PSK (MATLAB Code + Simulator)

📘 Overview 🧮 Simulator for calculating BER 🧮 MATLAB Codes for calculating theoretical BER 🧮 MATLAB Codes for calculating simulated BER 📚 Further Reading BER vs. SNR denotes how many bits in error are received for a given signal-to-noise ratio, typically measured in dB. Common noise types in wireless systems: 1. Additive White Gaussian Noise (AWGN) 2. Rayleigh Fading AWGN adds random noise; Rayleigh fading attenuates the signal variably. A good SNR helps reduce these effects. Simulator for calculating BER vs SNR for binary ASK, FSK, and PSK Calculate BER for Binary ASK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary FSK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary PSK Modulation Enter SNR (dB): Calculate BER BER vs. SNR Curves MATLAB Code for Theoretical BER % The code is written by SalimWireless.Com clc; clear; close all; % SNR va...
Read more