Skip to main content
Wireless Communication Modulation MATLAB Beamforming Project Ideas MIMO Computer Networks

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

People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

profile

  Website: www.salimwireless.com
  Interests: Signal Processing, Telecommunication, 5G Technology, Present & Future Wireless Technologies, Digital Signal Processing, Computer Networks, Millimeter Wave Band Channel, Web Development
  Seeking an opportunity in the Teaching or Electronics & Telecommunication domains.
  Possess M.Tech in Electronic Communication Systems.


Contact Us

Name

Email *

Message *

Popular Posts

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... 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. It is defined as,  In mathematics, BER = (number of bits received in error / total number of transmitted bits)  On the other hand, SNR refers to the signal-to-noise power ratio. For ease of calculation, we commonly convert it to dB or decibels.   What is Signal the signal-to-noise ratio (SNR)? SNR = signal power/noise power (SNR is a ratio of signal power to noise power) SNR (in dB) = 10*log(signal power / noise power) [base 10] For instance, the SNR for a given communication system is 3dB. So, SNR (in ratio) = 10^{SNR (in dB) / 10} = 2 Therefore, in this instance, the s...
Read more

Theoretical BER vs SNR for BPSK

Let's simplify the explanation for the theoretical Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) for Binary Phase Shift Keying (BPSK) in an Additive White Gaussian Noise (AWGN) channel.  Key Points Fig 1: Constellation Diagrams of BASK, BFSK, and BPSK [↗] BPSK Modulation: Transmits one of two signals: +√Eb ​ or -√Eb , where Eb​ is the energy per bit. These signals represent binary 0 and 1 . AWGN Channel: The channel adds Gaussian noise with zero mean and variance N0/2 (where N0 ​ is the noise power spectral density). Receiver Decision: The receiver decides if the received signal is closer to +√Eb​ (for bit 0) or -√Eb​ (for bit 1) . Bit Error Rate (BER) The probability of error (BER) for BPSK is given by a function called the Q-function. The Q-function Q(x) measures the tail probability of the normal distribution, i.e., the probability that a Gaussian random variable exceeds a certain value x.  Understanding the Q...
Read more

Constellation Diagrams of ASK, PSK, and FSK

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 of two signals: +√Eb​ ( On the y-axis, the phase shift of 90 degrees with respect to the x-axis, which is also termed phase offset ) or √Eb (on x-axis), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  BPSK (Binary PSK) Modulation: Transmits one of two signals: +√Eb​ or -√Eb (they differ by 180 degree phase shift), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  Key Points For Binary Amplitude Shift Keying (BASK), binary bit '0' can be represented as lower level voltage or no signal and bit '1' as higher level voltage.  For Binary Frequency Shift Keying (BFSK), you can map binary bit '0' to 'j' and bit '1' to '1'. So, signals are in phase.  A phase shift of 0 degrees could represent a binary '1...
Read more

Theoretical and simulated BER vs. SNR for ASK, FSK, and PSK

  BER vs. SNR denotes how many bits in error are received in a communication process for a particular Signal-to-noise (SNR) ratio. In most cases, SNR is measured in decibel (dB). For a typical communication system, a signal is often affected by two types of noises 1. Additive White Gaussian Noise (AWGN) 2. Rayleigh Fading In the case of additive white Gaussian noise (AWGN), random magnitude is added to the transmitted signal. On the other hand, Rayleigh fading (due to multipath) attenuates the different frequency components of a signal differently. A good signal-to-noise ratio tries to mitigate the effect of noise.  Calculate BER for Binary ASK Modulation The theoretical BER for binary ASK (BASK) in an AWGN channel is given by: BER  = (1/2) * erfc(0.5 * sqrt(SNR_ask));   Enter SNR (dB): Calculate BER BER vs. SNR curves for ASK, FSK, and PSK Calculate BER for Binary FSK Modulation The theoretical BER for binary FSK (BFSK) in a...
Read more

Simulation of ASK, FSK, and PSK using MATLAB Simulink

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 is a tool for displaying both modulated and unmodulated signals at the same time. The result section shows that binary '1' is modulated by a certain sine wave amplitude of 1 Volt, and binary '0' is modulated by zero amplitude. Simulation of Frequency Shift Keying (FSK) using MATLAB Simulink   Result The diagram above shows t...
Read more

Analog and Digital Communication Mini Projects | FM, Telecommunication, Mod...

  Mini Project Ideas 1. You can do your mini project on analog communication topic such as FM, walkie-talkie, etc. [1.1]  Analog Communication Based Project [1.2] MATLAB Code for Frequency Modulation (FM) 2. Compare the ASK, FSK, and PSK systems' relative performances. ( Include an introduction, concise descriptions of ASK, FSK, and PSK, MATLAB, and Simulink . You can then compare ASK, FSK, and PSK by creating BER vs. SNR graphs for each of those modulations, as well as by comparing their bandwidth, noise resistivity, complexity, and other characteristics. ) 3. M-ary Modulation Based Mini Projects (You can go for this project if you are interested in doing projects based on frequently used and modern modulation techniques. You can compare the performance analysis of various modulation schemes, like, bit rate, complexity, SNR v/s BER graph. You know frequently used modulation technique is m ary QPSK. But now QAM is also becoming popular due to its less complexity. But there is...
Read more