OFDM MATLAB Code Implementation

This section provides MATLAB source code for a basic OFDM transmitter and receiver chain.

OFDM Transmitter Chain

The basic OFDM transmitter chain consists of the following stages:

1. Binary data source
2. Data mapping
3. IFFT (Inverse Fast Fourier Transform)
4. CP (Cyclic Prefix) insertion

This time-domain data is then passed through a channel and subjected to Additive White Gaussian Noise (AWGN).

OFDM Receiver Chain

The OFDM receiver performs the inverse operations:

1. CP removal
2. FFT (Fast Fourier Transform)
3. Data demapping
4. Decoding

MATLAB Code Implementation

Here’s the MATLAB code that implements the OFDM transmitter and receiver chain:

clc;
clear all;
close all;

% ...............................................................
% Initiation
% ...............................................................
no_of_data_bits = 64; % Number of bits per channel extended to 128
M = 4; % Number of subcarrier channel
n = 256; % Total number of bits to be transmitted at the transmitter
block_size = 16; % Size of each OFDM block to add cyclic prefix
cp_len = floor(0.1 * block_size); % Length of the cyclic prefix

% .............................................................
% Transmitter
% ..........................................................
% ..........................................................
% Source generation and modulation
% .........................................................
% Generate random data source to be transmitted of length 64
data = randsrc(1, no_of_data_bits, 0:M - 1);
figure(1), stem(data);
grid on;
xlabel('Data Points');
ylabel('Amplitude')
title('Original Data ')

% Perform QPSK modulation on the input source data
qpsk_modulated_data = pskmod(data, M);
figure(2), stem(qpsk_modulated_data);
title('QPSK Modulation ')

% .............................................................
% ..............................................................
% Converting the series data stream into  four parallel data stream to form
% four sub carriers
S2P = reshape(qpsk_modulated_data, no_of_data_bits / M, M);
Sub_carrier1 = S2P(:, 1);
Sub_carrier2 = S2P(:, 2);
Sub_carrier3 = S2P(:, 3);
Sub_carrier4 = S2P(:, 4);

figure(3),
subplot(4, 1, 1), stem(Sub_carrier1), title('Subcarrier1'), grid on;
subplot(4, 1, 2), stem(Sub_carrier2), title('Subcarrier2'), grid on;
subplot(4, 1, 3), stem(Sub_carrier3), title('Subcarrier3'), grid on;
subplot(4, 1, 4), stem(Sub_carrier4), title('Subcarrier4'), grid on;

% ...................................................................
% ...................................................................
%   IFFT OF FOUR SUB_CARRIERS
% ..................................................................
% ...............................................................
number_of_subcarriers = 4;
cp_start = block_size - cp_len;

ifft_Subcarrier1 = ifft(Sub_carrier1);
ifft_Subcarrier2 = ifft(Sub_carrier2);
ifft_Subcarrier3 = ifft(Sub_carrier3);
ifft_Subcarrier4 = ifft(Sub_carrier4);

figure(4),
subplot(4, 1, 1), plot(real(ifft_Subcarrier1), 'r'), title('IFFT on all the sub-carriers')
subplot(4, 1, 2), plot(real(ifft_Subcarrier2), 'c')
subplot(4, 1, 3), plot(real(ifft_Subcarrier3), 'b')
subplot(4, 1, 4), plot(real(ifft_Subcarrier4), 'g')

% ............................................................
% ............................................................
%   ADD-CYCLIC PREFIX
% ..........................................................
% .............................................................
for i = 1:number_of_subcarriers,
    ifft_Subcarrier(:, i) = ifft((S2P(:, i)), 16); % 16 is the ifft point
    for j = 1:cp_len,
        cyclic_prefix(j, i) = ifft_Subcarrier(j + cp_start, i);
    end
    Append_prefix(:, i) = vertcat(cyclic_prefix(:, i), ifft_Subcarrier(:, i)); % Appends prefix to each subcarriers
end

A1 = Append_prefix(:, 1);
A2 = Append_prefix(:, 2);
A3 = Append_prefix(:, 3);
A4 = Append_prefix(:, 4);

figure(5),
subplot(4, 1, 1), plot(real(A1), 'r'), title('Cyclic prefix added to all the sub-carriers')
subplot(4, 1, 2), plot(real(A2), 'c')
subplot(4, 1, 3), plot(real(A3), 'b')
subplot(4, 1, 4), plot(real(A4), 'g')

figure(11), plot((real(A1)), 'r'), title('Orthogonality'), hold on, plot((real(A2)), 'c'), hold on, plot((real(A3)), 'b'), hold on, plot((real(A4)), 'g'), hold on, grid on

% Convert to serial stream for transmission
[rows_Append_prefix, cols_Append_prefix] = size(Append_prefix);
len_ofdm_data = rows_Append_prefix * cols_Append_prefix;

% OFDM signal to be transmitted
ofdm_signal = reshape(Append_prefix, 1, len_ofdm_data);
figure(6), plot(real(ofdm_signal));
xlabel('Time');
ylabel('Amplitude');
title('OFDM Signal');
grid on;

% ................................................................
% Passing time domain data through channel and AWGN
% ..............................................................
channel = randn(1, 2) + sqrt(-1) * randn(1, 2);
after_channel = filter(channel, 1, ofdm_signal);
awgn_noise = awgn(zeros(1, length(after_channel)), 0);
recvd_signal = awgn_noise + after_channel;

% With AWGN noise
figure(7), plot(real(recvd_signal)), xlabel('Time');
ylabel('Amplitude');
title('OFDM Signal after passing through channel');
grid on;

% ............................................................
% OFDM receiver part
% ...........................................................
recvd_signal_paralleled = reshape(recvd_signal, rows_Append_prefix, cols_Append_prefix);

% .........................................................
% .........................................................
%   Remove cyclic Prefix
% ........................................................
% .......................................................
recvd_signal_paralleled(1:cp_len, :) = [];
R1 = recvd_signal_paralleled(:, 1);
R2 = recvd_signal_paralleled(:, 2);
R3 = recvd_signal_paralleled(:, 3);
R4 = recvd_signal_paralleled(:, 4);

figure(8), plot((imag(R1)), 'r'), subplot(4, 1, 1), plot(real(R1), 'r'), title('Cyclic prefix removed from the four sub-carriers')
subplot(4, 1, 2), plot(real(R2), 'c')
subplot(4, 1, 3), plot(real(R3), 'b')
subplot(4, 1, 4), plot(real(R4), 'g')

% ....................................................
% ....................................................
%   FFT Of recievied signal
for i = 1:number_of_subcarriers,
    % FFT
    fft_data(:, i) = fft(recvd_signal_paralleled(:, i), 16);
end

F1 = fft_data(:, 1);
F2 = fft_data(:, 2);
F3 = fft_data(:, 3);
F4 = fft_data(:, 4);

figure(9),
subplot(4, 1, 1), plot(real(F1), 'r'), title('FFT of all the four sub-carriers')
subplot(4, 1, 2), plot(real(F2), 'c')
subplot(4, 1, 3), plot(real(F3), 'b')
subplot(4, 1, 4), plot(real(F4), 'g')

% ................................
% ..............................
%   Signal Reconstructed
% ..................................
% ..................................
%   Conversion to serial and demodulationa
recvd_serial_data = reshape(fft_data, 1, (16 * 4));
qpsk_demodulated_data = pskdemod(recvd_serial_data, 4);

figure(10)
stem(data)
hold on
stem(qpsk_demodulated_data, 'rx');
grid on;
xlabel('Data Points');
ylabel('Amplitude');
title('Recieved Signal with error')

OFDM Basic Tx-Rx Chain Image

The OFDM MATLAB code for the above block schematic is provided below for download.

In this example, the OFDM transmitter consists of a FEC encoder, a BPSK modulator, and a 256-point IFFT. The receiver includes an FFT, BPSK demodulator, and Viterbi decoder.

BER Curve

The BER (Bit Error Rate) curve for this OFDM MATLAB model, taken after passing the transmitter data through an AWGN channel, is shown below.