FFT-Based Channel Estimation with MATLAB Code

FFT-Based Channel Estimation Using OFDM in MATLAB

Modern wireless systems such as WiFi, LTE, and 5G rely heavily on Orthogonal Frequency Division Multiplexing (OFDM). One major advantage of OFDM is that it simplifies channel equalization using the Fast Fourier Transform (FFT).

When a cyclic prefix (CP) is inserted before each OFDM symbol, the wireless channel behaves like a circular convolution. This allows the channel response to be estimated easily in the frequency domain.

After applying FFT, the received signal can be written as:

Y(k) = X(k)H(k)

Therefore the channel response can be estimated using:

H(k) = Y(k) / X(k)

System Overview

The following simulation demonstrates the basic OFDM transmission chain:

Random data generation
BPSK modulation
OFDM modulation using IFFT
Cyclic prefix insertion
Multipath wireless channel
FFT-based channel estimation
Frequency-domain equalization

MATLAB Simulation Code


% --------------------------------------------------------
% FFT Based Channel Estimation using OFDM
% Educational example for understanding OFDM equalization
% --------------------------------------------------------

clc;
clear;
close all;

%% OFDM Parameters
Nsub = 64;          % Number of subcarriers
cp = 16;            % Cyclic prefix length
snr_db = 20;        % Channel SNR

%% Generate Random Data

bits = randi([0 1], Nsub, 1);

% BPSK modulation
symbols = 2*bits - 1;

%% OFDM Modulation

% Convert to time domain
tx_time = ifft(symbols);

% Append cyclic prefix
ofdm_tx = [tx_time(end-cp+1:end); tx_time];

%% Multipath Channel

% Example channel impulse response
h = [0.8 0.5 0.3];

% Linear convolution with channel
rx_channel = conv(ofdm_tx, h);

% Add AWGN noise
rx_channel = awgn(rx_channel, snr_db, 'measured');

%% Receiver Processing

% Remove cyclic prefix
rx_noCP = rx_channel(cp+1 : cp+Nsub);

% Convert back to frequency domain
Y = fft(rx_noCP);

% Known transmitted symbols
X = symbols;

%% Channel Estimation

H_est = Y ./ X;

%% Frequency Domain Equalization

X_est = Y ./ H_est;

%% Symbol Detection

bits_est = real(X_est) > 0;

%% BER Calculation

BER = sum(bits ~= bits_est)/length(bits);

disp(['Bit Error Rate = ', num2str(BER)])

%% Channel Response Visualization

figure

subplot(2,1,1)
stem(abs(fft(h,Nsub)))
title('Actual Channel Frequency Response')
xlabel('Subcarrier')
ylabel('|H(k)|')

subplot(2,1,2)
stem(abs(H_est))
title('Estimated Channel Frequency Response')
xlabel('Subcarrier')
ylabel('|H_{est}(k)|')

Understanding the Role of the Cyclic Prefix

Wireless channels introduce multipath propagation. This means the transmitted signal arrives at the receiver through several delayed paths.

Without protection, the received signal would be:

y(n) = x(n) * h(n)

This is a linear convolution which causes inter-symbol interference.

By inserting a cyclic prefix before each OFDM symbol, the linear convolution effectively becomes a circular convolution. After FFT, the relationship simplifies to:

Y(k) = X(k)H(k)

This allows each subcarrier to be equalized independently.