Pulse Shaping using Raised Cosine Filter in MATLAB

 

MATLAB Code for Raised Cosine Filter Pulse Shaping

clc; clear; close all;

%% =====================================================

%% PARAMETERS

%% =====================================================

N = 64; % Number of OFDM subcarriers

cpLen = 16; % Cyclic prefix length

modOrder = 4; % QPSK

oversample = 8; % Oversampling factor

span = 10; % RRC filter span in symbols

rolloff = 0.25; % RRC roll-off factor

%% =====================================================

%% Generate Baseband OFDM Symbols

%% =====================================================

data = randi([0 modOrder-1], N, 1); % Random bits

txSymbols = pskmod(data, modOrder, pi/4); % QPSK modulation

% IFFT to get OFDM symbol

tx_ofdm = ifft(txSymbols, N);

% Add cyclic prefix

tx_cp = [tx_ofdm(end-cpLen+1:end); tx_ofdm];

%% =====================================================

%% Oversample the Baseband Signal

%% =====================================================

tx_oversampled = upsample(tx_cp, oversample);

%% =====================================================

%% Root Raised Cosine (RRC) Pulse Shaping

%% =====================================================

rrcFilter = rcosdesign(rolloff, span, oversample, 'sqrt'); % RRC filter

tx_shaped = conv(tx_oversampled, rrcFilter, 'same');

%% =====================================================

%% Visualize Time-Domain Waveform

%% =====================================================

figure;

subplot(2,1,1);

plot(real(tx_oversampled), 'b'); hold on;

plot(real(tx_shaped), 'r');

xlabel('Sample Index'); ylabel('Amplitude');

title('OFDM Time-Domain Waveform');

legend('Before RRC','After RRC');

grid on;

%% =====================================================

%% Visualize Spectrum

%% =====================================================

subplot(2,1,2);

nFFT = 1024;

f = linspace(-0.5,0.5,nFFT)*oversample; % Normalized freq axis

TX_OS_F = fftshift(abs(fft(tx_oversampled,nFFT)));

TX_SH_F = fftshift(abs(fft(tx_shaped,nFFT)));

plot(f, TX_OS_F/max(TX_OS_F), 'b'); hold on;

plot(f, TX_SH_F/max(TX_SH_F), 'r');

xlabel('Normalized Frequency'); ylabel('Normalized Magnitude');

title('OFDM Spectrum');

legend('Before RRC','After RRC');

grid on;

%% =====================================================

 

Output

 

Summary

In the above figure, it is shown that Root Raised Cosine (RRC) pulse shaping further band-limits the OFDM waveform. Band-limiting a signal allows it to pass more efficiently through a bandwidth-limited channel. The signal bandwidth should not exceed the coherence bandwidth of the channel to avoid frequency-selective distortion. Another important purpose of pulse shaping is to reduce spectral leakage, ensuring that critical frequency components are not lost during transmission.