Pulse Shaping using Raised Cosine Filter (with MATLAB + Simulator)

 

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.

 

Further Reading

1.  Raised Cosine Filter Online Simulator
2. Applications of a Raise Cosine Filter