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GMSK Modulation Implementation in MATLAB

By RF Wireless Expert Team

This page provides MATLAB source code for GMSK (Gaussian Minimum Shift Keying) modulation. GMSK is a modulation technique commonly used in wireless systems.

A key advantage of GMSK modulation is that it can achieve continuous or zero phase shift between consecutive data symbols. This addresses a limitation of QPSK and OQPSK techniques, which can have 180-degree to 90-degree phase shifts between symbols. These abrupt phase shifts necessitate the use of linear power amplifiers in the wireless transmitter chain.

Refer to our page on [MSK GMSK modulation](your_link_here - placeholder, you’ll need to provide the actual link) for a complete, step-by-step guide on MSK and GMSK modulation.

The following is the basic GMSK modulation MATLAB code:

clear all;
close all;
clc;

nrz_data = [1 1 1 1 1 1 1 1];  % Sample data
Tb = 1;                           % Bit duration
BT = 0.3;                          % BT product of filter
sps = 32;                         % Samples per symbol
Ts = Tb/sps;                      % Sample period
t=(-2*Tb:Ts:2*Tb);

alpha = 2*pi*BT/(sqrt(log(2)));
gauss = Q(alpha*(2*t-0.5)) - Q(alpha*(2*t+0.5));
K=pi/2/sum(gauss);
gauss = K*gauss;

nrz = upsample(nrz_data,sps);
nrz_gauss = conv(gauss,nrz);

subplot(2,1,1);
stem(nrz_data);
title('NRZ bits');
xlabel('Time');
ylabel('Amplitude');

subplot(2,1,2);
plot(nrz_gauss);
title('NRZ bits, after Gaussian Filtering');
xlabel('Time');
ylabel('Amplitude');

nrz_gauss1 = cumsum(nrz_gauss);
nrz_gauss2 = exp(1i*nrz_gauss1);

noisy_real1 = real(nrz_gauss2);
noisy_imag1 = imag(nrz_gauss2);

filter_noisy_real1 = matched_filter(noisy_real1,Tb,sps);
filter_noisy_imag1 = matched_filter(noisy_imag1,Tb,sps);

GMSK Demodulation

Deconvolution is performed in GMSK demodulation using the same Gaussian filter coefficients generated during GMSK modulation.

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