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# Report of GMSK modulation

By Corey Diaz,2014-10-25 10:52
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Report of GMSK modulation

Report of GMSK Modulation

Theory of GMSK modulation:

GMSK——Gaussian minimum shift keying, signal of GMSK is produced by going through the Gaussian low-pass filter before passing the CPM modulator(h=0.5).

Schematic of GMSK modulation:

g(t) is rectangular impulse response of the Gaussian filter.

When BT=Bb*Tb=0.2, 0.3 and 0.5, the rectangular impulse responses of the Gaussian filter in one symbol period are as follows.

BT=0.5

BT=0.3

BT=0.2

Simulation in Matlab

Here, we set that input data is s=[1 1 1 0 0 0 1 1 0 1], symbol period is Tb=0.1s, Gaussian filters 3dB bandwidth is Bb=3; modulation index is h=0.5, sampling frequency is fs=2kHz, carrier frequency is fc=20Hz.

As with g(t), we choose the situation of BT=0.3, then we implement the simulation of GMSK modulation as the schematic in Matlab.

Here is the code:

function c=Q(x)

c=0.5*erfc(x/(2^0.5));

end

clc;

clear all;

N=200;

s=[1 1 1 0 0 0 1 1 0 1]; n=length(s);

a=s*2-1;

Tb=0.1;

Bb=3;

h=0.5;

fs=N/Tb;

fc=20;

t=-Tb/2:1/fs:Tb/2-Tb/N; g=Q(2*pi*Bb*(t-Tb/2)/((log(2))^0.5))-Q(2*pi*Bb*(t+Tb/2)/((log(2))^0.5));

figure(1);

plot(t,g);title('BT=0.3 g(t) in one symbol period');

sum=0;

for i=1:length(g)

sum=sum+g(i);

end

g=g/(2*sum);

c=[];

for i=1:n

b=g.*(a(i)*ones(1,N));

c=[c b];

end

d=2*pi*h*c;

fai=cumsum(d);

t=0:1/fs:n*Tb-Tb/N;

gmsk=cos(2*pi*fc*t+fai); figure(2);

subplot(2,1,1);plot(t,fai);grid on;

title('Phase route of GMSK'); subplot(2,1,2);plot(t,gmsk);grid on;

title('GMSK signal');

Results of simulation:

After the simulation, we get the results of GMSK signal phase route

and the GMSK waveform.

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