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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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