ESE 576 Final Project Report

ESE 576 Digital Communication System
Final Project Report

Learning of Gaussian Minimum Shift Keying Carrier Modulation (GMSK)

Name: XX

ESE 576 Final Project Report

Content
(1). Background and Motivation: ............................................................... 3
1. FSK:....................................................................................................... 3
2. CPFSK/CPM: ......................................................................................... 3

3. MSK:............................................................................................. 3
4. GMSK: ................................................................................................... 3

(2). Theoretical Analysis:........................................................................... 4
1 CPM:....................................................................................................... 4
2.CPFSK
3. MSK: ...................................................................................................... 5
4. GMSK: ................................................................................................... 5

(3). Simulation and Interpretation: ............................................................. 5
1. Modulation：.......................................................................................... 6
2. Demodulation： ..................................................................................... 6

(4). Implementation and Application: ......................................................... 7
(5). Reference: .......................................................................................... 7
Appendix: Matlab Code ............................................................................ 8

ESE 576 Final Project Report

(1). Background and Motivation:
Digital modulation offers many advantages over analog modulation. The modulation signal may be represented as a time sequence of symbols or pulses where each symbol has m finite states. Each symbol represents n bits, where n = log2m. Different modulation schemes are used in different scenarios.
Sometimes we want lower bit-rates at lower received signal-to-noise (SNR) ratios, sometimes we want it occupies a minimum of bandwidth, and it is easy for hardware to implement. Here are part of the modulation schemes and the development of GMSK.

1. FSK:
FSK (Frequency-shift keying), is a frequency modulation scheme using discrete frequencies to modulate W in the carrier wave. 2FSK could also be seen as superposition of two ASK for different frequencies carrier waves.
However, simple FSK has its own flaws. For example, the adjacent bit will have abrupt phase change when switch the carrier wave frequency. This discontinuity phase will require a relatively large percentage of the power to occur outside of the intended band. Thus, this will lead to poor spectral efficiency. 2. CPFSK/CPM:
In contrast to the modulation scheme where the carrier phase abruptly resets to zero at the start of every symbol, CPM (Continuous phase modulation) is a method where the carrier phase is modulated in a continuous manner. CPM is a constant-envelop waveform. Continuous phase yields high spectral efficiency, and the constant envelop yields high power efficiency. CPM is the combination of coding and modulation.
CPFSK (Continuous-phase frequency-shift keying) is a special case of CPM where modulation index

. And it is a variation of FSK.

3. MSK:
MSK (Minimum-shift-keying) is a type of CPFSK where frequency separation of one-half the bit rate. MSK encoded each bit as a half sinusoid. This results in a constant-modulus signal which reduces problems caused by non-linear distortion. 4. GMSK:
GMSK (Gaussian Minimum shift keying) is a variation of standard MSK where the digital data stream is first shaped with a Gaussian filter before applied to

ESE 576 Final Project Report

MSK. This could reduce sideband power, which in turn reduces out-of-band interference between signal carriers in adjacent frequency channels. GMSK has high spectral efficiency. It is used in a variety of digital radio communication systems with considerable spectrum efficiently.

(2). Theoretical Analysis:
Signal’s carrier-modulated signal could be express as:

And we want

to be continuous.

1. CPFSK:
CPFSK is a special case for FSK where phase is continuous in time domain.
Course signal is modulate on the phase. At time interval : nT have: =
=
Where:

t

(n+1) T we

ESE 576 Final Project Report

Here, we can see that

is the accumulation of phase. This is a memory

signal.

2. CPM:
Continuous-phase modulated (CPM) is the general case for continuous-phase modulation. The carrier phase is:

If g(t) = 0 for t> T, we call the signal full-response CPM, otherwise, it is called partial-response CPM. GMSK is partial-response CPM while CPFSK is full-response CPM. There are infinite type of CPM by varying h, and choosing different g(t).

3. MSK:
Minimum-shift keying (MSK) is a special case for CPFSK/CPM. h = 0.5 and g(t) is a rectangular phase of duration T.
Here the phase is:

4. GMSK:

(3). Simulation and Interpretation:

ESE 576 Final Project Report

1. Modulation：

2. Demodulation：

ESE 576 Final Project Report

(4). Implementation and Application:
Phase shift keying has sidebands extend outwards from the main carrier and these can cause interference to other radio communications systems using nearby channels.
GMSK modulation has been used in a number of radio communications applications in view of the efficient use of the spectrum. The most widely used is the GSM cellular technology which is used in worldwide and has well over 3 billion subscribers.
There are several advantages to the use of GMSK modulation for a radio communication system. One is obviously the improved spectral efficiency when compared to other phase shift keyed modes. What is more is that this is amplitude does not contain information which means that is immune to amplitude variations and therefore more resilient to noise than some other modulation scheme, because most noise is mainly amplitude based. A further advantage of GMSK is that it can be amplified by a non-linear amplifier and remain undistorted. This is because there are no elements of the signal that are carried as amplitude variance. This means that the power consumption for a given output is much less, and results in lower levels of battery consumption which is very important for cell phones.

(5). Reference:
[1]. Digital Communications
Proakis_Masoud Salehi 2008

McGraw-Hill

higher

education.

[2]. Wikipedia Minimum-shift keying. Gaussian minimum-shift keying.
[3]. Radio-Electronics.com What is GMSK Modulation.
[4]. GMSK in a nutshell.
[5]. Communication theory. Changxin Fan, Lina Cao.

John

G

ESE 576 Final Project Report

Appendix: Matlab Code clear all; close all; clc; % ***** Preparation : Generate soucre and prepare the gauss filter ******
% First generate the random sequence -1, 1. The probability is 0.5
N = 3000; p = 0.5; source_gmsk = randsrc(1,N,[1,0;p,1-p]); source = source_gmsk *2 -1; figure(1); stem(source);title('Source'); axis([0 10 -1.5 1.5]); nsamp = 16;

% nsamp per bit(symbol)

Rb = 16000;

% symbol rate

Fc = 32000;
Fs = Rb * nsamp;

% carrier's frequency
% Sample rate

BT = 0.3;
Bb = BT * Rb;
Tb = 1/Rb;
NT = 3; multi = Fc/Rb; mid = NT * nsamp/2 ;

% this is a whole band filter.

t = -mid/Fs:1/Fs:mid/Fs; ht =

qfunc( 2*pi*Bb*(t-1/2*Tb))-qfunc(2*pi*Bb*(t+1/2*Tb) );

% use

definition in the book qt = zeros(1,NT * nsamp); for i=1:length(qt)

% keep the same length with the gauss filter after

integer for j=1:i qt(i)=qt(i)+ht(j); end; end; qt = qt/2/nsamp;
%
% Second calculate the phase which is consist of two parts according to
MSK
% one is the accumulate phase, another is the phase multipled by integer of % gauss filter phase = zeros(1,length(source)*nsamp); k=1; ESE 576 Final Project Report
L=0;
for j=1:nsamp theta1=source(k+1)*qt(j); phase((k-1)*nsamp+j)= pi*theta1 ; end; k=2;
L=0;
for j=1:nsamp theta1=source(k+1)*qt(j)+source(k)*qt(j+1*nsamp); phase((k-1)*nsamp+j)=pi*theta1; end; L=0; for k=3: N-1 if k==3
L=0;
else
L = L + source(k-2); end; for j=1:nsamp theta1=source(k+1)*qt(j)+source(k)*qt(j+1*nsamp)+source(k-1)*qt(j+2*n samp); theta2 = L * pi/2; phase((k-1)*nsamp+j)=pi*theta1 + theta2; end; end; k= N;
L = L + source(k-2); for j=1:nsamp theta1=source(k)*qt(j+1*nsamp)+source(k-1)*qt(j+2*nsamp); theta2 = L * pi/2; phase((k-1)*nsamp+j)=pi*theta1 + theta2;

end;
% ************ Modulation ************
% the same as MSK modulation t_length = N/Rb;

% Total time for simulation

% make the phase matrix the same as carriers
G_phase = interp(phase,multi); t_int = 1/Fc/nsamp; % Time interval is 1/Fc/nsample tt = t_int : t_int : t_length;

ESE 576 Final Project Report
S_Gmsk = cos(2 * pi * Fc * tt + G_phase); figure(2); n = nsamp * 10 * multi; plot(tt(1:n)*Fc,G_phase(1:n)); figure(3); plot(tt*Fc,S_Gmsk); axis([0 8 -1.5 1.5]);
% Calculate the PSD of Gmsk;
R_I = xcorr(S_Gmsk); power=fft(R_I); figure(4); subplot(211); P_max = max(abs(power));
P_max = 10*log10(P_max);
Amplitude = 10*log10(abs(power(1:(length(power)+1)/2))) - P_max; plot(10*log10(abs(power( 1:(length(power)+1)/2

)))- P_max);

%axis([0,Fs/2,-70,1]); d = 4; y = reshape(Amplitude, d , length(S_Gmsk)/d ); y = max(y); x = linspace(0, N * nsamp * multi, length(S_Gmsk)/d); subplot(212); plot(x,y);

% Acquire the envelop.

title('PSD of GMSK'); xlabel('Frequency'); ylabel('dB');
% ******************* Demodulation ***********************
% Difference demodulation.
% Delay one symbol time. and pi/2 phase shift
D_phase = [zeros(1,multi*nsamp) G_phase(1:N*nsamp*multi-multi*nsamp)];
S_Gmskd = zeros(1,length(S_Gmsk));
S_Gmskd = cos(2 * pi * Fc * (tt-Tb) + D_phase + pi/2); xt = S_Gmsk.* S_Gmskd;
% Low-pass filter to get the base band information. order = 300;
F=[0,Fc,Fc,Fc*nsamp/2]*2/Fc/nsamp;
A=[1,1,0,0]; lpf=firls( order , F , A );
Dem1 = conv(lpf , xt);
Dem = Dem1(order/2+1: order/2+length(xt)); figure(5); plot(tt*Rb,Dem);

ESE 576 Final Project Report axis([0 ,30, -0.8, 0.8]); title('Phase after low pass filter');
%**************** Hard decision *****************
D_source = zeros(1,N); for i=1:N if Dem( i* multi * nsamp )>0
D_source(i)=1;
else
D_source(i)= 0; end end
Ber =

sum(xor(D_source,source_gmsk))/N;

D_source = D_source * 2 -1; figure(6); subplot(211); stem(source(1:30)); subplot(212); stem(D_source(1:30));