Gaussian Minimum Shift Keying
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Transcript of Gaussian Minimum Shift Keying
Submitted To:
Dr.Farrukh Aziz Bhatti
Group Members
1. Aiman Anwar
2. Fatima Tahir
Gaussian Minimum Shift Keying
GMSK
CONTENT
1. GMSK
2. Performance Measurements
3. Bit Rate
4. Modulation
5. Demodulation
6. Transmission System
GMSK
Gaussian minimum shift keying or GMSK is a continuous-phase frequency shift keying modulation scheme
It is similar to standard minimum-shift keying (MSK).
The digital data stream is first shaped with a Gaussian filter before being applied to a frequency modulator.
A Gaussian filter uses a square wave to shape a signal to a more desirable output, allowing it to be transmitted to mobile devices without any flaws.
MSK Expanded version of MSK
Like MSK- keeps amplitude constant
Unlike MSK- use Gaussian filter
keeps Phase transition smooth.
• Gaussian pulse shaping to MSK
- smoothens phase
-stabilizes instantaneous frequency
-reduction of side lobe
• GMSK detection can be
coherent (like MSK)
Non-coherent (like FSK)
PERFORMANCE MEASUREMENTS
The of GMSK modem is qualified by the performance measurements of
signal to noise ratio (SNR) versus bit error rate . The SNR is related to
Eb /No ;
FREQUENCY RESPONSE
TIME-DOMAIN RESPONSE
Since lower time-bandwidth products a faster power- spectrum roll-off,
why not have a very small time bandwidth product.
It happens that with lower time-bandwidth products the pulse is spread
over a longer time, which can cause ISI
Therefore as a compromise between spectral efficiency and time –domain
performance , an intermediate time-bandwidth product must be chosen.
GMSK BIT-RATE
GMSK bit rate offers better performance within one decibel of optimum
MSK when the 3dB bandwidth bit duration product BT is equal to 0.25
The bit error probability for the GMSK transmission is expressed as,
GMSK MODULATION
There are two main methods of GMSK transmission.
1. Frequency modulated VCO
2. Quadrature modulation
1. FREQUENCY MODULATED
This method requires that the modulation index of the VCO equals 0.5 ,
but the modulation index of convection VCO based transmitter drifts
over time and temperature
It is not suitable for coherent demodulation due to component tolerance
problems.
2. QUADRATURE MODULATION
This implementation employs a baseband process followed by a
quadrature modulator .
With this implementation , the modulation index can be maintained
at exactly 0.5
This method is cheaper to implement.
I & Q MODULATOR –Generating a
GMSK Waveform
Example
Bb is the bandwidth of the low pass filter having a Gaussian shaped
spectrum ,T is the bit period.
BN=Bb * T is the normalized bandwidth.
Let Bb=1000, T=1/2000 ,then BN=0.5
The impulse response of the Gaussian low pass filter has to be truncated and
scaled , according to the BN value
CONT. – Gaussian LPF
For BN = 0.5 the filter response is truncated , symmetrically around zero, to two
bit periods, i.e. from –T to +T . The truncated filter response is represented
graphically in the following figure
Ensuring that the response of the filter to a single 1 is a phase change of ∏ /2,
is equivalent to choosing the constant K to satisfy the following equation
To demonstrate the modulation, randomly chosen data stream
{1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,,1,-1,1,1,-1,-1,1,-1,1,-1,-1,……}
CONT. – Filter Response
CONT. – Bit Stream Graphically
The beginning of this data stream can be represented graphically by the
following
As the data passes through the filter it is shaped and ISI is introduced since
more than one bit is passing through the filter at any one time .
For BN=0.5 , since the bits are spread over two bit period , the second bit
enters the filter as the first is half way through , the third enters as the first
leaves etc…….
The first few Gaussian shaped pulses are represented graphically as ,
CONT. - Gaussian Shaped Pulses
These individual shaped pulses are then added together to give a function
which is represented graphically in the following figures. This is the
function denoted by b(t)
CONT.- Summing
This function ,b(t), is then integrated w.r.t. time from t to ∞, to give the
function c(t)
CONT.- Integrate
Once we have the function c(t) , we take sine and consine functions to
produce the I and Q-baseband signals.
Taking the consine of c(t) produces the I-baseband signal I(t) i.e.
I(t) = cos [c(t)]
CONT. – I Baseband Signal
Taking the sine of c(t) produces the Q-baseband signal Q(t) i.e.
Q(t) = sin[c(t)]
CONT. – Q Baseband Signal.
These two function I(t) and Q(t) are passed through the I/Q modulator which
leads to the output signal m(t) which can be written as
m(t)= sin (2∏fct) I(t) + cos (2∏fct) Q(t)
Where
fc = carrier frequency
CONT.- I/Q Modulator
The GMSK signal m(t) is represented
CONT. - GMSK Signal
TRANSMITTER
To generate GMSK signal a message stream (NRZ data) is passed through
a Gaussian filter with a determined response.
For example a GMSK filter with the impulse response given as
where
α= roll of factor of the filter related to bandwidth B
t=time period, t=K*Tb
Tb=bit period
K= integer
CONT.
In the generation of GMSK , a simple scheme adopted in GMSK transmitter
is shown in fig.
Input data is given to the Gaussian LPF . It is also known as pre-modulation
filter.
The impulse response of the filter is given by:
GMSK Transmission By I And Q
Method
It is an effective method in elimination synthesizer shortcoming.
That is if synthesizer unit is used for GMSK generation there is a problem
that it does not respond to low frequency signals.
The consecutive 1’s and 0’s may not be recognized by it.
This problem of allowing only the high frequency signals is overcome in
quadrature I and Q modulator.
DEMODULATION
GMSK modulator basically derives back Φ using arc tan function, which
is applied to derivator block to obtain NRZ signal back.
Before doing this mixing and Low pass filtering is done to obtain I and Q
components from two chains.
GMSK DETECTION
In detection process orthogonal coherent detectors can be used .
The input modulated signal is given in two mixer stages .
TRANSMISSION SYSTEM
The two main systems that specifies GMSK modulation are ;
1. Cellular Digital Packets Data
2. Mobitex system
1.CDPD
The CDPD transmits packets on an idle cellular voice channels.
The data rate transmitted at 19.2 Kb/sec with bandwidth –bit duration
(BT) as 0.5. such a high data rate is compatible with 30kHz,channel
spacing .
The CDPD systems guarantees.
Wide spread radio converge
Ease of adaption
2.MOBITEX SYSTEM
The Mobitex system is a dedicated data system.
It has a lower data rate than the CDPD networks i.e 8 kb/sec .
It does not share its channels with cellular voice transmission .
It has BT equal to 0.3 and affords a tighter channel spacing as 12.5kHz
when compared to CDPD.
The system has better ISI tolerance.
Both CDPD and Mobitex employs forward error correction technique in their
packets transmission
PROS
Provide constant envelop.
It has good spectral efficiency.
ISI is tolerable.
GMSK is highly useful in wireless communication.
CONS
Irreducible error rate problem
The average probability of error is ,
GMSK reduces sideband power.
APPLICATIONS
Transmission of digital data from satellites and radio broadcasting towers to
mobile devices as well as from mobile devices to satellites and radio
broadcasting towers.
In remote controlled devices, cellular phones, Bluetooth headsets.
GSM.
CONCLUSION
GMSK provides a straightforward, spectrally efficient modulation
method for wireless data transmission system.
Such modulation is implemented in GSM and CDPD methods.
Improved spectral efficiency.
Power Spectral Density,
Reduced main lobe over MSK
Requires more power to transmit data than many comparable
modulation schemes.
REFERENCE Arokiamary, V. Jeyasri. Mobile Communications. Technical Publications,
2009.
Arokiamary, V. Jeyasri. Mobile computing. Technical Publications, 2009.
http://www.tech-faq.com/gmsk.html
http://www.rfwireless-world.com/Terminology/MSK-GMSK.html
http://www.emc.york.ac.uk/reports/linkpcp/appD.pdf
http://www.radio-electronics.com/info/rf-technology-design/pm-phase-
modulation/what-is-gmsk-gaussian-minimum-shift-keying-tutorial.php
http://poujouly.net/2012/12/07/modulation-gmsk/
http://mobilorus.blogspot.com/2013/03/which-modulation-types-are-
being-used.html
http://www.emc.york.ac.uk/reports/linkpcp/appD.pdf
QUESTION TIME !