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 !