1. Gaussian Minimum Shift Keying

2. Gaussian Minimum Shift Keying
GMSK is based on minimum shift keying which is a special form of frequency shift keying.
Minimum shift keying (MSK) is generated as follows:

3. Gaussian Minimum Shift Keying
GMSK is similar to MSK except it incorporates a premodulation Gaussian LPF
Used extensively in 2nd generation digital cellular and cordless telephone apps. such as GSM

4. GMSK Block Diagram h( ): Gaussian impulse response
b( ): rectangular pulse train
p( ): smoothed (Gaussian filtered) pulse train

5. GMSK: Impulse Response, Pulse Width
B: -3dB bandwidth of the Gaussian filter
Pulse shape characterized by –3dB bandwidth times the bit period, BTb
Pulse width increases as BTb decreases

6. GMSK Example

7. GMSK Improvement
Achieves smooth phase transitions between signal states which can significantly reduce bandwidth requirements

8. GMSK Tradeoffs
There are no well-defined phase transitions to detect for bit synchronization at the receiving end.
With smoother phase transitions, there is an increased chance in intersymbol interference which increases the complexity of the receiver.

9. GMSK Tradeoffs Continued
As can be seen from Figure 4, GMSKs power spectrum drops much quicker than MSK's. Furthermore, as WTb is decreased, the roll-off is much quicker.
It happens that with lower time-bandwidth products the pulse is spread over a longer time, which can cause intersymbol interference.
A compromise between spectral efficiency and time-domain performance must be made.

10. GMSK-Modulation Differential Encoding
The output from the GSM Burst is a binary {0, 1} bit sequence. This sequence is first
mapped from the RTZ (Return To Zero) signal representation to a NRZ representation before being input to the GMSK-modulator. This task is accomplished by the differential encoding function .
GSM makes use of the following combined differential encoding and level shifting scheme, where
d {0,1},… a{-1,1}
d’[n]=d[n] d[n-1]
a[n]=1-2*d’[n]
To avoid the start condition problem the GSM-recommendation prescribes that an infinite length sequence of all ones are assumed to precede the burst to be processed. Hence, when calculating a[0] and thereby also d’[0] ,it may be assumed d[-1]=1.

11. GMSK baseband modulator implementation

12. GMSK Modulation Algorithms

13. Channel = AWGN + Rayleigh Fading
Rayleigh distributed sequence
Where A is uniformly distributed in
the interval[0,1)
Two-ray Rayleigh fading model.
Rayleigh fading
AWGN noise 
Input Signal
Output signal
Channel Model
*Wireless Communications, T. Rappaport, Prentice Hall Communications Engineering and Emerging Tech. Series
* Noise& Fast Correlations Course notes

14. GMSK DEMODULATION WITH INPUT FROM AGILENT DIGITAL SIGNAL GENERATOR

15. Receiver Structure Correlation(EQ1,EQ2) EQ1=26 equalization bits
EQ2=16 central EQ1 bits and 5 zeros on either end
Correlation(EQ1,EQ2)

16. EQ21=the central 16 bits of equalization bit stream
h=channel response
w=noise
EQ21=the central 16 bits of equalization bit stream