Gaussian Minimum Shift Keying

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:

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

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

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

GMSK Example

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

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.

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.

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.

GMSK baseband modulator implementation

GMSK Modulation Algorithms

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 18-551 Course notes

GMSK DEMODULATION WITH INPUT FROM AGILENT DIGITAL SIGNAL GENERATOR

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

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