Gaussian Minimum Shift Keying (GMSK)

PROBLEMS IN GMSK

The main lobe of MSK is wide. This makes MSK unsuitable for the applications where extremely narrow bandwidths and sharp cutoffs are required.
Slow decay of MSK power spectral density curve creates adjacent channel interference. Hence MSK cannot be used for multi-user communications. This problem can be overcome with Gaussian MSK.

INTRODUCTION

GMSK is a simple binary modulation scheme which may be viewed as a derivative of MSK. It is used in European second generation wireless systems such as GSM.
The word Gaussian refers to the shape of a filter that is used before the modulator (transmitter) to reduce the transmitted bandwidth of the signal. GMSK uses less bandwidth than conventional FSK.

(i) GMSK Transmitter

Gaussian MSK transmitter.

Fig.1. Gaussian MSK transmitter

In GMSK, the sideband levels of the spectrum are further reduced by passing the modulating NRZ data waveform through a pre modulation Gaussian pulse shaping filter.
Gaussian pulse – shaping filter which is particularly effective when used in conjunction with Minimium Shift Keying (MSK) modulation, or other modulations which are well suited for power efficient non linear amplifiers.
Pre modulation Gaussian filtering converts the full response message signal (Where each base band symbol occupies a single bit period $T$ ) into a partial response scheme where each transmitted symbol spans several bit periods.

(II) GMSK BIT ERROR RATE(BER)

The bit error probability for Gaussian Minimum Shift Keying is given by

$P_e=Q\left\{\sqrt{\frac{2 {\gamma} \mathrm{E}_{\mathrm{b}}}{\mathrm{N}_0}}\right\}$

where, $𝛾$ is a constant related to $BT$ .
B is bandwidth,
$T$ is message symbol duration.
$𝐸𝑏$ is transmitted bit energy, and
$No$ is noise spectral density

$\gamma=\left\{\begin{array}{c} 0.68 \text { for GMSK with } \mathrm{BT}=0.25 \\ 0.85 \text { for simple MSK }(\mathrm{BT}=\infty) \end{array}\right\}$ ….eqn (2)