Graphical demonstration of the coherent demodulation of GMSK

In this paper, we demonstrate through graphical means the coherent demodulation of Gaussian Minimum-Shift-Keying (GMSK) that is made possible because the pulses after the Gaussian lowpass filter retain the unit area such that the phase deviation has the π/2 value. Although it is straightforward to show analytically that the MSK waveform can be split into two antipodal pulse streams modulating an in-phase and quadrature carriers, so that coherent demodulation can be applicable, it is not the case with GMSK, because the modulating signal consists of overlapping pulses with analytically intractable Q function describing the pulse shape. By computing the access phase function θ(t) and plotting cos θ(t) and sin θ(t), we can see that the plots of cos θ(t) and sin θ(t) for GMSK retain the synchronized and staggered nature of those of MSK, suggesting the possibility of coherent demodulation as in MSK. We then show a simple way to compute the bit error probability of GMSK for a few values of the Gaussian lowpass filter bandwidth.