GMSK overview

[Glossary]
+ FSK: Frequency shift keying. Use M frequencies (carriers) to represent M symbols.
+ MSK: Minimum frequency Shift Keying. In a M-FSK, choose the phase of each carrier such that switching the carriers does not cause phase shift, which broadens the spectrum and reduces spectral efficiency.
+ CPFSK: Continuous Phase FSK. The phase is the integration of M-PAM. The integration guarantees the phase is continuous. M-PAM is the differentiation of the phase, which is the instantaneous frequency. So the instantaneous frequency fluctuates with M-PAM modulation.
+ GMSK: Gaussian Minimum Shift Keying. Choosing the shape function of the M-PAM by Gaussian to reach the best spectral efficiency is called Gaussian-MSK (GMSK).
+ PAM: Pulse Amplitude Modulation. Each symbol is represented by a distinct amplitude of a shape function. si(t) = Aig(t), where g(t) is the shape function valid within a symbol time.[Example 1]
The above example is an example of symbol time Ts = 50us, strong ISI case (sigma = 20). In the M-PAM figure, Gaussian-shape signals overlap. Phi(t) is the integration of the phase and s(t) is the real baseband. For the first symbol = 10, the corresponding frequency is 5 cycles per Ts. It's roughly true. The slight deviation (the real cycle is around 4) is the Gaussian tail not integrated in the phase (A Gaussian has infinite long tail).

[Example 2]
The following example is the same case with different sigma. The ISI is weaker. Each Gaussian is distinct in M-PAM figure. The required bandwidth is larger. The frequency is more precise (see signal s(t)).


[Advantages of GMSK]
+ High Spectral Efficiency.
+ Constant envelop--> non-linear amplifier is OK (cheaper).
+ Use simple non-coherent detection for demodulation (no good PLL is required). Use M-non-coherent IQ components and add them by square root. The carrier with the maximum frequency is the estimated symbol.
+ Good for voice (LOW BER 10^(-3) is OK).

[Disadvantages of GMSK]
+ Large ISI. Gaussian waveform extents to infinity and inevitably causes ISS. Gaussian waveform does not satisfy Nyquist criterion. Increasing spectral efficiency (smaller bandwidth) also increasing ISI (larger temporal extend) according to Uncertainty Principle.
+ Bad for data (require high BER).