Also known as: GMSK
GMSK (Gaussian minimum-shift keying) is a continuous-phase FSK variant in which the data is passed through a Gaussian filter before modulation, smoothing phase transitions for a compact spectrum and constant envelope.1 It is the Gaussian-shaped refinement of minimum-shift keying (MSK), and one of the most widely deployed digital modulations in history thanks to GSM.
How it works
GMSK starts from MSK, which is the special case of continuous-phase 2FSK where the frequency deviation is exactly one-quarter of the bit rate — the minimum separation that keeps the two tones orthogonal. At that deviation each bit advances the carrier phase by exactly ±90°, so MSK can equivalently be viewed as a form of offset QPSK with sinusoidal pulse shaping. GMSK adds one step: it passes the data through a Gaussian low-pass filter before the phase integrator. The Gaussian filter has no overshoot and a very fast spectral roll-off, so it suppresses the side-lobes that plain MSK still radiates, buying an even more compact spectrum.
The filter’s aggressiveness is set by the BT product — the Gaussian’s bandwidth times the bit period. A small BT (GSM uses 0.3) gives a very narrow spectrum but spreads each symbol’s energy across neighbours, deliberately introducing controlled intersymbol interference that the receiver must untangle (often with a Viterbi/MLSE equaliser). A larger BT keeps the eye open at the cost of wider occupied bandwidth. Because the phase path is smooth and the amplitude never varies, GMSK keeps a constant envelope, which — like C4FM — lets it be amplified by efficient non-linear power amplifiers, a decisive advantage for battery-powered handsets.
Variants
GMSK sits in the continuous-phase modulation (CPM) family alongside MSK, C4FM, and GFSK (Gaussian FSK, the near-identical scheme Bluetooth uses — the line between “GFSK” and “GMSK” is mostly whether the deviation index is set to the MSK value of 0.5). Compared with 4FSK modes, GMSK is binary — 1 bit per symbol — trading throughput for an exceptionally clean, robust, constant-envelope signal.
Relevance to SDR
GMSK carries AIS ship transponders (9600 bps GMSK on marine VHF), GSM cellular, D-STAR amateur digital voice, and many satellite and telemetry links. A software receiver demodulates it either coherently (recovering carrier phase and detecting the ±90° increments) or non-coherently as an FSK discriminator followed by a matched filter and slicer. GopherTrunk uses a GMSK demodulator in its AIS pipeline, recovering the underlying bit transitions after frequency/phase detection; it does not target GSM, which is out of scope.
Sources
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Minimum-shift keying — Wikipedia, for MSK/GMSK, Gaussian shaping, the BT product, and the constant-envelope property. ↩