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In this work we introduce the so called polynomial minimum shift keying (PMSK) modulation as a particular case of continuous phase modulations (CPM), the standard used in GSM or DECT systems. The demodulation is based on the high order ambiguity function and leads to simple implementations essentially based on FFT. The most important feature of the demodulation process of PMSK signals is Doppler tolerance and the capability, under some bandwidth constraints, for blind equalization for transmissions over multipath fading channels. The price paid is essentially in terms of oversampling and increased modulation indices to obtain satisfactory performance.