Method for tracking the phase of a signal modulated by continuous phase modulation and synchronization device implementing said method

A method for tracking the phase of a signal modulated by an M-state continuous phase modulation, sampled so that at least two samples are obtained per symbol period and processed in portions of N symbols, the method comprising:

• a complex vector V(n) representative of the state of amplitude and phase of the received signal is determined for each symbol period with an offset of a half symbol period relative to the symbol rate of the receiver;
• a level measurement is performed for each symbol period on the real or imaginary part of two complex samples U(n) and U(n−1) distributed with an offset roughly of a half symbol period either side of the instant of estimation of the complex vector V(n);
• the complex vectors V(n) are associated for each symbol period with one of the M points of the constellation of the continuous phase modulation by a mapping function which takes as input the levels of the samples U(n) and U(n−1) and makes it possible to find the point of the constellation which is closest;
• an average estimation of the offset of the phase over a period of N symbols is calculated for each of the M points of the constellation of the continuous phase modulation by calculating the difference between the average estimation of the phase of the signal and the theoretical phase value associated with each point of the constellation of the continuous phase modulation;
• an absolute estimation of the offset of the phase over a period of N symbols is calculated by calculating the average of the average estimations of the offset of the phase associated with each of the M points of the constellation of the continuous phase modulation;
• a differential estimation of the offset of the phase over a period of N symbols is calculated by calculating the average of the average offset of the phase differences between consecutive points of the constellation.