Soft carrier phase recovery for continuous phase modulations

In this paper a general soft-based synchronization technique for continuous phase modulations (CPM) is presented. In particular two soft carrier phase estimation algorithms are derived, being the phase the parameter that shows the lower implementation complexity. These algorithms exploit the trellis structure inherent in the modulator of CPM signals and make use of a symbol-based BCJR, developed in an ad-hoc way for an uncoded CPM signal. The algorithms are blind and are designed to work with all CPM family. Simulation results for the soft carrier phase estimation are presented in terms of Root Mean Square Estimation Error (RMSEE). The modified Cramer-Rao bound (MCRB) is also shown for reference. RMSEE of soft recovery approach is very close to MCRB for all the examined formats.