We consider a satellite-based mobile communication scheme based on continuous-phase modulated (CPM) signals used in conjunction with trellis-coded modulation (TCM). This scheme provides a power saving due to the coding gain of TCM, and simultaneously a reduced bandwidth occupancy due to the particular structure of CPM signals. Moreover, CPM provides constant-envelope signals, which is a requirement for satellite transponders operating in a time-division multiple-access mode.To keep the complexity manageable, a detection scheme based on differential detection of CPM is used. After a description of the system and of its performance, we study how to estimate the frequency shift induced in the received signal by the Doppler effect.