A maximum-likelihood-based frequency synchronizer for dual-h continuous-phase modulation (CPM)

Maximum-likelihood (ML) techniques are useful in finding synchronizer structures for various cases. Synchronizers for frequency,. phase and timing have been found for various bandpass signaling techniques such as PSK, DPSK, QAM, MSK and CPM. These include data-aided, decision-directed and clock-aided cases. For CPM, however, apparently only the single modulation index case has ML-based synchronizers. This paper describes a new non-data-aided, non-decision-directed ML-based frequency synchronizer (with no phase or timing information), derived for a full-response, dual-h (two modulation indices), 4-ary CPM signaling scheme. Simulation results provide a preliminary indication that the new synchronizer offers potentially significant advantages compared with ad hoc techniques, but these simulations will need to be expanded in scope before final design choices can be made.