Symbol synchronization in digital communication systems using partial response CPM signaling

The applicability of standard symbol synchronization schemes in digital communication systems using partial-response CPM (continuous phase modulation) signaling has been analyzed. Using the theory of maximum a posteriori estimation of the unknown parameter in Gaussian noise, a theoretical structure for the optimum symbol synchronizer in a system using partial-response CPM signaling is derived. As the first approximation, a closed-loop configuration, known as the early-late loop, is derived and discussed. Due to signal correlation in adjacent symbol time intervals, even this configuration is impractical for a hardware realization. For these reasons, different approximations of the general maximum-likelihood function, leading to the discrete bit timing loop realizations, are derived and discussed. The influence of the carrier phase synchronization error on these synchronizers is also discussed.