Innovations-based MAP estimation with application to phase synchronization for serially concatenated CPM

A novel adaptive soft-input soft-output (A-SISO) module is developed for maximum a posteriori (MAP) symbol detection with parameter uncertainty. In contrast to the existing A-SISO algorithms that use linear prediction, the parameter estimation in the proposed structure is operated in a more general least-squares sense. Based on this scheme, a family of fixed-interval A-SISO (FI-A-SISO) algorithms is utilized to implement blind iterative phase synchronization for serially concatenated continuous phase modulation (SCCPM). For SCCPM systems, the forward-only FI-A-SISO algorithms are shown to be much more robust than the forward-backward FI-A-SISO algorithms in acquiring and tracking a time-varying carrier phase. The reason has to do with rotational invariance of CPM signals. This result can be extended to any rotationally invariant convolutional coded system with an unknown carrier phase.