Convergence behavior of iterative phase synchronization and detection

Serially concatenated systems with rotational invariance (RI-SCS) can tolerate certain phase ambiguities and, therefore, for these systems coherent detection is robust even when cycle slipping, false-lock and hangup exist during phase synchronization. However, the convergence behavior of iterative phase synchronization and detection is still not well-understood. In this paper, we present a simplified phase model to analyze the convergence of iterative receivers with/without occurrence of phase rotations. Particularly, an oscillatory convergence behavior due to cycle slipping is explained by means of density evolution. Moreover, based on per-survivor processing (PSP) and single-estimator processing (SEP) techniques, a family of adaptive soft-input soft-output algorithms are employed to implement joint phase tracking and demodulation in the context of maximum a posteriori symbol detection. Both analytical and simulation results show that for RI-SCS the convergence performance of the SEP method is more robust than that of the PSP method when carrier phase has high and random dynamics.