Robust time and phase synchronization for continuous phase modulation

A novel joint timing and phase-recovery technique is proposed for continuous phase modulation (CPM) systems based on Kalman filtering and an approximate representation of CPM signals with nonorthogonal exponential expansions (nOEE). Compared with existing techniques, the proposed synchronizer requires a less complex front-end processor, and can achieve reliable acquisition performance with a shorter preamble. The asymptotic stability and convergence of the proposed synchronizer is analyzed, including the effect of statistical channel-modeling errors on the convergence characteristics. The selection of suboptimal nOEEs and the design of triple-initialized Kalman filters are also discussed. Both theoretical and simulation results show that the proposed synchronizer is robust in acquiring and tracking both the time shift and the phase offset on either time-invariant or time-variant channels.