Simple joint and nonjoint data-aided maximum-likelihood (ML) estimators are derived for the carrier phase and symbol timing at coherent continuous phase modulation (CPM) receivers, which implement 4- or 6-time-limited sinusoidal basis functions. It is shown that, due to the choice of proper basis functions for the signal space, the estimation of symbol timing becomes a special form of phase estimation and leads to a simple synchronizer and that the synchronizers based on this estimation structure work robustly in steady state, even at low signal-to-noise ratios (SNRs). Several approaches to solving the hang-up problem of symbol-timing tracking loops are discussed, and simulation results are presented to show both the steady-state and acquisition performances of the proposed synchronizers.
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