In this letter, an optimum frame synchronizer is proposed for coded modulations in channels with uncertainties. Coded modulations include various frame synchronization scenarios, e.g., convolutionally coded transmissions and nonlinear modulations with memory. Frame synchronization is proposed as a maximum a posteriori probability estimation implemented using trellis path search for Markov chain decoding. In addition, time-varying uncertainties such as frequency offset and phase noise are jointly estimated via per-survivor processing as frame synchronization proceeds. The proposed frame synchronizer exploits the coding gain of coded modulations to achieve better performance than conventional frame synchronizers. We show that the resulting frame synchronizer consists of a correlation term and two data correction terms. Numerical results show that the proposed frame synchronizer is robust to uncertainties at the receiver and it exhibits improved performance.

In this paper, we present a unified approach for optimum frame synchronization where the observed symbols are modeled as the output of a Markov chain corrupted by additive white Gaussian noise (AWGN). This model encompasses many different frame synchronization situations e.g., convolutionally coded transmissions and nonlinear modulations with memory, such as continuous-phase modulation. The proposed frame synchronizer is implemented with trellis path search used for Markov chain decoding and provides better performance than conventional synchronizers because it is able to exploit coding gain. The proposed synchronizer includes many previously proposed synchronizers either as special cases or as suboptimal approximations. The numerical results show the performance gain of the proposed frame synchronizer for convolutional codes with linear modulation, transmission over known intersymbol-interference channels, and nonlinear continuous-phase modulation signals. The proposed frame synchronizer is derived for the case of continuous transmission but may also be applied to certain packet transmission scenarios