Frame synchronization play a very important role in coding of AIS. There are much arithmetic like maximum-likelihood, correlation and so on. But most of those cannot achieve good performance with large frequency offset. As satellite-based AIS system exist larger time delay and Doppler frequency offset, this paper propose arithmetic of frame synchronization. It is based on folding auto-correlation, where the top half and second half of training sequence have largest correlation after it is modulated by GMSK. Simulation experiments indicate that this arithmetic has good anti-frequency-offset performance.
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