On Some Practical Approximations to the Ideal Group Synchronization Process

The best possible group synchronization process is the one that selects the most probable starting position of a sync pattern known to have been inserted into the transmission format. Such a device involves computation of an inverse probability function in each possible location of the sync position. The computer proves to be impractical to instrument, in general, but for a waveform such as PCM with equal positive and negative pulses it reduces simply to a cross correlator as the signal-to-noise ratio increases. This suggests a new and practical philosophy of group synchronization based on statistical hypothesis testing. Practical group synchronizers based on this new philosophy are described that approximate the ideal and their performances are analyzed for a PCM waveform, for hypothesis tests for least squared error, maximum cross correlation and maximum digital cross correlation.