Frame synchronization for optical multi-pulse pulse position modulation

We investigate frame synchronization algorithms for direct detection multi-pulse pulse position modulation (MPPM) optical communication systems. The optimal rules (in a maximum likelihood sense) are derived, approximations to them that are computationally easier to implement are identified, and upper bounds on the synchronization probability are obtained. It is seen that the high SNR rules have a performance nearly equal to that of the ML rules, but provide a significant performance improvement over the simple correlation rules and are virtually as simple to implement for a wide range of signal energies. We also address the problem of designing periodic MPPM synchronization sequences with good autocorrelation properties, based on a maximum, worst case, peak-to-sidelobe distance criterion. Upper bounds on the peak-to-sidelobe distance for such sequences are derived, and a few sequences, generated by computer simulations, for different synchronization sequence lengths are given.<>