Joint Baud and Frame Synchronization in Direct Detection Optical Communications

The maximum-likelihood frame synchronizer was recently derived for direct-detection optical communications assuming baud synchronization. In this paper we present an extension to those results when pulse-position modulation is used and jointly derive baud and frame synchronization from slot synchronization. The optimum rule is seen to consist of a simple correlation term and a nonlinear correction term. Simulation results for the optimum rule compared to analytical and simulation results for the simple correlation rule show that equivalent performance for the simple correlation rule requires a substantial increase in signal power. To design good synchronization patterns, we use a divergence measure derived from the optimum rule. A simple algorithm is derived to test whether a given sequence is good or not.