Maximum Likelihood Symbol Synchronization for the Direct-Detection Optical On-Off-Keying Channel

The maximum-likelihood symbol synchronization statistic is derived from noisy observations of randomly modulated on-off-keying data for the direct-detection optical channel. A similar statistic for the case when the transmitter sends a special pattern of alternating O´s and 1´s for synchronization purposes only is also derived. Various approximations to the optimal statistic are introduced and their performance compared to the optimal one under a new criterion, believed to be more appropriate for the Poisson channel than the mean-square error criterion routinely used with other channels. It is shown that although the variable associated with symbol transitions is continuous, the possible values of it that maximize the maximum-likelihood (ML) statistic belong to a discrete set with relatively few elements.