A maximum-likelihood statistic for pulse-position-modulation (PPM) symbol synchronization in the absence of slot synchronization is derived for the direct-direction optical channel from noisy observations of randomly modulated data, observed through a window

symbols wide. Two approximations to the optimal rule that are easier to implement are also derived and their performance analyzed by computer simulations. It is seen that the performance of one approximation, which is quite easy to implement, is almost identical to the more complex approximation.