Locating Data Frames in Direct-Detection Optical Communication Systems

The maximum-likelihood rule for locating a frame-synchronization pattern in a direct-detection optical communication system employing either
Q
-ary pulse-position modulation or on-off keying is identified. We show that equivalent performance for the simple correlation and postdctection-correlation rules used in practice can require substantially more than a 3 dB increase in signal power over that required using the maximum-likelihood rule.