On the synchronizability and detectability of random PPM sequences

The problem of synchronization and detection of random pulse-position modulation (PPM) sequences is investigated under the assumption of perfect slot synchronization. Maximum-likelihood PPM symbol synchronization and receiver algorithms are derived that make decisions based on both soft as well as hard data; these algorithms are seen to be easily implementable. Bounds were derived on the symbol error probability as well as the probability of false synchronization that indicate the existence of a rather severe performance floor, which can easily be the limiting factor in the overall system performance. The performance floor is inherent in the PPM format and random data and becomes more serious as the PPM alphabet size Q is increased. A way to eliminate the performance floor is suggested by inserting special PPM symbols in the random data stream.