On the Synchronizability and Detectability

The problem of synchronization and detection of random pulse-position-modulation . . pp?.I 1 sqct ! :ces :s ~:~~;e~ti~:...!.p(! ::z?.t.r ~ ~ ~ ~ ! : : : n + ~ n i i nf ~ p r f p ~ f ~ !n t c \ ~ ~ c ! h r r > ~ ~ i z = t i f i ~ ~ r . a > > ~ I a x i ~ ~ ~ u ~ n l i k e l i l i c , o t l PPh synibol syiicliroxiiza.t.iori and receiver algorit.linis are derived that 111ilkt’ decisions 1 x 1 ~ ~ 1 bot 11 0 1 1 soft as well as hard clat a: t liese algorit lims are seen to be easily implementable. We derive bounds on the synbol error probabilit,y as well as t,he probability of false synchronizat,ion that indicate t lie exist.ence of a rather severe performance floor: which can easily be the limiting factor in the overall syst,em 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.