We analyze the cycle-slipping behavior of the Mth-power nondecision-aided (NDA) feedforward carrier synchronizer for M-ary phase-shift keying (MPSK). The averaging filter is a block window accumulator, and postprocessing is used to eliminate equivocation. An asymptotic (high E/sub s//N/sub o/) expression for the cycle-slip probability is derived and verified by computer simulation. A "hybrid" approach, combining analytical results with importance sampling simulation techniques, allows for the fast and accurate determination of the cycle-slip probability for all E/sub s//N/sub o/ values of practical interest.

We point out that the nondecision-aided (NDA) carrier synchronizer, maximizing the low E/sub s//N/sub o/ limit of the likelihood function averaged over a general 2/spl pi//N-rotationally symmetric signal constellation, reduces to the familiar timing-aided Nth power synchronizer; this extends a result of D'Andrea, Mengali and Reggiannini (1988) where only M-PSK constellations have been considered. Whereas in the case of M-PSK the tracking error variance of this NDA ML synchronizer is known to converge to the Cramer-Rao bound (CRB) with increasing E/sub s//N/sub o/. We show that for other rotationally symmetric constellations (such as QAM) the tracking error variance is substantially larger than the CRB.>

The authors deal with two types of feedforward carrier-independent non-decision-aided (NDA) symbol synchronizers for PAM, which are based upon the maximum-likelihood criterion. Their timing error variances are compared, for two important classes of signal constellations.>