Cycle-slip analysis of the Mth-power NDA feedforward carriersynchronizer for MPSK

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_s/N_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_s /N_o values of practical interest