Asymptotic cycle slip probability expression for the NDA feedforward carrier synchronizer for M-PSK

The authors extend their previous results on cycle slipping in feedforward M-th power carrier synchronizers for M-PSK (M-ary phase shift keying) by deriving an asymptotic (high E_S/N₀) cycle slip probability expression. Computer simulation results indicate that the convergence of the actual slip probability to the asymptotic probability is not very fast. It is shown that approximating the BWA (block window accumulator) output by a Gaussian random variable yields inaccurate asymptotic results but, for practical values of the BWA length K, happens to be fairly accurate in the region where convergence of the true slip probability to the asymptotic slip probability is not yet obtained. It is found that the feedforward M-th power synchronizer yields a larger cycle slip rate than its feedback counterpart: for K=64, the asymptotic difference in E_S /N₀ is about 6 dB