The effect of the averaging filter on the cycle slipping of NDA feedforward carrier synchronizers for MPSK

The authors deal with the cycle slipping of a non-decision-aided (NDA) feedforward carrier synchronizer for multiple phase shift keying (MPSK). As an averaging filter, they consider both a block window accumulator (BWA) and a gliding window accumulator (GWA). Approximations for both low and high signal to noise power ratios (E_s /N₀) are derived for the cycle slip probability and compared with computer simulations. For the BWA, the asymptotic (high E_s/N₀) expression is accurate for moderate and large E_s/N₀, where the asymptotic expression is valid, the GWA yields a larger cycle slip probability than the BWA, although the exponential cycle slip behavior is the same for both averaging filters. For low E_s/N₀ , the cycle slip probability is larger for the BWA than for the GWA