Cycle slip analysis of the NDA FF carrier synchronizer based on the Viterbi & Viterbi algorithm

The cycle slipping behaviour of the feedforward carrier phase synchronizer based on the Viterbi & Viterbi algorithm is analysed. The synchronizer uses a block window accumulator (BWA) as averaging filter and postprocessing to eliminate equivocation. Approximate expressions for the cycle slip probability, valid for sufficiently large E_s/N_o, are derived for both wideband and narrowband postprocessing. Two methods to (numerically) evaluate these expressions are presented and are verified by Monte Carlo simulations of the cycle slips for the case of QPSK. The hybrid method combines simulation and theoretical results and is very accurate. The Gaussian approximation yields accurate results only for the case of narrowband postprocessing and moderate and large values of the BWA length. The computational requirements of the Gaussian approximation are considerably less than for the hybrid method, because the former requires no simulation; in turn, the hybrid method is computationally more efficient than straightforward Monte Carlo simulations of the cycle slips. It is found that the synchronizer nonlinearities yielding the lowest linearized phase error variance also yield the lowest cycle slipping probability, for both wideband and narrowband postprocessing