Effects of Jitter and Cycle Slipping of Phase Reference Upon Unique Word Missed Detection in QPSK Systems

The effects of phase jitter and cycle slipping of the recovered carrier upon unique word (UW) missed detection in QPSK systems are investigated. Schrempp et al. have already presented the relationship between the UW missed detection probability (UWMP) and the bit error probability, which is simple and useful as long as the phase reference is noiseless. However, when the authors recently made some theoretical and experimental assessments of UW missed detection, they found that the above disturbances of the recovered carrier significantly affected the UW missed detection performance. Specifically, the actual UWMP was often worse than that predicted hy Schrempp et al. In fact, a bottoming effect takes place in the UWMP versus UW length characteristic. In this paper, after obtaining the conditional symbol and bit error probabilities for the recovered carrier with some phase error, we discuss the nature of phase fluctuation and cycle slipping for the recovered carrier. Consequently, we derive general expressions for the UWMP in both CPSK and DCPSK transmissions. The UWMP's are numerically calculated, and are then compared to our experimental data.