The performance of a coherent residual carrier PSK system using hybrid carrier phase synchronization

This paper presents a generic theory for the behavior and performance of hybrid carrier synchronization loops, i.e., loops composed of a combination of discrete and suppressed carrier types, and evaluates their impact on the error probability performance of a PSK communication system. Since hybrid loops are characterized by two not necessarily equiprobable lock points (one at zero phase error and one at 180 degrees phase error), it is necessary to properly take this phenomenon into account in predicting their performance. As such, a new form of solution for the phase error probability density is proposed based on the solution of the Zakai equation. Using this mathematical model, the mean-squared phase error of the hybrid loop is derived and numerically compared with results obtained from a computer simulation. Two methods of resolving the inherent 180 degrees phase ambiguity associated with using a hybrid loop for carrier synchronization are discussed and the corresponding average error probability performances of an associated PSK system are evaluated.