Combining Decision-Feedback Equalization and Carrier Recovery for Two-Dimensional Signal Constellations

In this paper, the combination of decision feedback equalizer and digital phase-locked loop (DPLL) is investigated in detail in channels impaired by intersymbol interference and phase noise. Various methods for carrier phase recovery in several system configurations are analyzed and compared. Two cases of phase noise are considered. In the first one, the significant phase noise is in the receiver side, whereas in the second case, the significant noise is in the transmitter side. We select the best estimation schemes for the two cases and analyze them in terms of residual phase jitter, optimal loop gain, and complexity of implementation. Their performances relative to the other schemes are verified by simulations under both high and low signal-to-noise ratio conditions, where in the latter, the mean time to lose lock criterion is used. We show the relevance of knowing the source of the phase noise. We also treat the special case of one-dimensional signal constellations, such as binary phase-shift keying and gaussian minimum-shift keying (GMSK), where further optimizations are employed. Finally, the more general case of phase noise, which originates both in the transmitter and the receiver in the same order of magnitude is introduced. For this case, the new transmitter phase noise loop is combined with the receiver loop to a double DPLL.