ML-oriented NDA carrier synchronization for general rotationally symmetric signal constellations

In this contribution we point out that the nondecision-aided (NDA) carrier synchronizer, maximizing the low E s / N o limit of the likelihood function averaged over a general 2r/N-rotationally symmetric signal constellation, reduces to the familiar timing-aided Nth power synchronizer; this extends a result from [6] where only M-PSK constellations have been considered. Whereas in the case of M-PSK the tracking error variance of this NDA ML synchronizer is known to converge to the Cramer-Rao bound (CRB) with increasing E s / N o [2], we show that for other rotationally symmetric constellations (such as QAM) the tracking error variance is substantially larger than the CRB.