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

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 2π/N-rotationally symmetric signal constellation, reduces to the familiar timing-aided Nth power synchronizer; this extends a result of D´Andrea, Mengali and Reggiannini (1988) 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. We show that for other rotationally symmetric constellations (such as QAM) the tracking error variance is substantially larger than the CRB