  This paper introduces a novel blind carrier phase recovery estimator for
general 2{\Pi}/M-rotationally symmetric constellations. This estimation method
is a generalization of the non-data-aided (NDA) nonlinear Phase Metric Method
(PMM) estimator already designed for general quadrature amplitude
constellations. This unbiased estimator is seen here as a fourth order PMM then
generalized to Mth order (Mth PMM) in such manner that it covers general
2{\Pi}/M-rotationally symmetric constellations such as PAM, QAM, PSK.
Simulation results demonstrate the good performance of this Mth PMM estimation
algorithm against competitive blind phase estimators already published for
various modulation systems of practical interest.
