The eighth-order (EOE) phase estimator  is modified to work for an eight-symbol symmetrical constellation, so that the large signal-to-noise (SNR) performance is not limited by self-noise. By using only the eight highest energy points of cross- QAM constellations, a reduced constellation eighth-order estimator (RCEOE) is proposed. Computer simulations for 128-QAM show that this new method performs substantially better than the recently introduced APP phase estimator of Wang et al. . However, simulations with 32-QAM show little performance advantage of the RCEOE over the APP estimator, for SNR values normally of interest, whereas for low SNR, the improvement is significant. Application to any constellation which can be reduced to an 8-symbol quadrant symmetrical sub-constellation is straightforward.
K. Cartwright and E. Kaminsky, "An Optimum Hardware Detector for Constant Envelope Quadrature-Quadrature Phase Shift Keying (CEQ2PSK)", in IEEE Globecom 2005 Conf. Proc., St. Louis, MO, 28 Nov-2 Dec. 2005, paper 13_2, vol.1, pp. 393-396.