An expression for the true variance of the Pth powerlaw phase estimator, as the number of samples approaches infinity, is given. This expression is an extension to the linear approximation of Moeneclaey and de Jonghe  which is known to be inadequate in some practical systems. Our new expression covers general 2π/P-rotationally symmetric constellations that include those of PAM, QAM, PSK, Star M-QAM, MR-DPSK, and others. This expression also generalizes the known expressions for QAM and PSK. Additionally, our expression reduces to the Cramer-Rao bound given by Steendam and Moeneclaey , as SNR goes to zero. Monte Carlo simulations provide experimental verification of the theoretical expression for various constellations.
Cartwright, K. and E. Kaminsky, "Asymptotic Performance of the Pth Power Law Phase Estimator," in IEEE Globecom 2005 Conf. Proc., St. Louis, MO, 28 Nov-2 Dec. 2005, paper10_5, vol. 1, pp. 331-336.