Asymptotic Performance of the Pth Power-Law Phase Estimator

An expression for the true variance of the P 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 [1] 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 [9], as SNR goes to zero. Monte Carlo simulations provide experimental verification of the theoretical expression for various constellations.