—In this paper, we study Bayesian and hybrid Cramer-Rao bounds for the dynamical phase estimation of QAM modulated signals. We present the analytical expressions for the various CRBs. This avoids the calculation of any matrix inversion and thus greatly reduces the computation complexity. Through simulations, we also illustrate the behaviors of the BCRB and of the HCRB with the signal-to-noise ratio. Index Terms—Bayesian Cramer-Rao Bound (BCRB), Hybrid Cramer-Rao Bound (HCRB), Synchronization Performance