MSE lower bounds for phase estimation based on overlapped Gaussian distribution

The Cramér-Rao bound (CRB) has been widely used as a mean square error (MSE) lower bound for unbiased parameter estimations. For phase estimation, however, the CRB is not valid at low signal-to-noise ratio (SNR) due to the effect of phase wrapping. In this paper, closed-form approximations of the MSE lower bounds for the phase estimation are derived under both Gaussian and Rayleigh fading channels, which are particularly useful at low SNR. The derivation is based on an overlapped Gaussian distribution which is used to approximate the true posterior phase distribution. Analytical and simulation results show that the derived closed-form MSE lower bounds provide more meaningful indications to the phase estimation performance than the CRB.