A lower performance bound for phase estimation over slowly-fading Ricean channels

In this paper we present a fundamental lower bound to the mean-square error of estimators of the phase of a sine wave passed through a Ricean fading channel. As particular cases, expressions of the bound inherent to Gaussian and Rayleigh channels are also provided. The bound is derived from the performance analysis of the Bayes minimum mean-square error phase estimator. The salient features of this bound as compared to other bounds proposed in the literature are: (i) the bound holds for all values of the signal-to-noise ratio and not only for high values, as happens with the Cramer-Rao bound, (ii) for high signal-to-noise ratios and over the Gaussian channel the bound approaches the Cramer-Rao bound, while it may considerably exceed the latter for a generic Ricean channel, (iii) the bound can be physically attained, albeit possibly with considerable computational effort. In other terms, the proposed bound represents the highest performance limit attainable by physically realizable phase estimators over the above mentioned channel.