The Bayesian inference of phase

Bayesian recursive inference of phase in additive Gaussian noise environments is studied. A tractable conjugate system is established using a von Mises distribution. Its shaping parameter, re, is studied, to reveal the link with classical phase estimation via matched transforms. Uncertainty quantifiers involve a modified Bessel function kernel. The optimal predictor of data is derived in the presence of phase uncertainty. The theory is applied in phase synchronization for a digital receiver, where phase is distributed as a mixture of von Mises. A fully Bayesian treatment of the decoding problem for phase-uncertain carriers results. Simulation results provide evidence for the improvement in accuracy over a certainty-equivalent-based prediction.