Precise estimation of synchronization parameters is essential for reliable
data detection in digital communications and phase errors can
result in significant performance degradation. The literature on estimation
of synchronization parameters, including the carrier frequency
offset, are based on approximations or heuristics because
the optimal estimation problem is analytically intractable for most
cases of interest. We develop an online Bayesian inference procedure
for blind estimation of the frequency offset, for arbitrary signal
constellations. Our unified approach is built on a sequential inference
procedure that leverages a novel result on conjugacy of the von
Mises and Gaussian distributions. This conjugacy allows for an easily
computable, closed form parametric expression for the posterior
distribution of the parameters given the streaming data, in which hyperparameters
are recursively updated, making the optimal sequential
estimation problem mathematically tractable. Our algorithm is
computationally efficient and can be implemented in real-time with
very low memory requirements. Numerical experiments are also
provided and show that our methods outperform approximate sequential
maximum-likelihood carrier frequency offset estimators.