A sequential Bayesian inference framework for blind frequency offset estimation

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.