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This paper addresses the problem of data detection in orthogonal frequency division multiplexing (OFDM) systems operating under a time-varying multipath fading channel. Optimal detection in such a scenario is infeasible, which makes the introduction of approximations necessary. The typical joint data-channel estimators are decision directed, that is, assume perfect past data decisions. However, their performance is subject to error propagation phenomena. The variational Bayes method is employed here, which approximates the joint data and channel distribution as a separable one, greatly simplifying the problem. The data detection part of the resulting algorithm provides soft data estimates that are used for channel tracking. The channel itself is modeled as an autoregressive process allowing for a Kalman-like tracking algorithm. According to the developed algorithm, both data and channel estimates are exchanged and updated in an iterative manner. The performance of the proposed algorithm is evaluated by simulations. Furthermore, since OFDM is extremely sensitive to the presence of phase noise, the algorithm is extended to operate under severe phase noise conditions, with moderate performance degradation.