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This paper addresses soft estimation of time-varying frequency selective channels using Kalman smoothing. The proposed estimator uses soft extrinsic information provided by a channel decoder. It is intended to improve the performance of an already existing Kalman filtering-based estimator by exploiting all - rather than part of - the data at the receiver disposal. It is the linear estimator exhibiting for the case of interest the minimum mean-squared estimation error. Its complexity is shown to be quite low. An approximated analytical calculation of the mean- squared estimation error (MSEE), both for Kalman filtering and Kalman smoothing, is also proposed. Simulation results illustrate the performance gain of smoothing over filtering and validate our calculation of the MSEE.