In this paper, we consider the problem of equalizing a time-varying channel in the presence of Doppler rate. Blind estimation of a time-varying channel in the presence of Doppler frequency alone based on a Complex-Exponential, Basis Expansion Model (CE-BEM) has been studied by several researchers in the field. Recently, we proposed a fractionally spaced channel model that does not require basis expansion and possesses a structure that models Doppler rate. We presented a data-aided, LS method for channel estimation. In this work we analyze the performance of the channel estimator using exact and perturbed Doppler estimates. We present a symbol-by-symbol based, decision-feedback equalizer for the time-varying channel and assess its performance in terms of BER.