This paper addresses joint channel and data estimation for transmission over frequency-selective and timevarying channels based on a Doppler-variant channel impulse response (CIR). A discrete spreading function (DSF), which corresponds to the Doppler Fourier series of the time-varying channel taps, is introduced. The spectral leakage associated with the Fourier series representation is reduced by oversampling in Dopplerdirection. This approach, however, requires joint channel estimation and equalisation (JCE). Therefore, a recursive least squares (RLS) algorithm for the DSF estimation is combined with the data detection in a reduced state diagram. Furthermore, an enhanced metric, previously introduced in De Broeck et al. published by Kluwer Academic Publishers: Dordrecht, 2000) for time-invariant channels, is applied here for path selection. The performance of this metric is investigated here for time-varying and frequency-selective (TV-FS) channels. The performance of the proposed approach is compared with the JCE algorithm which uses RLS estimation of a CIR by simulations.