In this paper we propose soft decision feedback equalization for OFDM transmission over doubly selective channels which is used for turbo equalization. The doubly selective channel is approximated using the basis expansion model (BEM). The decision feedback equalizer is obtained and updated for every sub-carrier that results in a per-tone decision feedback equalizer (DFE). Using the Gaussian approximation, expressions for the a posteriori log likelihood ratio (LLR) and the extrinsic LLR are derived for QPSK modulation. The channel BEM coefficients are used to design the feed forward and feedback filters, which are used to equalize the underlying channel simulated according to the BEM as well as according to Jakes' channel models. Numerical results for the bit error rate performance assuming the BEM and Jakes' channel models are shown to confirm our findings.