In orthogonal frequency division multiplexing (OFDM) based cellular systems, co-channel interference (CCI) from adjacent interfering base stations (BSs) would greatly degrade the bit error rate (BER) performance of cell-border users. In the previous work, a blind single antenna interference cancellation (SAIC) algorithm named least mean square-blind joint maximum likelihood sequence estimation (LMS-BJMLSE) has been proposed. The proposed LMS-BJMLSE algorithm is blind with respect to interfering signals and neither the training sequence (TS) nor pilot signal from interferers is needed. However, the conventional LMS-BJMLSE requires a long training sequence (TS) for channel estimation. In this paper, we propose a TS reduction scheme in which the subcarriers are divided into small groups based on the coherence bandwidth, and the slowest converging subcarrier in each group is identified by exploiting the correlation between the mean-square error (MSE) produced by LMS and the mean-square deviation (MSD) of the desired signal. The identified subcarrier's channel estimate is replaced by the interpolation result using the adjacent subcarriers' channel estimates. Simulation results demonstrate that the proposed algorithm could reduce the required TS length by 80%.