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Channel estimation for single-input–multiple-output systems over doubly selective channel using superimposed training and discrete prolate spheroidal basis expansion model is considered. To remove the interference from unknown data, a two-step interference cancellation scheme is proposed, where in the first step, a first-order statistics-based estimator with cyclic mean removal before transmission is proposed. In this step, only interference components corresponding to cyclic mean of data sequence are removed, which avoids the conflict between total interference elimination and symbol recovery. In the second step, a low complexity iterative interference cancellation scheme is proposed to further improve estimation performance with detected symbols at the receiver's end. Simulation results show that the proposed iterative scheme has the symbol error rate (SER) performance slightly inferior to that of the partially-data-dependent approach but with less computational complexity and outperforms the data-dependent scheme in terms of SER as well as mean-square error over doubly selective channels.