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Time-varying channel and dc-offset estimation using superimposed training and first-order statistics are considered. A weighted first-order statistics-based estimator using complex exponential basis expansion model (CE-BEM) is proposed, which explicitly exploits the cyclostationary characteristic of periodic training sequence and extends to time-varying channel estimation. By subtracting the cyclic mean from each data block, only partial unknown data interference is removed to make a tradeoff between interference cancellation and symbol recovery. A theoretical performance analysis is presented. Simulation results show that the proposed scheme has low computational complexity and exhibits good performance in terms of the symbol error rate.