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Channel estimation and data detection for frequency-selective time-varying channels are considered using superimposed training. We employ a discrete prolate spheroidal basis expansion model (DPS-BEM) to describe the time-varying channel. A periodic (nonrandom) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission; therefore, there is no loss in data transmission rate compared to time-multiplexed (TM) training. We first estimate the channel using DPS-BEM and only the first-order statistics of the observations. In this estimator the unknown information sequence acts as interference resulting in a poor signal-to-noise-and-interference ratio (SNIR) for channel estimation. We then apply a data-dependent superimposed training sequence, to either totally or partially cancel out the effects of the unknown information sequence at the receiver on channel estimation. In total cancellation, at certain frequencies, the information-bearing components are nulled. To compensate for this information loss, we investigate a partially-data-dependent (PDD) superimposed training scheme where a tradeoff is made between interference cancellation and frequency integrity. Design of certain parameters for PDD superimposed training is also investigated. Finally, a deterministic maximum likelihood (DML) approach is used iteratively to enhance channel estimation and data detection. Computer simulation examples show that the proposed approaches are competitive with the conventional TM training without incurring data-rate loss.