Channel estimation schemes suitable for interleave-division multiple access (IDMA) systems are presented. Training and data are superimposed. Training-based and semiblind linear channel estimators are derived and their performance is discussed and compared. Monte Carlo simulation results are presented showing that the derived channel estimators in conjunction with a superimposed pilot sequence and chip-by-chip processing are able to track fast-fading frequency-selective channels. As opposed to conventional channel estimation techniques, the BER performance even improves with increasing Doppler spread for typical system parameters. An error performance close to the case of perfect channel knowledge can be achieved with high power efficiency.