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We propose a time domain maximum likelihood channel estimator for the uplink of multicarrier DS-CDMA communication systems in the presence of slowly varying frequency-selective fading. The expectation maximization algorithm is developed for estimating the carrier phases, amplitudes and propagation delays of the uplink channel based on the training sequence which is transmitted with the subcarriers used for data transmission. The performance of the resulting estimator is evaluated via simulation. The results indicate that the estimator is well suited for coherent data detection at the receiver associated with maximal ratio combining.