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This paper deals with channel estimation in the uplink of a direct-sequence code-division multiple-access system operating in a multipath environment. The parameters of interest are the delays and the complex attenuations incurred by the signal echoes along the propagation paths. We propose an iterative approach for estimating the channel parameters of a new user entering the system. The method is based on the space-alternating generalized expectation-maximization algorithm and exploits a training sequence. In comparison to other estimation algorithms, it reduces a complicated multidimensional optimization problem to a sequence of one-dimensional problems. In addition, it can be effectively used in applications over fast-fading channels. Computer simulations are employed to assess the performance of the proposed scheme. It is found that it is resistant to multiuser interference and has accuracy close to the Cramer-Rao lower bound even with very short training sequences.