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We consider the uplink of a multicarrier code-division multiple-access (MC-CDMA) network and assume that the base station is endowed with a uniform linear array. Transmission takes place over a multipath channel and the goal is the estimation of the directions of arrival (DOAs) of the signal from the active users. In a multiuser scenario, difficulties are primarily due to the large number of parameters involved in the estimation of the DOAs which makes this problem much more challenging than in single-user transmissions. The solution we propose allows estimating the DOAs of different users independently, thereby leading to a significant reduction in the system complexity. In the presence of multipath propagation, however, estimating the DOAs of a given user through maximum-likelihood methods remains a formidable task since it involves a search over a multidimensional domain. Therefore, we look for simpler solutions and discuss two alternative schemes based on the SAGE and ESPRIT algorithms.