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In this paper, we present a powerful technique for the blind extraction of direct-sequence code-division multiple access (DS-CDMA) signals from convolutive mixtures received by an antenna array. The technique is based on a generalization of the canonical or parallel factor decomposition (CANDECOMP/PARAFAC) in multilinear algebra. We present a bound on the number of users under which blind separation and deconvolution is guaranteed. The solution is computed by means of an alternating least squares (ALS) algorithm. The excellent performance is illustrated by means of a number of simulations. We include an explicit expression of the Cramer-Rao bound (CRB) of the transmitted symbols.