In this paper we present new deterministic tensor-based techniques for the blind separation of a mixture of DS-CDMA signals received by an antenna array. First, we show that the blind receiver follows from a simultaneous matrix decomposition. We present a new, relaxed, bound on the number of users that can be allowed at the same time. We further derive two algorithms that jointly exploit the CDMA structure and the constant modulus property of the transmitted signals. (c) 2006 Elsevier B.V. All rights reserved.