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In this paper, a new interference cancellation scheme is presented for the direct-sequence code-division multiple access (DS/CDMA) downlink. The proposed technique is blind in the sense that only the desired user's spreading code is assumed to be known a priori. The remaining parameters required for the interference cancellation such as spreading codes and energies of interfering users are estimated using subspace decomposition and the constant-modulus (CM) property of the transmitted symbols. Therefore, unlike standard interference cancellers which can be used only in the uplink, the proposed method can be implemented at the mobile terminal. Identifiability results are presented as well as numerical studies demonstrating the efficiency of the proposed algorithm.