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The problem of blind multiuser detection for a direct sequence code division multiple access (DS/CDMA) system employing multiple transmit and receive antennae over a fading dispersive channel is considered. Relying upon a well-known signal representation, the strategy of two-stage multiuser detection is extended to the multiantenna case. Several design criteria are considered for both interference suppression and integration of the signals available at each antenna. In all cases, substantial immunity to multiple access interference (MAI) and intersymbol interference (ISI) is achieved, with no prior information as to the channel state and as to the number and the signatures of the interfering users. Interestingly, the newly proposed strategy, while being practically equivalent to existing competitors for low users' number, proves much more effective as the network load increases. Additionally, a closed-form formula for the bit-error-rate and a lower bound to the near-far resistance are derived for uncoded systems and subsequently extended to space-time coded systems, showing that these analytical results apply not only to the system under consideration but also to any linear receiver performing differential detection.