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A batch Kalman-based blind adaptive multiuser detection (K-BA-MUD) with multiple receiver (Rx) antennas is investigated for asynchronous CDMA systems in the uplink direction. In this paper, we consider two receiver structures: the independent and the cooperative structure. Previous results had stated that the cooperative structure always outperforms the independent one. However, with a limited number of samples available for signal detection, we need to justify how cooperative the processing should be to maintain that statement. Toward this end we propose the partially cooperative structure that relaxes the identifiability condition (IC) of a single Rx antenna K-BA-MUD. It is concluded that the proposed structure outperforms the fully cooperative one in any condition, given the number of samples is small and the IC is not violated. Finally, by reducing the size of the steering vector, we also reduce its computational complexity for updating the detector parameters.