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In an effort to increase capacity and performance, many researchers have investigated space-time signal processing techniques for cellular systems. Generally speaking, these techniques involve the use of multiple transmit or receive antennas in conjunction with some form of coding to exploit spatial diversity. Very little work, however, has been attempted on practical (simple, blind, adaptive) receivers employing multiuser detection and multiple antennas at both the transmitter and receiver. In this paper, we develop a blind adaptive implementation of a space-time receiver for CDMA in fading multipath channels. Specifically, we consider a system with two transmit and two receive antennas, though the work can be easily be extended to other configurations. We employ the Alamouti space-time block code at the transmitter since it has previously been adopted for a number of 3G WCDMA standards. We investigate the performance of this receiver via simulation.