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This paper considers multiuser MIMO CDMA systems with high rate space-time linear dispersion codes (LDC) and orthogonal space-time block codes (O-STBC) in time-varying Rayleigh fading MIMO channels. We propose a multi-function process integrating multi-user detection, space-time decoding and symbol demodulation, which can be coupled with soft channel decoding to improve the system performance in an iterative fashion. We show that the space-time coded CDMA systems approach the single-user bound with only two iterations, and full diversity LDCs enable the systems to utilize the time diversity inherent in fast fading channels. The space-time coded CDMA systems are also compared to the MIMO CDMA system based on spatial multiplexing, some recommendations are made on how to design a practical MIMO CDMA system based on the comparative studies.