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We consider the asynchronous multiple-input multiple-output (MIMO) uplink CDMA systems employing BLAST space-time turbo codes (STTuC) over frequency-selective fading channel. In this case, the mixture of multiple access interference (MAI), inter-antenna interference (IAI) and intersymbol interference (ISI) needs to be suppressed at the base station (BS). Here we develop an iterative receiver structure that can combat the different species of interferences at the same time. The proposed receiver is designed following the turbo principle and based on the parallel interference cancellation (PIC) with linear minimum mean-squared error (MMSE) detector serving as its first stage. In every iteration, the soft output of the space-time turbo decoder is fed back to improve the PICs performance. The simulation results suggest that the proposed iterative receiver can suppress the interferences for STTuC CDMA systems effectively. A performance comparison between urban, rural and flat fading channel is also given and the reason of the performance differences is discussed based on the analysis of the interference structure.