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Space-time coding (STC) is an efficient technique to combat severe fading effects and improve system capacity in wireless communications. However, for CDMA communications, multi-antenna transmission increases the multiuser interference (MUI). In addition, if the data rate is high, the processing gain can be quite small, and thus the MUI is further enhanced. In this paper we propose a new non-iterative multiuser decoder for space-time coded asynchronous DS-CDMA. Non-iterative decoding schemes are important in situations where decoding delay must be minimized, for example in interactive applications such as videoconferencing. The proposed scheme introduces a novel reduced-state multiuser sequence detection algorithm suitable to decode few co-located users with high data rates (i.e. users within a beam with short spread sequences). We evaluate the performance of the proposed scheme in high and moderate multiuser interference channels. Simulation results show that a major performance improvement over a conventional receiver is achieved with the proposed scheme even in moderate interference channels. In high interference channels, where the conventional receiver is useless, the proposed scheme performs near the single user bound at practical frame error rates and with reasonable complexity.