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The performance of direct-sequence code division multiple access (DS-CDMA) using space-time spreading system, over frequency-selective fading channels, is investigated. The underlying transmit diversity scheme, previously introduced in the literature, is based on two transmit and one receive antenna. It was shown that when employed in flat fast-fading channels, the received signal quality can be improved by utilising the spatial and temporal diversities at the receiver side. We study the problem of multiuser interference in asynchronous CDMA systems that employ transmit/receive diversity using space-time spreading. To overcome the effects of interference, a decorrelator detector is used at the base station. Considering binary phase-shift keying transmission, we analyse the system performance in terms of its probability of bit error. In particular, we derive the probability of error over frequency-selective Rayleigh fading channels for both fast and slow-fading channels. For the fast-fading channel, both simulations and analytical results show that the full system diversity is achieved. On the other hand, when considering a slow-fading channel, we show that the scheme reduces to conventional space-time spreading schemes where the diversity order is half of that of fast-fading.