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This contribution deals with the performance of joint space-time multi-user turbo carrier phase and propagation delay estimation in a bit interleaved coded modulation scheme for asynchronous direct-sequence code division multiple access (DS-CDMA) transmission over frequency selective, slowly fading channels. As it has great impact on the overall BER performance, accurate estimation of the channel parameters is critical. We present an iterative space-time multi-user (STMU) turbo detection and estimation scheme. We show through computer simulation that the proposed low complexity STMU synchronizer considerably outperforms conventional synchronization schemes and achieves excellent performance, both in terms of BER and estimation error variance.