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In this paper, a space-time soft receiver is developed for convolutionally coded DS-CDMA systems with time-selective fading in both Gaussian and nonGaussian channels. The whole interference, including intersymbol interference (ISI), multiple access interference (MAI), and narrowband interference (NBI), is considered. Low-complexity continuously iterative nonlinear space-time soft interference cancellation and decoding techniques are proposed. The estimation of the parameters of the probability density function (PDF) of the whole interference and noise per propagation path per antenna element is directly computed by using the outputs of a chip-matched filter. The optimal combining weight is used to combine all the soft receiving signals to make the final statistic decision. Simulation results demonstrate that the proposed receiver structure offers significant performance gain over some existing approaches in both Gaussian and nonGaussian time-selective fading channels.