Multiuser detection (MUD) and turbo coding are two of the most powerful techniques for enhancing the direct spread code-division multiple-access systems (DS/CDMA). Since the optimal MUD of DS/CDMA uplink has prohibited complexities, efficient detectors are desirable. We investigate MUD for three types of DS/CDMA channels, from the simple to the complex. First, we provide a geometric view for MUD and a way for computing the optimal decision regions for synchronous uncoded DS/CDMA over known fading channels. It is shown that Verdus algebraic notion of "indecomposable error sequences"...