Abstract-Multiuser detection for overloaded CDMA systems, in which the number of users is larger than the dimension of the signal space, is of particular interest when bandwidth is at a premium. In this paper, certain fundamental questions are answered regarding the asymptotic forms and performance of suboptimum multiuser detectors for cases where the desired and/or interfering signal subspaces are of reduced rank and/or have a non-trivial intersection. In the process, two new suboptimum detectors are proposed that are especially well suited to overloaded systems, namely the group pseudo-decorrelator and the group MMSE detector, and the former is seen to be the correct extension of the group decorrelator in the sense that it is the limiting form (in the low-noise regime) of the group MMSE detector. Pseudo-decorrelation is also used as a feedforward filter in a new decision feedback scheme. For the particular case of real-valued modulation, it is shown that the recent proposals of the so-called "improved" linear (aka "linear-conjugate" or "widely linear") detectors were more simply derived earlier using the idea of minimal sufficiency which we also apply to the new detectors of this paper.