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Multiuser detection for overloaded code-division multiple-access (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 nontrivial 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 minimum mean-squared error (MMSE) detector. 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 proposals of the so-called "improved" linear (also known as "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.