On Multiuser Detection for Low-Rank CDMA Systems

We revisit suboptimum linear and group detection for CDMA systems and focus on “over-loaded” or low-rank CDMA systems wherein the total number of signals can be larger than the dimension of the signal space. Such systems are of particular interest when bandwidth is at a premium. Specifically, we consider cases where the desired and/or the interfering signal spaces can be of reduced rank and/or have a non-trivial intersection. Because it generalizes linear detection, we consider group detection and analyze its behavior and asymptotic performance. In particular, we introduce the Group Pseudo-Inverse Detector and the Group MMSE Detector and show the asymptotic (low-noise) equivalence of the two. We also consider a signal design problem wherein an additional user must be introduced into a system which is already either “fully loaded” or “over-loaded” to achieve optimum performance of that user without increasing the system bandwidth.