  We explore several reduced-dimension multiuser detection (RD-MUD) structures
that significantly decrease the number of required correlation branches at the
receiver front-end, while still achieving performance similar to that of the
conventional matched-filter (MF) bank. RD-MUD exploits the fact that the number
of active users is typically small relative to the total number of users in the
system and relies on ideas of analog compressed sensing to reduce the number of
correlators. We first develop a general framework for both linear and nonlinear
RD-MUD detectors. We then present theoretical performance analysis for two
specific detectors: the linear reduced-dimension decorrelating (RDD) detector,
which combines subspace projection and thresholding to determine active users
and sign detection for data recovery, and the nonlinear reduced-dimension
decision-feedback (RDDF) detector, which combines decision-feedback orthogonal
matching pursuit for active user detection and sign detection for data
recovery. The theoretical performance results for both detectors are validated
via numerical simulations.
