  We present a reduced-dimension multiuser detector (RD-MUD) structure for
synchronous systems that significantly decreases 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, in some wireless systems, the number of active
users may be small relative to the total number of users in the system. Hence,
the ideas of analog compressed sensing may be used to reduce the number of
correlators. The correlating signals used by each correlator are chosen as an
appropriate linear combination of the users' spreading waveforms. We derive the
probability-of-symbol-error when using two methods for recovery of active users
and their transmitted symbols: the reduced-dimension decorrelating (RDD)
detector, which combines subspace projection and thresholding to determine
active users and sign detection for data recovery, and the reduced-dimension
decision-feedback (RDDF) detector, which combines decision-feedback matching
pursuit for active user detection and sign detection for data recovery. We
derive probability of error bounds for both detectors, and show that the number
of correlators needed to achieve a small probability-of-symbol-error is on the
order of the logarithm of the number of users in the system. The theoretical
performance results are validated via numerical simulations.
