The primary purpose of this work is to provide a perspective on adapti
ve code-division multiple-access (CDMA) MU receivers that have been pr
oposed for future digital wireless systems. Adaptive receivers can pot
entially adapt to unknown and time-varying environmental parameters su
ch as the number of users, their received powers, spreading codes and
time-delays. Two adaptive receiver architectures are primarily conside
red - one in which the sampled received signal is filtered, and can be
used in both the uplink (i.e., at the base station) and downlink (i.e
., at the mobile handset), and another in which the spreading codes of
users are filtered (assuming knowledge of users' codes and its timing
at the receiver) for use in the uplink. Relevant issues such as train
ing-based and blind implementations of the adaptive receiver are discu
ssed, as well as (transient) convergence rates and estimation noise in
steady-state.