Substantial progress has been made in the receiver signal-processing algori
thms for wireless commmunications to minimise the requirements on signal-to
-noise (and/or interference) power ratio and computational complexities for
the same quality of service. In cellular infrastructure systems, one of th
e key system design objectives is the base stations is to maximize the rece
iver sensitivity, so that the required signal level from the mobile station
s can be minimized. The use of advanced signal-processing algorithms, based
on maximum a posteriori (MAP) estimation, iterative (turbo) channel estima
tion, equalization, and decoding, allows for a reduction of the required tr
ansmitter power by one-third to one-half. Lower computational complexities
in the terminals, which implies a reduced power drain on the digital circui
ts, can be achieved by using techniques that adapt the state complexity of
the receiver to the propagation channel. We give an in-depth review of thes
e algorithms, and discuss their performance and implementation requirements
.