# Multiuser detection

Multiuser detection (MUD) (also known as joint detection) is one of the receiver design technology for detecting desired signal(s) from interference and noise. Multiuser detectors jointly detect the desired signal and some or all interference, so that the detected interference can be mitigated or cancelled out.

The optimal multi-user receiver for CDMA was discovered and advanced by Verdu in the mid 1980s, having been foreshadowed by Van Etten’s multi-user sequence estimator in the mid-1970s and Cover’s work on broadcast channels. Although Verdu’s maximum likelihood receiver was able to optimally decode multiple users in parallel with dramatic gains, it is extremely complex, with the computational needs increasing as $O(|A|^K)$,where $|A|$ is the alphabet size (2 for binary) and $K$ is the number of users.

The complexity of MUD can be decreased at the expense of optimality. Many suboptimal MUDs have been developed with various trade-offs with respect to performance, complexity,and requirements regarding channel knowledge. Suboptimal MUDs fall into two broad categories:linear and nonlinear. Linear MUDs apply a linear operator or filter to the output of the matched filter bank. These detectors have complexity that is linear in the number of users, a significant complexity improvement over the optimal detector. The most common linear MUDs are the decorrelating detector and the minimum mean-square error (MMSE) detector. Nonlinear MUDs can have much better performance than linear detectors – although not necessarily in all cases, especially with little or no coding. The most common nonlinear MUD techniques are multistage detection, decision-feedback detection, and successive interference cancellation.

The MUD methods can be applied to intercell interference signals – both at the base station, where processing complexity is less of a constraint, and at the mobile users near cell edges to decode messages transmitted by the base station in neighbor cells for achieving a higher signal-to-noise ratio. Implementation of MUD exhibits good perspective in future wireless networks where hierarchical cellular structures such as femotcells heavily overlap with macrocell deployment.