Multiuser detection is central to the fulfillment of the capabilities of code-division multiple access (CDMA), which is becoming the ubiquitous air-interface in future generation communication systems. In DS-CDMA communications, all user signals overlap in time and frequency and cause mutual interference. The conventional DS-CDMA detector follows a single-detection strategy in which each user is detected separately without regard for the other users. A better strategy is multi-user detection, where information about multiple users is to improve detection of each individual user. Multi-user detection (MUD) is the intelligent estimation/demodulation of transmitted bits in presence of multiple access interference (MAI). Unlike additive white Gaussian noise (AWGN), MAI has a nice correlative structure that is quantified by the correlation matrix of the signature sequences. This paper describes and analyses linear multi-user DS-CDMA detectors. The most popular detectors include the decorrelating detector and MMSE detector.