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We consider the problem of multiuser detection for randomly spread direct-sequence (DS) code-division multiple access (CDMA) over flat fading channels. The analysis focuses on the case of many users, and large spreading sequences such that their ratio, which is the system load, is kept fixed. Spectral efficiency of practical linear detectors such as match-filter and decorrelator employing successive interference cancellation (SIC) at the receiver is derived. This is used to extend the notion of strongest users detectors for SIC receivers. The strongest users detectors system design relies on an outage approach where each user transmits in a single layer (fixed rate), and only users experiencing good channel conditions may be reliably decoded, while the other users are in outage, i.e., not decoded. In this scheme, iterative SIC decoding is studied, and it is shown that for equal power users, the optimal rate allocation, for maximizing the expected spectral efficiency, is equal rates for all users. This outage approach analysis is extended for multilayer coding broadcast approach per user. The expected sum-rate, under iterative decoding with linear multiuser detectors, is optimized, and the optimal layering power distribution is obtained. For small system loads, the achievable spectral efficiency with the continuous broadcast approach and a linear matched filter detector exhibits significant gains over the single layer coding approach.