  Since Tse and Verdu proved that the global maximum likelihood (GML) detector
achieves unit asymptotic multiuser efficiency (AME) in the limit of large
random spreading (LRS) CDMA, no suboptimal detector has been found to achieve
unit AME. In this letter, we obtain that the WSLAS detector with a linear
per-bit complexity achieves unit AME in the LRS-CDMA with a channel load < 1/2
- 1/(4ln2) bits/s/Hz. For a practical system with any user number, a quasi
LRS-CDMA is then proposed to approach the single-user performance in the high
SNR regime.
