This correspondence analyzes the high signal-to-noise ratio (SNR) performan
ce of optimum multiuser detectors for synchronous direct-sequence spread sp
ectrum with random spreading in an additive white Gaussian noise channel. U
nder very general conditions on the received powers, we show that the optim
um asymptotic efficiency of a K-user system with spreading gain N converges
to 1 almost surely as K --> infinity, and K/N is kept equal to an arbitrar
y nonzero constant. Therefore, the asymptotic behavior of the minimum bit e
rror rate is equivalent to that of a single-user system.