Optimum asymptotic multiuser efficiency of randomly spread CDMA

This correspondence analyzes the high signal-to-noise ratio (SNR) performance of optimum multiuser detectors for synchronous direct-sequence spread spectrum with random spreading in an additive white Gaussian noise channel. Under very general conditions on the received powers, we show that the optimum 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 arbitrary nonzero constant. Therefore, the asymptotic behavior of the minimum bit error rate is equivalent to that of a single-user system.