Asymptotic normality of linear CDMA multiuser detection outputs

This paper studies the asymptotic distribution of the output of a family of linear multiuser receivers. Every receiver in the family is a function of the channel correlation matrix of a simple form. It is proved that conditioned on almost all spreading codes, the output decision statistic of such a receiver converges to a Gaussian law in distribution as the system size goes to infinity. This set of receivers encompasses the matched filter, the MMSE receiver, the parallel interference cancelers, and many other linear receivers of interest. The normality principle solidifies the importance of the signal-to-interference ratio in the many-user analysis of linear multiuser detectors.