Asymptotic normality of linear CDMA multiuser detect

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 a matched filter, MMSE receiver, 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.