SystemsAsymptotic Normality of the Cross - Correlation of aCDMA System with Phase Drift

Code division multiple access (CDMA) has been proposed for use in ber and free space optical communications. Sophisticated new receivers for CDMA are based on coherent reception, that is, reception where the phases of all the many users are known or can be tracked. While coherent detection is a reasonable assumption in many radio frequency systems, semiconductor lasers suffer from serious phase variation that precludes fully coherent detection. Receiver performance in a coherent system is a function of the known, deterministic value of the cross-correlation between two signals. When phase drift is present this cross-correlation is instead random. In this paper we show that asymptotically (as the length of the spreading code grows without bound) the cross-correlation has a Gaussian distribution, when the codes are modeled as a random sequence of ff1g and the phase is modeled as a Brownian motion.