An asymptotic analysis of DS/SSMA communication systems with general linear modulation and error control coding

We investigate direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems with general linear modulation and error control coding. By the central limit theorem for martingale difference arrays, it is proved that under general conditions, the overall multiple-access interference (MAI) across different symbol intervals tends to a jointly complex Gaussian random vector as both the number of chips per symbol interval and the number of interferers tend to infinity. The result allows the calculation of the limiting exact error probabilities, and justifies the use of the popular standard Gaussian approximation. The asymptotic properties of the MAI from each individual interferer are also examined. The results lead to another approximation, the conditional Gaussian approximation, which provides better estimates to the error probabilities, especially in near-far situations.