Efficient approximations in DS/SSMA communication systems with general linear modulation and error control coding

Abstract

In this paper, we use the central limit theorem for martingale difference arrays (m.d.a.) to provide, to our best knowledge, the first rigorous proof that under very 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 N per symbol interval and the number of interferers K tend to infinity with K/N approaching a fixed ratio. The result covers most systems with general linear modulation and error control coding. It allows us to find the limiting exact error probabilities and to prove that the standard Gaussian approximation (SGA) gives asymptotically exact results. Thus, the use of the SGA is justified when both N and K are large. The availability of the limiting exact error probabilities also provides important insights into the design of DS/SSMA systems.