Bounds for optimum multiuser DS-CDMA systems

In this paper, we evaluate the performance of optimum multiuser detection by union bounding techniques for a large number of users. It is a difficult task to analytically compute the average bit error probability of multiuser DS-CDMA systems. In this paper we aim to use bounds to accurately evaluate the optimal performance of a multiuser DS-CDMA system, both synchronous and asynchronous. We present a general algorithm to compute the partial distance spectrum of the multiuser system. Numerical results for both systems with binary random signature waveforms of length 31 are used to illustrate the method. It has been found that the optimal bounds for the asynchronous system have a lower bit error probability (BEP) than synchronous systems. Focus is given to two areas namely 1) computing bit error probability (BEP) given a particular correlation matrix, 2) applying optimal conditional importance sampling and computing bit error probability for randomly generated correlation matrices