Analysis of multistage linear successive interference cancellation in long-code CDMA systems using graphical representation

The bit error probability of the multistage linear successive interference canceller (LSIC) in a long-code code division multiple access (CDMA) system is analyzed with a graphic approach in this research. The receiver decision statistic is modelled as a Gaussian random variable, whose conditional mean and variance are related to the moments of functions of matrix L, where L is the strict lower triangular part of the correlation matrix of the signature sequences. The complexity of calculating these moments increases rapidly with the growth of the stage index. A graphical representation of moments is developed here to facilitate their computation. For the multistage linear parallel interference canceller (LPIC), we showed previously that its moment calculation can be decomposed into several well known problems in graph theory. Besides graphic tools developed by Hwang, Kim and Jay Kuo (see Proc. IEEE Int. Conf. Commun., 2002) we introduce a new tool, i.e. the chromatic polynomial of a directed graph, to carry out the current task. It is shown that analytic results match well with simulation results in the bit error probability of the LSIC.