Analysis of multistage linear parallel interference cancellation in CDMA systems using graphical representation

The bit error probability of the multistage linear parallel interference canceller in a long-code code division multiple access (CDMA) system is analyzed with a graphic approach in this research. The decision statistic is modelled as a Gaussian random variable, whose mean and variance can be expressed as functions of moments of (R - I), where R is the correlation matrix of signature sequences. Since the complexity of calculating these moments increases rapidly with the growth of the stage index, a graphical representation of moments is developed to facilitate the computation. Propositions are presented to relate the moment calculation problem to several well known problems in graph theory, i.e., the coloring, the graph decomposition, the biconnected component, and the Euler tour problems. It is shown that the analytic results of the bit error probability match well with simulation results.