### Abstract

In this paper, we analyze the bit error probability of the multistage linear parallel interference canceller in a long-code code division multiple access (CDMA) system. To obtain the bit error probability, we approximate the decision statistic as a Gaussian random variable, and compute its mean and variance. The mean and variance of the decision statistic can be expressed as functions of the moments of (R - I), where R is the correlation matrix of the signature sequences. Since the complexity of calculating the moments increases rapidly with the growth of the stage index, a graphical representation for the moments is developed to alleviate the complexity. Propositions are presented to interpret the calculation of moments as several graph problems that are well known in the literature, i.e., the coloring, graph decomposition and Euler tour problems. It is shown that the graphical representation facilitates the analytic evaluation of the bit error probability, and the analytic results match well with the simulation results.

Original language | English |
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Pages (from-to) | 69-80 |

Number of pages | 12 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 4529 |

DOIs | |

Publication status | Published - 2001 Jan 1 |

### Keywords

- Code division multiple access (CDMA)
- Linear parallel interference cancellation (LPIC)
- Multiuser detection

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

## Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*,

*4529*, 69-80. https://doi.org/10.1117/12.447385