Asymptotic normality of linear multiuser receiver outputs

Dongning Guo, Sergio Verdú, Lars K. Rasmussen

Research output: Contribution to journalArticlepeer-review

90 Scopus citations


This paper proves large-system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers. This family of receivers encompasses the single-user matched filter, the decorrelator, the minimum mean square error (MMSE) receiver, the parallel interference cancelers, and many other linear receivers of interest. Both with and without the assumption of perfect power control, we show that the output decision statistic for each user converges to a Gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed. Analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution, which is also the unconditional distribution. This normality principle allows the system performance, e.g., the multiuser efficiency, to be completely determined by the output signal-to-interference ratio (SIR) for large linear systems.

Original languageEnglish (US)
Pages (from-to)3080-3095
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 2002

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Central limit theorem
  • Code-division multiple access (CDMA)
  • Multiple-access interference
  • Multiuser detection
  • Multiuser efficiency
  • Signal-to-interference ratio (SIR)


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