Eigenvalue distributions of sums and products of large random matrices via incremental matrix expansions

Matthew J.M. Peacock*, Iain B. Collings, Michael L. Honig

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using R- and S-transforms in free probability theory. We also give a direct derivation of the a.e.d. of the sum of certain random matrices which are not free. This is used to determine the asymptotic signal-to-interference-ratio of a multiuser code-division multiple-access (CDMA) system with a minimum mean-square error linear receiver.

Original languageEnglish (US)
Pages (from-to)2123-2138
Number of pages16
JournalIEEE Transactions on Information Theory
Volume54
Issue number5
DOIs
StatePublished - May 2008

Keywords

  • Code-division multiple access (CDMA)
  • Free probability
  • Large system
  • Minimum mean square error (MMSE)

ASJC Scopus subject areas

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

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