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

Matthew J.M. Peacock; Iain B. Collings; Michael L. Honig

doi:10.1109/TIT.2008.920221

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

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

18 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 language	English (US)
Pages (from-to)	2123-2138
Number of pages	16
Journal	IEEE Transactions on Information Theory
Volume	54
Issue number	5
DOIs	https://doi.org/10.1109/TIT.2008.920221
State	Published - 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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10.1109/TIT.2008.920221

Cite this

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title = "Eigenvalue distributions of sums and products of large random matrices via incremental matrix expansions",

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.",

keywords = "Code-division multiple access (CDMA), Free probability, Large system, Minimum mean square error (MMSE)",

author = "Peacock, {Matthew J.M.} and Collings, {Iain B.} and Honig, {Michael L.}",

note = "Funding Information: Manuscript received November 11, 2005; revised September 15, 2007. This work was supported in part by the U.S. Army Research Office under DAAD19-99-1-0288, the National Science Foundation under Grant CCR-0310809, and CSIRO ICT Centre, Australia.",

year = "2008",

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doi = "10.1109/TIT.2008.920221",

language = "English (US)",

volume = "54",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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T1 - Eigenvalue distributions of sums and products of large random matrices via incremental matrix expansions

AU - Peacock, Matthew J.M.

AU - Collings, Iain B.

AU - Honig, Michael L.

N1 - Funding Information: Manuscript received November 11, 2005; revised September 15, 2007. This work was supported in part by the U.S. Army Research Office under DAAD19-99-1-0288, the National Science Foundation under Grant CCR-0310809, and CSIRO ICT Centre, Australia.

PY - 2008/5

Y1 - 2008/5

N2 - 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.

AB - 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.

KW - Code-division multiple access (CDMA)

KW - Free probability

KW - Large system

KW - Minimum mean square error (MMSE)

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

Abstract

Keywords

ASJC Scopus subject areas

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