Eigenvalue Distributions of Sums and Products of Large Random Matrices Via Incremental Matrix Expansions

Author

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

Author_Institution

Univ. of Sydney, Sydney

Volume

54

Issue

5

fYear

2008

fDate

5/1/2008 12:00:00 AM

Firstpage

2123

Lastpage

2138

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 - and -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; eigenvalues and eigenfunctions; least mean squares methods; matrix algebra; probability; random processes; asymptotic eigenvalue distribution; asymptotic signal-to-interference-ratio; incremental matrix expansion approach; large random matrix; minimum mean-square error linear receiver; multiuser code-division multiple-access system; probability theory; Australia; Communication systems; Eigenvalues and eigenfunctions; Laboratories; MIMO; Mean square error methods; Multiaccess communication; Performance analysis; Physics; Random variables; ${rm R}$-transform; ${rm S}$-transform; Code-division multiple access (CDMA); free probability; large system; minimum mean square error (MMSE);

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2008.920221

Filename

4494697