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

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

2005-11-15

arxiv.org/abs/cs/0511054v1

Computer Science

Information Theory

Submitted to Trans IT

Scientific paper

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 CDMA system with a minimum mean-square error linear receiver.

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