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) |
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Pages (from-to) | 2123-2138 |
Number of pages | 16 |
Journal | IEEE Transactions on Information Theory |
Volume | 54 |
Issue number | 5 |
DOIs | |
State | Published - May 2008 |
Funding
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.
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