## 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 |
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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 | |

Publication status | Published - May 2008 |

Externally published | Yes |

## Keywords

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