### Abstract

Several works addressed the problem of deriving the asymptotic capacity of a wireless system with space diversity in random fading. However, the theory of random matrices was never used in evaluating the asymptotic optimal performance in closed form. By increasing the number of transmit and receive antennas the resulting capacity tend to be a stable value independent of the fading realization. This surprising result is a consequence of Girko's law, stating that the asymptotic distribution of the eigenvalues of a random matrix, with independent identically distributed zero mean complex entries, is a circle. The conditions on the probability density function of the matrix entries are satisfied by the majority of random non-line of sight fading models. Using this theory in this paper we derive the close form expression for the asymptotic capacity of a system with transmit and receive diversity, assuming independent flat fading for each transmit-receive antenna link, with equal distribution. Our formula fits the numerical results even if the number of transmit an receive antennas as small as ten.

Original language | English (US) |
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Title of host publication | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |

Pages | 2509-2511 |

Number of pages | 3 |

Volume | 4 |

State | Published - 2001 |

Externally published | Yes |

Event | 2001 IEEE Interntional Conference on Acoustics, Speech, and Signal Processing - Salt Lake, UT, United States Duration: May 7 2001 → May 11 2001 |

### Other

Other | 2001 IEEE Interntional Conference on Acoustics, Speech, and Signal Processing |
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Country | United States |

City | Salt Lake, UT |

Period | 5/7/01 → 5/11/01 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Signal Processing
- Acoustics and Ultrasonics

### Cite this

*ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings*(Vol. 4, pp. 2509-2511)

**Asymptotic capacity of space-time coding for arbitrary fading : A closed form expression using Girko's law.** / Scaglione, Anna; Sakoglu, U.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings.*vol. 4, pp. 2509-2511, 2001 IEEE Interntional Conference on Acoustics, Speech, and Signal Processing, Salt Lake, UT, United States, 5/7/01.

}

TY - GEN

T1 - Asymptotic capacity of space-time coding for arbitrary fading

T2 - A closed form expression using Girko's law

AU - Scaglione, Anna

AU - Sakoglu, U.

PY - 2001

Y1 - 2001

N2 - Several works addressed the problem of deriving the asymptotic capacity of a wireless system with space diversity in random fading. However, the theory of random matrices was never used in evaluating the asymptotic optimal performance in closed form. By increasing the number of transmit and receive antennas the resulting capacity tend to be a stable value independent of the fading realization. This surprising result is a consequence of Girko's law, stating that the asymptotic distribution of the eigenvalues of a random matrix, with independent identically distributed zero mean complex entries, is a circle. The conditions on the probability density function of the matrix entries are satisfied by the majority of random non-line of sight fading models. Using this theory in this paper we derive the close form expression for the asymptotic capacity of a system with transmit and receive diversity, assuming independent flat fading for each transmit-receive antenna link, with equal distribution. Our formula fits the numerical results even if the number of transmit an receive antennas as small as ten.

AB - Several works addressed the problem of deriving the asymptotic capacity of a wireless system with space diversity in random fading. However, the theory of random matrices was never used in evaluating the asymptotic optimal performance in closed form. By increasing the number of transmit and receive antennas the resulting capacity tend to be a stable value independent of the fading realization. This surprising result is a consequence of Girko's law, stating that the asymptotic distribution of the eigenvalues of a random matrix, with independent identically distributed zero mean complex entries, is a circle. The conditions on the probability density function of the matrix entries are satisfied by the majority of random non-line of sight fading models. Using this theory in this paper we derive the close form expression for the asymptotic capacity of a system with transmit and receive diversity, assuming independent flat fading for each transmit-receive antenna link, with equal distribution. Our formula fits the numerical results even if the number of transmit an receive antennas as small as ten.

UR - http://www.scopus.com/inward/record.url?scp=0034857795&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034857795&partnerID=8YFLogxK

M3 - Conference contribution

VL - 4

SP - 2509

EP - 2511

BT - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

ER -