### Abstract

We consider ergodic coherent MIMO channels. We characterize the optimal input distribution for various fading matrix distributions. First, we describe how symmetries in the fading matrix distribution and the constraint set are preserved as symmetries in the optimal input covariance and thus yield to specification of the optimal input. We will see that group structures and notion of commutant appear as key elements. Second, we investigate the Kronecker model, in this case we will show how an asymmetric structure in the problem is also preserved in the optimal input structure, leading to a new water-filling situation.

Original language | English (US) |
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Title of host publication | 43rd Annual Allerton Conference on Communication, Control and Computing 2005 |

Publisher | University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering |

Pages | 317-326 |

Number of pages | 10 |

Volume | 1 |

ISBN (Electronic) | 9781604234916 |

State | Published - Jan 1 2005 |

Externally published | Yes |

Event | 43rd Annual Allerton Conference on Communication, Control and Computing 2005 - Monticello, United States Duration: Sep 28 2005 → Sep 30 2005 |

### Other

Other | 43rd Annual Allerton Conference on Communication, Control and Computing 2005 |
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Country | United States |

City | Monticello |

Period | 9/28/05 → 9/30/05 |

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Computer Science Applications

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## Cite this

*43rd Annual Allerton Conference on Communication, Control and Computing 2005*(Vol. 1, pp. 317-326). University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering.