## Abstract

In this paper, derivatives of mutual information for a general linear Gaussian vector channel are considered. We consider two applications. First, it is shown how the corresponding gradient relates to the minimum mean squared error (MMSE) estimator and its error matrix. Secondly, we determine the directional derivative of mutual information and use this geometrically intuitive concept to characterize the capacity-achieving input distribution of the above channel subject to certain power constraints. The well-known water-filling solution is revisited and obtained as a special case. Also for shaping constraints on the maximum and the Euclidean norm of mean powers explicit solutions are derived. Moreover, uncorrelated sum power constraints are considered. The optimum input can here always be achieved by linear precoding.

Original language | English |
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Title of host publication | Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007 |

Place of Publication | Piscataway, NJ |

Publisher | Institute of Electrical and Electronics Engineers (IEEE) |

Pages | 2296-2300 |

Number of pages | 5 |

ISBN (Print) | 1424414296, 9781424414291 |

DOIs | |

Publication status | Published - 2007 |

Externally published | Yes |

Event | 2007 IEEE International Symposium on Information Theory, ISIT 2007 - Nice, France Duration: 24 Jun 2007 → 29 Jun 2007 |

### Other

Other | 2007 IEEE International Symposium on Information Theory, ISIT 2007 |
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Country/Territory | France |

City | Nice |

Period | 24/06/07 → 29/06/07 |