### Abstract

Tight bounds on the minimum mean square error for the additive Gaussian noise channel are derived, when the input distribution is constrained to be ϵ-close to a Gaussian reference distribution in terms of the Kullback-Leibler divergence. The distributions that attain the bounds are shown be Gaussian whose means are identical to that of the reference distribution and whose covariance matrices are defined implicitly via systems of matrix equations. The estimator that attains the upper bound is identified as a minimax optimal estimator that is robust against deviations from the assumed prior. The lower bound is shown to provide a potentially tighter alternative to the Cramér-Rao bound. Both properties are illustrated with numerical examples.

Original language | English (US) |
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Title of host publication | 2018 IEEE Statistical Signal Processing Workshop, SSP 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 308-312 |

Number of pages | 5 |

ISBN (Print) | 9781538615706 |

DOIs | |

State | Published - Aug 29 2018 |

Event | 20th IEEE Statistical Signal Processing Workshop, SSP 2018 - Freiburg im Breisgau, Germany Duration: Jun 10 2018 → Jun 13 2018 |

### Publication series

Name | 2018 IEEE Statistical Signal Processing Workshop, SSP 2018 |
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### Other

Other | 20th IEEE Statistical Signal Processing Workshop, SSP 2018 |
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Country | Germany |

City | Freiburg im Breisgau |

Period | 6/10/18 → 6/13/18 |

### All Science Journal Classification (ASJC) codes

- Signal Processing
- Instrumentation
- Computer Networks and Communications

### Keywords

- Cramér-Rao bound
- MMSE bounds
- minimax optimization
- robust estimation

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## Cite this

*2018 IEEE Statistical Signal Processing Workshop, SSP 2018*(pp. 308-312). [8450756] (2018 IEEE Statistical Signal Processing Workshop, SSP 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SSP.2018.8450756