Tight MMSE Bounds for the AGN Channel under KL Divergence Constraints on the Input Distribution

Michael Faub, Abdelhak M. Zoubir, Alex Dytso, H. Vincent Poor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

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 languageEnglish (US)
Title of host publication2018 IEEE Statistical Signal Processing Workshop, SSP 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages308-312
Number of pages5
ISBN (Print)9781538615706
DOIs
StatePublished - Aug 29 2018
Event20th IEEE Statistical Signal Processing Workshop, SSP 2018 - Freiburg im Breisgau, Germany
Duration: Jun 10 2018Jun 13 2018

Publication series

Name2018 IEEE Statistical Signal Processing Workshop, SSP 2018

Other

Other20th IEEE Statistical Signal Processing Workshop, SSP 2018
CountryGermany
CityFreiburg im Breisgau
Period6/10/186/13/18

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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