Tight Bounds on the Weighted Sum of MMSEs with Applications in Distributed Estimation

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

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

Abstract

In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian reference distribution in terms of the Kullback-Leibler divergence. The distributions that attain these bounds are shown to be Gaussian whose covariance matrices are defined implicitly via systems of matrix equations. Furthermore, the estimators that attain the upper bound are shown to be minimax robust against deviations from the assumed input distribution. The lower bound provides a potentially tighter alternative to well-known inequalities such as the Cramér-Rao lower bound. Numerical examples are provided to verify the theoretical findings of the paper. The results derived in this paper can be used to obtain performance bounds, robustness guarantees, and engineering guidelines for the design of local estimators for distributed estimation problems which commonly arise in wireless communication systems and sensor networks.

Original languageEnglish (US)
Title of host publication2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781538665282
DOIs
StatePublished - Jul 2019
Event20th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019 - Cannes, France
Duration: Jul 2 2019Jul 5 2019

Publication series

NameIEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC
Volume2019-July

Conference

Conference20th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019
CountryFrance
CityCannes
Period7/2/197/5/19

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Information Systems

Keywords

  • Cramér-Rao bound
  • MMSE bounds
  • convex optimization
  • distributed estimation
  • robust estimation

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