@inproceedings{5ed6692f981e49ff8cb0d6a24d4d63db,

title = "Tight MMSE Bounds for the AGN Channel under KL Divergence Constraints on the Input Distribution",

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 Cram{\'e}r-Rao bound. Both properties are illustrated with numerical examples.",

keywords = "Cram{\'e}r-Rao bound, MMSE bounds, minimax optimization, robust estimation",

author = "Michael Faub and Zoubir, {Abdelhak M.} and Alex Dytso and Poor, {H. Vincent}",

note = "Funding Information: ∗This work was supported in part by the U.S. National Science Foundation under Grants CCF-1420575 and ECCS-1549881.; 20th IEEE Statistical Signal Processing Workshop, SSP 2018 ; Conference date: 10-06-2018 Through 13-06-2018",

year = "2018",

month = aug,

day = "29",

doi = "10.1109/SSP.2018.8450756",

language = "English (US)",

isbn = "9781538615706",

series = "2018 IEEE Statistical Signal Processing Workshop, SSP 2018",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "308--312",

booktitle = "2018 IEEE Statistical Signal Processing Workshop, SSP 2018",

address = "United States",

}