eprintid: 4335
rev_number: 7
eprint_status: archive
userid: 17
dir: disk0/00/00/43/35
datestamp: 2020-12-25 11:15:15
lastmod: 2020-12-25 11:15:15
status_changed: 2020-12-25 11:15:15
type: article
metadata_visibility: show
creators_name: Mohamed, Nait-Meziane
creators_name: Karim, Abed Meraim
creators_name: Zhipeng, Zhao
creators_name: Nguyen, Linh Trung
creators_id: karim.abed-meraim@univ-orleans.fr
creators_id: linhtrung@vnu.edu.vn
title: On the Gaussian Cramér-Rao Bound for Blind Single-Input
Multiple-Output System Identification: Fast and Asymptotic
Computations
ispublished: pub
subjects: ECE
subjects: isi
divisions: avitech
divisions: fac_fet
abstract: The Cramér-Rao Bound (CRB) is a powerful tool to assess the performance limits of a parameter estimation problem for a given statistical model. In particular, the Gaussian CRB (i.e., the CRB obtained assuming the data are Gaussian) corresponds to the worst case; giving the largest CRB among a large class of data distributions. This makes it very useful in practice since optimizing under the Gaussian data assumption can be interpreted as a min-max optimization (i.e., minimizing the largest CRB). The Gaussian CRB is also the corresponding bound of Second-Order Statistics (SOS)-based estimation methods, which are frequently used in practice. Despite its practicality, computing this bound might be cumbersome in some cases, particularly in the case where the input is assumed deterministic and has a large number of samples. In this paper, we address this computational issue by proposing a fast computation for the deterministic Gaussian CRB of Single-Input Multiple Output (SIMO) blind system identification. More precisely, we exploit circulant matrix properties to reduce the cost from cubic to quadratic with respect to the sample size. Moreover, we derive a closed-form formula for the asymptotic (large sample size) Gaussian CRB and show how it can be computed using the residue theorem.
date: 2020-09-08
date_type: published
publisher: IEEE
official_url: https://ieeexplore.ieee.org/abstract/document/9187805
id_number: DOI: 10.1109/ACCESS.2020.3022710
full_text_status: public
publication: IEEE Access
volume: 8
pagerange: 166503-166512
refereed: TRUE
issn: 2169-3536
funders: NAFOSTED
projects: System identification: from blind to informed paradigm
citation:   Mohamed, Nait-Meziane and Karim, Abed Meraim and Zhipeng, Zhao and Nguyen, Linh Trung  (2020) On the Gaussian Cramér-Rao Bound for Blind Single-Input Multiple-Output System Identification: Fast and Asymptotic Computations.  IEEE Access, 8 .   pp. 166503-166512.  ISSN 2169-3536     
document_url: https://eprints.uet.vnu.edu.vn/eprints/id/eprint/4335/1/Paper.pdf