Limitations of Constrained CRB and an Alternative Bound

Eyal Nitzan; Tirza Routtenberg; Joseph Tabrikian

doi:https://doi.org/10.1109/SSP.2018.8450829

Limitations of Constrained CRB and an Alternative Bound

Eyal Nitzan, Tirza Routtenberg, Joseph Tabrikian

Department of Electrical & Computer Engineering

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The constrained Cramér-Rao bound (CCRB) is a mean-squared-error (MSE) lower bound for non-Bayesian constrained parameter estimation under some unbiasedness conditions. In this paper, we demonstrate limitations of this bound in the case of nonlinear parametric constraints. We consider the problem of constant modulus signal estimation. It is shown that in this problem the CCRB unbiasedness conditions are too restrictive and that the commonly-used constrained maximum likelihood (CML) estimator does not satisfy them and has lower MSE than the CCRB. An alternative lower bound, which is based on the Lehmann-unbiasedness conditions, is used as an alternative benchmark for constrained parameter estimation. As opposed to the CCRB, it is shown that this alternative bound is valid for the CML estimator in the considered problem.

Original language	American English
Title of host publication	2018 IEEE Statistical Signal Processing Workshop, SSP 2018
Pages	841-845
Number of pages	5
DOIs	https://doi.org/10.1109/SSP.2018.8450829
State	Published - 29 Aug 2018
Event	20th IEEE Statistical Signal Processing Workshop, SSP 2018 - Freiburg im Breisgau, Germany Duration: 10 Jun 2018 → 13 Jun 2018

Publication series

Name	2018 IEEE Statistical Signal Processing Workshop, SSP 2018

Conference

Conference	20th IEEE Statistical Signal Processing Workshop, SSP 2018
Country/Territory	Germany
City	Freiburg im Breisgau
Period	10/06/18 → 13/06/18

Keywords

Constrained Cramér-Rao bound (CCRB)
Lehmann-unbiasedness
constant modulus signal estimation
constrained parameter estimation
mean-squared-error (MSE)

All Science Journal Classification (ASJC) codes

Signal Processing
Instrumentation
Computer Networks and Communications

Access to Document

https://doi.org/10.1109/SSP.2018.8450829

Cite this

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title = "Limitations of Constrained CRB and an Alternative Bound",

abstract = "The constrained Cram{\'e}r-Rao bound (CCRB) is a mean-squared-error (MSE) lower bound for non-Bayesian constrained parameter estimation under some unbiasedness conditions. In this paper, we demonstrate limitations of this bound in the case of nonlinear parametric constraints. We consider the problem of constant modulus signal estimation. It is shown that in this problem the CCRB unbiasedness conditions are too restrictive and that the commonly-used constrained maximum likelihood (CML) estimator does not satisfy them and has lower MSE than the CCRB. An alternative lower bound, which is based on the Lehmann-unbiasedness conditions, is used as an alternative benchmark for constrained parameter estimation. As opposed to the CCRB, it is shown that this alternative bound is valid for the CML estimator in the considered problem.",

keywords = "Constrained Cram{\'e}r-Rao bound (CCRB), Lehmann-unbiasedness, constant modulus signal estimation, constrained parameter estimation, mean-squared-error (MSE)",

author = "Eyal Nitzan and Tirza Routtenberg and Joseph Tabrikian",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 20th IEEE Statistical Signal Processing Workshop, SSP 2018 ; Conference date: 10-06-2018 Through 13-06-2018",

year = "2018",

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day = "29",

doi = "https://doi.org/10.1109/SSP.2018.8450829",

language = "American English",

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Nitzan, E, Routtenberg, T & Tabrikian, J 2018, Limitations of Constrained CRB and an Alternative Bound. in 2018 IEEE Statistical Signal Processing Workshop, SSP 2018., 8450829, 2018 IEEE Statistical Signal Processing Workshop, SSP 2018, pp. 841-845, 20th IEEE Statistical Signal Processing Workshop, SSP 2018, Freiburg im Breisgau, Germany, 10/06/18. https://doi.org/10.1109/SSP.2018.8450829

TY - GEN

T1 - Limitations of Constrained CRB and an Alternative Bound

AU - Nitzan, Eyal

AU - Routtenberg, Tirza

AU - Tabrikian, Joseph

PY - 2018/8/29

Y1 - 2018/8/29

N2 - The constrained Cramér-Rao bound (CCRB) is a mean-squared-error (MSE) lower bound for non-Bayesian constrained parameter estimation under some unbiasedness conditions. In this paper, we demonstrate limitations of this bound in the case of nonlinear parametric constraints. We consider the problem of constant modulus signal estimation. It is shown that in this problem the CCRB unbiasedness conditions are too restrictive and that the commonly-used constrained maximum likelihood (CML) estimator does not satisfy them and has lower MSE than the CCRB. An alternative lower bound, which is based on the Lehmann-unbiasedness conditions, is used as an alternative benchmark for constrained parameter estimation. As opposed to the CCRB, it is shown that this alternative bound is valid for the CML estimator in the considered problem.

AB - The constrained Cramér-Rao bound (CCRB) is a mean-squared-error (MSE) lower bound for non-Bayesian constrained parameter estimation under some unbiasedness conditions. In this paper, we demonstrate limitations of this bound in the case of nonlinear parametric constraints. We consider the problem of constant modulus signal estimation. It is shown that in this problem the CCRB unbiasedness conditions are too restrictive and that the commonly-used constrained maximum likelihood (CML) estimator does not satisfy them and has lower MSE than the CCRB. An alternative lower bound, which is based on the Lehmann-unbiasedness conditions, is used as an alternative benchmark for constrained parameter estimation. As opposed to the CCRB, it is shown that this alternative bound is valid for the CML estimator in the considered problem.

KW - Constrained Cramér-Rao bound (CCRB)

KW - Lehmann-unbiasedness

KW - constant modulus signal estimation

KW - constrained parameter estimation

KW - mean-squared-error (MSE)

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U2 - https://doi.org/10.1109/SSP.2018.8450829

DO - https://doi.org/10.1109/SSP.2018.8450829

M3 - Conference contribution

SN - 9781538615706

T3 - 2018 IEEE Statistical Signal Processing Workshop, SSP 2018

SP - 841

EP - 845

BT - 2018 IEEE Statistical Signal Processing Workshop, SSP 2018

T2 - 20th IEEE Statistical Signal Processing Workshop, SSP 2018

Y2 - 10 June 2018 through 13 June 2018

ER -

Limitations of Constrained CRB and an Alternative Bound

Abstract

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Conference

Keywords

All Science Journal Classification (ASJC) codes

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