Liang, Y., Liu, W. orcid.org/0000-0003-2968-2888, Shen, Q. et al. (2 more authors) (2020) A review of closed-form Cramér-Rao Bounds for DOA estimation in the presence of Gaussian noise under a unified framework. IEEE Access, 8. pp. 175101-175124.
Abstract
The Cramér-Rao Bound (CRB) for direction of arrival (DOA) estimation has been extensively studied over the past four decades, with a plethora of CRB expressions reported for various parametric models. In the literature, there are different methods to derive a closed-form CRB expression, but many derivations tend to involve intricate matrix manipulations which appear difficult to understand. Starting from the Slepian-Bangs formula and following the simplest derivation approach, this paper reviews a number of closed-form Gaussian CRB expressions for the DOA parameter under a unified framework, based on which all the specific CRB presentations can be derived concisely. The results cover three scenarios: narrowband complex circular signals, narrowband complex noncircular signals, and wideband signals. Three signal models are considered: the deterministic model, the stochastic Gaussian model, and the stochastic Gaussian model with the a priori knowledge that the sources are spatially uncorrelated. Moreover, three Gaussian noise models distinguished by the structure of the noise covariance matrix are concerned: spatially uncorrelated noise with unknown either identical or distinct variances at different sensors, and arbitrary unknown noise. In each scenario, a unified framework for the DOA-related block of the deterministic/stochastic CRB is developed, which encompasses one class of closed-form deterministic CRB expressions and two classes of stochastic ones under the three noise models. Comparisons among different CRBs across classes and scenarios are presented, yielding a series of equalities and inequalities which reflect the benchmark for the estimation efficiency under various situations. Furthermore, validity of all CRB expressions are examined, with some specific results for linear arrays provided, leading to several upper bounds on the number of resolvable Gaussian sources in the underdetermined case.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For more information, see https://creativecommons.org/licenses/by/4.0/ |
Keywords: | Circular and noncircular; Cramér-Rao bound; Direction of arrival estimation; Narrowband and wideband; Underdetermined and overdetermined |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Electronic and Electrical Engineering (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/T517215/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 13 Oct 2020 11:23 |
Last Modified: | 13 Oct 2020 11:23 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Refereed: | Yes |
Identification Number: | 10.1109/access.2020.3026203 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:166004 |