Liu, Chun-Lin and Vaidyanathan, P. P. (2016) New Cramér-Rao bound expressions for coprime and other sparse arrays. In: 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM). IEEE , Piscataway, NJ, pp. 1-5. ISBN 978-1-5090-2104-8. https://resolver.caltech.edu/CaltechAUTHORS:20160921-132608343
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Abstract
The Cramér-Rao bound (CRB) offers a lower bound on the variances of unbiased estimates of parameters, e.g., directions of arrival (DOA) in array processing. While there exist landmark papers on the study of the CRB in the context of array processing, the closed-form expressions available in the literature are not easy to use in the context of sparse arrays (such as minimum redundancy arrays (MRAs), nested arrays, or coprime arrays) for which the number of identifiable sources D exceeds the number of sensors N. Under such situations, the existing literature does not spell out the conditions under which the Fisher information matrix is nonsingular, or the condition under which specific closed-form expressions for the CRB remain valid. This paper derives a new expression for the CRB to fill this gap. The conditions for validity of this expression are expressed as the rank condition of a matrix defined based on the difference coarray. The rank condition and the closed-form expression lead to a number of new insights. For example, it is possible to prove the previously known experimental observation that, when there are more sources than sensors, the CRB stagnates to a constant value as the SNR tends to infinity.
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 2016 IEEE. This work was supported in parts by the ONR grant N00014-15-1-2118, and the California Institute of Technology. | |||||||||
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| Subject Keywords: | Cramér-Rao bounds, Fisher information matrices, Coprime arrays, Sparse arrays, Difference coarray | |||||||||
| Record Number: | CaltechAUTHORS:20160921-132608343 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160921-132608343 | |||||||||
| Official Citation: | C. L. Liu and P. P. Vaidyanathan, "New Cramér-Rao bound expressions for coprime and other sparse arrays," 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM), Rio de Janerio, Brazil, 2016, pp. 1-5. doi: 10.1109/SAM.2016.7569620 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7569620&isnumber=7569603 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 70518 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 29 Sep 2016 21:04 | |||||||||
| Last Modified: | 03 Oct 2019 10:31 |
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