NDLI: Improved, Approximate, Time-Domain ML Estimators of Chirp Signal Parameters and Their Performance Analysis

Content Provider	IEEE Xplore Digital Library
Author	Yan Li Hua Fu Pooi Yuen Kam
Copyright Year	1991
Abstract	We derive an improved, approximate, maximum likelihood (ML) estimator for the parameters of a single-component chirp signal in the time domain, which has much lower computational complexity than that of the traditional estimators in the frequency domain. We term it the zero-order amplitude weighted phase-based estimator (AWPE). It is a weighted linear combination of the phases of the received signal samples, where the weights are determined by the amplitudes of the received signals. It achieves better performance than the only existing time-domain estimator in the literature that only exploits the phase information. A phase unwrapping (PU) algorithm is needed to recover the phase information correctly from the received signal samples. Several PU algorithms are compared and analyzed. A new, robust PU algorithm based on the first-order phase differences of the consecutive received signal samples is proposed. This new unwrapping algorithm has smaller PU failure probability than that based directly on the phases of the received signal samples. The need for PU can even be removed by using the second-order phase differences of the consecutive received signal samples. Two additional structures for the ML-based AWPE using the phase differences are derived starting from using the zero-order AWPE obtained. The first is based on the first-order phase differences and the second on the second-order phase differences. When the PU algorithm works perfectly, i.e., no phase unwrapping failure occurs, the estimators based on phase differences do not perform as well as the original one based on absolute phase information due to the increased noise variance. This is also applicable when the chirp parameters take on very small values. However, when no knowledge of the ranges of the chirp parameters is available, and the possible PU failures are taken into account, the estimators based on the phase differences could perform better. Performance analysis of the estimators is given based on an improved phase noise model. It is easy to verify that the estimates obtained are unbiased. The cramer-rao lower bound (CRLB) on the mean-square error (MSE) is derived. The MSE performance of the estimators approaches the CRLB at high signal-to-noise ratios. The variance performance of the estimators based on phase differences is analyzed, whose validity is demonstrated by simulation results.
Sponsorship	IEEE Signal Processing Society
Starting Page	1260
Ending Page	1272
Page Count	13
File Size	1082768
File Format	PDF
ISSN	1053587X
Volume Number	57
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-04-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Time domain analysis Maximum likelihood estimation Chirp Performance analysis Phase estimation Frequency estimation Phase noise Parameter estimation Computational complexity Frequency domain analysis synthetic aperture radars Amplitude weighted phase-based estimator chirp signals maximum likelihood estimation performance analysis phase unwrapping
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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