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Asymptotic Bounds for Frequency Estimation in the Presence of Multiplicative Noise

Abstract

We discuss the asymptotic Cramer-Rao bound (CRB) for frequency estimation in the presence of multiplicative noise. To improve numerical stability, covariance matrix tapering is employed when the covariance matrix of the signal is singular at high SNR. It is shown that the periodogram-based CRB is a special case of frequency domain evaluation of the CRB, employing the covariance matrix tapering technique. Using the proposed technique, large sample frequency domain CRB is evaluated for Jake's model. The dependency of the large sample CRB on the Doppler frequency, signal-to-noise ratio, and data length is investigated in the paper. Finally, an asymptotic closed form CRB for frequency estimation in the presence of multiplicative and additive colored noise is derived. Numerical results show that the asymptotic CRB obtained in frequency domain is accurate, although its evaluation is computationally simple.

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Correspondence to Zhi Wang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wang, Z., Abeysekera, S.S. Asymptotic Bounds for Frequency Estimation in the Presence of Multiplicative Noise. EURASIP J. Adv. Signal Process. 2007, 017090 (2006). https://doi.org/10.1155/2007/17090

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Keywords

  • Information Technology
  • Covariance Matrix
  • Frequency Domain
  • Closed Form
  • Sample Frequency