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  • Research Article
  • Open Access

Asymptotic Bounds for Frequency Estimation in the Presence of Multiplicative Noise

EURASIP Journal on Advances in Signal Processing20062007:017090

https://doi.org/10.1155/2007/17090

  • Received: 29 January 2006
  • Accepted: 13 August 2006
  • Published:

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.

Keywords

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

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Authors’ Affiliations

(1)
School of Electrical and Electronic Engineering, Nanyang Technological University, Block S1, Nanyang Avenue, 639798, Singapore

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