Harmonics in Gaussian Multiplicative and Additive Noise: Cremér-Rao Bounds

Guotong Zhou, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


The concern here is retrieval of single and multiple tone harmonics observed in white Gaussian multiplicative and additive noise. Computable Cramér-Rao bound (CRB) expressions are derived on the frequency and phase estimates as well as on the sample mean or variance of the multiplicative noise processes. The zero-and nonzero-mean multiplicative noise cases are addressed separately and are shown to yield distinct CRB’s on the frequency and phase estimates. Tight lower and upper bounds on the CRB’s themselves are developed, which, relative to the CRB’s, are intuitively more appealing and easier to implement. Well-established formulas on the achievable accuracy for estimates of constant amplitude harmonics turn out to be special cases of our results. Numerical studies support our claims.

Original languageEnglish (US)
Pages (from-to)1217-1231
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number5
StatePublished - May 1995

Bibliographical note

Funding Information:
Manuscript received February 24, 1994; revised December 1, 1994. Some results of this paper were presented at the Seventh SSAP Workshop, Quebec City, Canada, June 1994. This work was supported by ONR Grant no. N00014-93-1-0485. The authors are with the Department of Electrical Engineering, University of Virginia, Charlottesville. VA 22903-2442 USA. IEEE Log Number 9410296.


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