Harmonics in Multiplicative and Additive Noise: Performance Analysis of Cyclic Estimators

Guotong Zhou, Georgios B. Giannakis

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73 Scopus citations


Multiplicative noise causes smearing of spectral lines and thus hampers frequency estimation relying on conventional spectral analysis. In contrast, cyclic mean and correlation statistics have proved to be useful for harmonic retrieval in the presence of multiplicative and additive noise of arbitrary color and distribution. Performance analysis of cyclic estimators is carried through both for nonzero and zero mean multiplicative noises. Cyclic estimators are shown to be asymptotically equivalent to certain nonlinear least squares estimators, and are also compared with the maximum likelihood ones. Large sample variance expressions of the cyclic estimators are derived and compared with the corresponding Cramér-Rao bounds when the noises are white Gaussian. It is demonstrated that previously well established results on constant amplitude harmonics are special cases of our analysis. Simulations not only validate the large sample performance analysis, but also provide concrete examples regarding relative statistical efficiency of the cyclic estimators.

Original languageEnglish (US)
Pages (from-to)1445-1460
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number6
StatePublished - Jun 1995

Bibliographical note

Funding Information:
Manuscript received March 18, 1994; revised November 4, 1994. Some results of this paper were presented at the 28th CISS Conf., Princeton Univ., NJ. Mar 1994. This work was supported by ONR Grant N00014-93-1-0485. The associate editor coordinating the review of this paper and approving it for publication was Prof. D. Fuhrmann.


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