Harmonics in Gaussian multiplicative and additive noise: Cramer-Rao bounds

Abstract

The concern here is retrieval of single and multiple tone harmonics observed in white Gaussian multiplicative and additive noise. Computable Cramer-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 CRBs on the frequency and phase estimates. Tight lower and upper bounds on the CRBs themselves are developed, which, relative to the CRBs, are intuitively more appealing and easier to implement. Well-established formulas on the achievable accuracy for estimates of constant amplitude harmonics turn put to be special cases of our results. Numerical studies support our claims. >