Harmonics in multiplicative and additive noise: performance analysis of cyclic estimators

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 Cramer-Rao bounds when the noises are white Gaussian. It is demonstrated that previously well established results on constant amplitude harmonics are special cases of the present analysis. Simulations not only validate the large sample performance analysis, but also provide concrete examples regarding relative statistical efficiency of the cyclic estimators