Non-linear least squares estimation for harmonics in multiplicative and additive noise

We consider the problem of estimating the frequency of a complex harmonic i n the presence of additive and multiplicative noise. Two non-linear least-s quares (NLLS) estimators, NLLS1 and NLLS2, are proposed, which consist of m atching the data and the squared data, respectively, with a constant amplit ude harmonic. Expressions for the asymptotic covariances of the NLLS estima tors are derived. It is shown that at high SNR, NLLS2 should be used instea d of NLLS1, regardless of the value of the coherent to non-coherent power r atio of the multiplicative noise. On the other hand, at low SNR, there is a trade-off between NLLS1 and NLLS2. The latter should be preferred when the coherent to non-coherent power ratio is below a threshold which is a funct ion of the SNR and the kurtosis of the additive noise. (C) 1999 Elsevier Sc ience B.V. All rights reserved.