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.