Analysis of frequency modulated signals in multiplicative noise

We address the problem of analysing nonlinear frequency modulated (FM) signals in the presence of complex circular Gaussian multiplicative and additive noise processes. In particular, we consider the estimation of the instantaneous frequency of these signals using the peak of the polynomial Wigner-Ville distribution. We derive the bias and the variance of this estimator. We show that for the case of polynomial FM signals, the present results reduce to those obtained when a different method (see Barkat, B., Proc. of the Inter. Conf. on Acou. Speech and Signal Processing, 2001) was used in the derivations