IF estimation of higher-order polynomial FM signals corrupted by multiplicative and additive noise

We propose the peak of the polynomial Wigner-Ville distribution as an instantaneous frequency estimator for polynomial frequency modulated signals in the presence of multiplicative and additive complex Gaussian processes. We show that this estimator is unbiased and we derive an analytic expression of its asymptotic variance. Simulation results, based on Monte-Carlo realisations, are presented in order to show the validity of the theoretical derivations.