Bias and variance of the PWVD-based IF estimator for polynomial FM signals in additive Gaussian noise

The peak of the polynomial Wigner-Ville distribution has been proposed as an instantaneous frequency estimator for a polynomial frequency modulated signal. We consider the statistical performance of such an estimator in the case of additive white Gaussian noise for a finite sample. It is shown that this estimator is unbiased and its variance is a function of the kernel coefficients of the PWVD. Results obtained by running Monte-Carlo simulations verify the theoretical derivations.