Generalized High-Order Phase Function for Parameter Estimation of Polynomial Phase Signal

The high-order phase function (HPF) has been introduced recently to estimate the parameters of a polynomial phase signal (PPS). In this correspondence, we generalize the standard HPF by introducing multiple time instants. Thus, the standard HPF can be treated as a special example of the generalized HPF with identical time instants. We propose a procedure for finding time instants minimizing the mean-square error (MSE). The proposed method achieves better performances than the high-order ambiguity function (HAF) and polynomial Wigner–Ville distribution (PWVD). The theoretical analysis as well as the Monte Carlo simulations verify the advantages such as lower MSE and lower SNR threshold for the PPS.