Product high-order ambiguity function for multicomponent polynomial-phase signal modeling

Parameter estimation and performance analysis issues are studied for multicomponent polynomial-phase signals (PPSs) embedded in white Gaussian noise. Identifiability issues arising with existing approaches are described first when dealing with multicomponent PPS having the same highest order phase coefficients. This situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis. A new approach is proposed based on a transformation called product high-order ambiguity function (PHAF). The use of the PHAF offers a number of advantages with respect to the high-order ambiguity function (HAF). More specifically, it removes the identifiability problem and improves noise rejection capabilities. Performance analysis is carried out using the perturbation method and verified by simulation results.