On the use of high order ambiguity function for multicomponent polynomial phase signals

Nonstationary signals appear often in real-life applications and many of them can be modeled as polynomial phase signals (PPS). The high-order ambiguity function (HAF) was first introduced to estimate the parameters of single component PPS. But due to its high nonlinearity, HAF has not been widely used for multi-component PPS which appear, for example, in Doppler radar applications when multiple targets are tracked simultaneously. We present a theory in this paper that HAF is virtually additive for multi-component PPS and illustrate our findings with numerical simulations