Exploring lag diversity in the high-order ambiguity function for polynomial phase signals

High-order ambiguity function (HAF) is an effective tool for retrieving coefficients of polynomial phase signals (PPS). The lag choice is dictated by conflicting requirements: a large lag improves estimation accuracy but drastically limits the range of the parameters that can be estimated. By using two (large) co-prime lags and solving linear Diophantine equations using the Euclidean algorithm, we are able to recover the PPS coefficients from aliased peak positions without-compromising the dynamic range and the estimation accuracy. Separating components of a multi-component PPS whose phase polynomials have very similar leading coefficients has been a challenging task, but can now be tackled easily with the two-lag approach. Numerical examples are presented to illustrate the effectiveness of our method.