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

Abstract

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.