Polynomial phase signal processing via warped high-order ambiguity function

The high-order ambiguity function (HAF) was introduced for the estimation of polynomial-phase signals (PPS). Currently the HAF suffers from noise-masking effects and from the appearance of undesired cross terms in the presence of multi-components PPS. The multi-lag product HAF (PHAF) concept was then proposed as a way to improve the performances of the HAF. Nevertheless, the “optimal” choice of lag sets implies many tries, undesirable in an automatically signal processing context. On the other hand, multiplying many mlHAFs might lead to abnormal results. In this paper we propose a warped-based algorithm in order to accurately estimate the coefficients of the polynomial phase. We compute the HAF for different lag values. Knowing the variation law of the frequency with respect to these values, we can construct a warping function leading to a linear dependence between the HAF maxima coordinates and the lag set.