Polynomial phase signal modeling using warping-based order reduction

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 concept was then proposed as a way to improve the performance of the HAF. Nevertheless, the performance of the new methods are affected by the error propagation. This effect is due to the technique used for polynomial order reduction, common for current approaches: signal multiplication with the complex exponentials formed with the estimated coefficients. In this paper, we introduce an alternative method to reduce the polynomial order, based on the successive unitary signal transformation, according to each polynomial order. We prove that this method considerably reduces the effect of error propagation.