On the unitary equivalence application in the polynomial phase signal processing

The high-order ambiguity function (HAF) was introduced for the estimation of polynomial-phase signals (PPS) embedded in noise. Since the HAF is a nonlinear operator, it suffers from noise-masking effects and from the appearance of undesired cross terms in the presence of multicomponents PPS. The multilag HAF concept was then proposed as a way to improve the performances of the HAF. Nevertheless, performances of the new methods are affected by the error propagation effect which drastically limits the order of the polynomial approximation. This effect is due to the technique used for polynomial order reduction, common for actual 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 will prove that this method considerably reduces the effect of error propagation.