ASYMPTOTIC STATISTICAL-ANALYSIS OF THE HIGH-ORDER AMBIGUITY FUNCTION FOR PARAMETER-ESTIMATION OF POLYNOMIAL-PHASE SIGNALS

The high-order ambiguity function (HAF) is a nonlinear operator design ed to detect, estimate, and classify complex signals whose phase is a polynomial function of time. The HAF algorithm, introduced by Peleg an d Porat, estimates the phase parameters of polynomial-phase signals me asured in noise, The purpose of this correspondence is to analyze the asymptotic accuracy of the HAF algorithm in the case of additive white Gaussian noise, It is shown that the asymptotic variances of the esti mates are close to the Cramer-Rao bound (CRB) for high SNR. However, t he ratio of the asymptotic variance and the CRB has a polynomial growt h in the noise variance.