Statistical analysis of the product high-order ambiguity function

The high-order ambiguity function (HAF) was introduced for the estimation o f polynomial-phase signals (PPS) embedded in noise. Since the HAF is a nonl inear operator, it suffers from noise-masking effects and from the appearan ce of undesired cross terms and, possibly, spurious harmonics in the presen ce of multicomponent (mc) signals. The product HAF (PHAF) was then proposed as a way to improve the performance of the HAF in the presence of noise an d to solve the ambiguity problem. In this correspondence we derive a statis tical analysis of the PHAF in the presence of additive white Gaussian noise (AWGN) valid for high signal-to-noise ratio (SNR) and a finite number of d ata samples. The analysis is carried out in detail for single-component PPS but the multicomponent case is also discussed. Error propagation phenomena implicit in the recursive structure of the PHAF-based estimator are explic itly taken into account. The analysis is validated by simulation results fo r both single- and multicomponent PPS's.