Statistical analysis of the product high-order ambiguity function

Anna Scaglione, Sergio Barbarossa

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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 and, possibly, spurious harmonics in the presence of multicomponent (me) signals. The product HAF (PHAF) was then proposed as a way to improve the performance of the HAF in the presence of noise and to solve the ambiguity problem. In this correspondence we derive a statistical analysis of the PHAF in the presence of additive white Gaussian noise (AWGN) valid for high sisgnalto-noise ratio (SNR) and a finite number of data 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 explicitly taken into account. The analysis is validated by simulation results for both singleand multicomponent PPS's.

Original languageEnglish (US)
Pages (from-to)343-356
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - 1999
Externally publishedYes


  • High-order ambiguity function
  • Parameter estimation
  • Polynomial-phase signals

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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