Two-dimensional polynomial phase signals: Parameter estimation and bounds

Joseph M. Francos, Benjamin Friedlander

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


This paper considers the problem of parametric modeling and estimation of nonhomogeneous two-dimensional (2-D) signals. In particular, we focus our study on the class of constant modulus polynomial-phase 2-D nonhomogeneous signals. We present two different phase models and develop computationally efficient estimation algorithms for the parameters of these models. Both algorithms are based on phase differencing operators. The basic properties of the operators are analyzed and used to develop the estimation algorithms. The Cramer-Rao lower bound on the accuracy of jointly estimating the model parameters is derived, for both models. To get further insight on the problem we also derive the asymptotic Cramer-Rao bounds. The performance of the algorithms in the presence of additive white Gaussian noise is illustrated by numerical examples, and compared with the corresponding exact and asymptotic Cramer-Rao bounds. The algorithms are shown to be robust in the presence of noise, and their performance close to the CRB, even at moderate signal to noise ratios.

Original languageEnglish
Pages (from-to)173-205
Number of pages33
JournalMultidimensional Systems and Signal Processing
Issue number2
StatePublished - 1 Jan 1998


  • Cramer-Rao bound
  • High-order ambiguity function
  • Parameter estimation of nonhomogeneous signals
  • Two-dimensional nonhomogeneous signals
  • Two-dimensional phase differencing operator

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Information Systems
  • Hardware and Architecture
  • Computer Science Applications
  • Artificial Intelligence
  • Applied Mathematics


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