Fast communication: On the Cramér-Rao bound for polynomial phase signals

  • Authors:
  • Robby Mckilliam;André Pollok

  • Affiliations:
  • -;-

  • Venue:
  • Signal Processing
  • Year:
  • 2014

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Abstract

Polynomial-phase signals have applications including radar, sonar, biology, and radio communication. Of practical importance is the estimation of the parameters of a polynomial phase signal from a sequence of noisy observations. Assuming that the noise is additive and Gaussian, the direct evaluation of the Cramer-Rao lower bound for this estimation problem involves evaluating the inverse of a matrix. Computing this inverse is numerically difficult for polynomial phase signals of large order. By making use of a family of orthogonal polynomials, we derive formulae for the Cramer-Rao bounds that are numerically stable and easy to compute.