On the Cramér-Rao bound for polynomial phase signals

Polynomial-phase signals have applications including radar, sonar, geophysics, and radio communication. Of practical importance is the estimation of the parameters of a polynomial phase signal from a sequence of noisy observations. We derive closed form formulae for the Cramér-Rao lower bounds of these parameters under the assumption that the noise is additive white and Gaussian. This is achieved by making use of a family of orthogonal polynomials.