Cramér-Rao bound on the estimation accuracy of complex-valued homogeneous Gaussian random fields

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20 Scopus citations


This paper considers the problem of the achievable accuracy in jointly estimating the parameters of a complex-valued two-dimensional (2-D) Gaussian and homogeneous random field from a single observed realization of it. Based on the 2-D Wold decomposition, the field is modeled as a sum of purely indeterministic, evanescent, and harmonic components. Using this parametric model, we first solve a key problem common to many open problems in parametric estimation of homogeneous random fields: that of expressing the field mean and covariance functions in terms of the model parameters. Employing the parametric representation of the observed field mean and covariance, we derive a closed-form expression for the Fisher information matrix (FIM) of complex-valued homogeneous Gaussian random fields with mixed spectral distribution. Consequently, the Cramér-Rao lower bound on the error variance in jointly estimating the model parameters is evaluated.

Original languageEnglish
Pages (from-to)710-724
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - 1 Mar 2002


  • 2-D wold decomposition
  • Craméer-Rao bounds
  • Fisher information
  • Homogeneous random fields

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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