The rank of the covariance matrix of an evanescent field

Mark Kliger, Joseph M. Francos

Research output: Contribution to journalArticlepeer-review


Evanescent random fields arise as a component of the 2D Wold decomposition of homogeneous random fields. Besides their theoretical importance, evanescent random fields have a number of practical applications, such as in modeling the observed signal in the space-time adaptive processing (STAP) of airborne radar data. In this paper we derive an expression for the rank of the low-rank covariance matrix of a finite dimension sample from an evanescent random field. It is shown that the rank of this covariance matrix is completely determined by the evanescent field spectral support parameters, alone. Thus, the problem of estimating the rank lends itself to a solution that avoids the need to estimate the rank from the sample covariance matrix. We show that this result can be immediately applied to considerably simplify the estimation of the rank of the interference covariance matrix in the STAP problem.

Original languageEnglish
Pages (from-to)692-705
Number of pages14
JournalJournal of Multivariate Analysis
Issue number3
StatePublished - 1 Mar 2010


  • Covariance matrix
  • Evanescent random fields
  • Homogeneous random fields
  • Linear Diophantine equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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