Spectral factorization of wide sence stationary processes on Z2
Journal of Multivariate Analysis
Topics in matrix analysis
On the prediction theory of two-parameter stationary random fields
Journal of Multivariate Analysis
The prediction theory of stationary random fields. III: fourfold Wold decompositions
Journal of Multivariate Analysis
Interference mitigation in STAP using the two-dimensional Wold decomposition model
IEEE Transactions on Signal Processing
Maximum likelihood parameter estimation of textures using a Wold-decomposition based model
IEEE Transactions on Image Processing
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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.