The Rank of the Covariance Matrix of an Evanescent Field

TL;DR

This paper derives a formula for the rank of the covariance matrix of evanescent random fields, linking it directly to spectral support parameters, which simplifies rank estimation in space-time adaptive processing applications.

Contribution

It provides a closed-form expression for the covariance matrix rank of evanescent fields based solely on spectral support, avoiding direct sample covariance estimation.

Findings

Rank determined by spectral support parameters

Simplifies interference covariance matrix estimation in STAP

Reduces computational complexity in practical applications

Abstract

Evanescent random fields arise as a component of the 2-D Wold decomposition of homogenous 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.