First- and Second-Order Moments of the Normalized Sample Covariance Matrix of Spherically Invariant Random Vectors

Author

Bausson, Sébastien ; Pascal, Frédéric ; Forster, Philippe ; Ovarlez, Jean-Philippe ; Larzabal, Pascal

Author_Institution

Groupe d´´Electromagnetisme Applique, Univ. Paris X, Ville D´´Avray

Volume

14

Issue

6

fYear

2007

fDate

6/1/2007 12:00:00 AM

Firstpage

425

Lastpage

428

Abstract

Under Gaussian assumptions, the sample covariance matrix (SCM) is encountered in many covariance based processing algorithms. In case of impulsive noise, this estimate is no more appropriate. This is the reason why when the noise is modeled by spherically invariant random vectors (SIRV), a natural extension of the SCM is extensively used in the literature: the well-known normalized sample covariance matrix (NSCM), which estimates the covariance of SIRV. Indeed, this estimate gets rid of a fluctuating noise power and is widely used in radar applications. The aim of this paper is to derive closed-form expressions of the first- and second-order moments of the NSCM

Keywords

Gaussian processes; covariance matrices; impulse noise; radar signal processing; signal sampling; Gaussian assumption; NSCM; SIRV; closed-form expression; first-order moments; impulsive noise; normalized sample covariance matrix; radar application; second-order moments; spherically invariant random vectors; Closed-form solution; Clutter; Covariance matrix; Eigenvalues and eigenfunctions; Fading; Matrix decomposition; Maximum likelihood estimation; Performance analysis; Radar applications; Sonar; Estimation; normalized sample covariance matrix (NSCM); performance analysis; spherically invariant random vectors (SIRV);

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2006.888400

Filename

4202611