Approximate eigenvalue distribution of a cylindrically isotropic noise sample covariance matrix

TL;DR

This paper introduces a computationally efficient method to approximate the eigenvalue density function of a sample covariance matrix for cylindrically isotropic noise, aiding adaptive beamforming performance analysis.

Contribution

It presents a novel atomic density model for the eigenvalue distribution of the SCM in cylindrically isotropic noise fields, reducing computational complexity.

Findings

Approximate eigenvalue density closely matches simulation results.

Model significantly reduces computational effort compared to direct methods.

Applicable to finite snapshot scenarios in noise covariance estimation.

Abstract

The statistical behavior of the eigenvalues of the sample covariance matrix (SCM) plays a key role in determining the performance of adaptive beamformers (ABF) in presence of noise. This paper presents a method to compute the approximate eigenvalue density function (EDF) for the SCM of a \cin{} field when only a finite number of shapshots are available. The EDF of the ensemble covariance matrix (ECM) is modeled as an atomic density with many fewer atoms than the SCM size. The model results in substantial computational savings over more direct methods of computing the EDF. The approximate EDF obtained from this method agrees closely with histograms of eigenvalues obtained from simulation.