STATISTICAL ANALYSIS OF A HIGH RESOLUTION SPATIAL SPECTRUM ESTIMATOR UTILIZING AN AUGMENTED COVARIANCE MATRIX.

Unnikrishna Pillai, Fred Haber

Research output: Contribution to journalArticle

Abstract

Using an M-element array with elements arranged in a minimum-redundancy fashion and by augmenting the array output covariance matrix to create a covariance-type matrix of larger dimensions, the authors address the statistical properties and related issues of the augmented covariance matrix. They examine the case when the array output sample covariances are estimated from finite data using the maximum-likelihood method. Using a matrix factorization technique, the distribution of the sample Bartlett spatial spectrum estimator based on the augmented covariance matrix is shown to be a sum of weighted and dependent kappa **2-distributed random variables. The degradation in performance in making use of the augmented matrix is found in terms of the variance of the Bartlett estimator. This is shown to be on the order of twice the variance obtained with a uniform array of actual elements, the latter being equal in number to the dimension of the augmented array. To match the performance of the uniform array of actual elements using the augmented array would then require about twice the number of data samples.

Original languageEnglish (US)
Pages (from-to)1517-1523
Number of pages7
JournalIEEE Transactions on Acoustics, Speech, and Signal Processing
VolumeASSP-35
Issue number11
StatePublished - Nov 1987

Fingerprint

Covariance matrix
Statistical methods
Factorization
Random variables
Maximum likelihood
Redundancy
Degradation

ASJC Scopus subject areas

  • Signal Processing

Cite this

@article{bf73d611eb4e44c8807236c520953377,
title = "STATISTICAL ANALYSIS OF A HIGH RESOLUTION SPATIAL SPECTRUM ESTIMATOR UTILIZING AN AUGMENTED COVARIANCE MATRIX.",
abstract = "Using an M-element array with elements arranged in a minimum-redundancy fashion and by augmenting the array output covariance matrix to create a covariance-type matrix of larger dimensions, the authors address the statistical properties and related issues of the augmented covariance matrix. They examine the case when the array output sample covariances are estimated from finite data using the maximum-likelihood method. Using a matrix factorization technique, the distribution of the sample Bartlett spatial spectrum estimator based on the augmented covariance matrix is shown to be a sum of weighted and dependent kappa **2-distributed random variables. The degradation in performance in making use of the augmented matrix is found in terms of the variance of the Bartlett estimator. This is shown to be on the order of twice the variance obtained with a uniform array of actual elements, the latter being equal in number to the dimension of the augmented array. To match the performance of the uniform array of actual elements using the augmented array would then require about twice the number of data samples.",
author = "Unnikrishna Pillai and Fred Haber",
year = "1987",
month = "11",
language = "English (US)",
volume = "ASSP-35",
pages = "1517--1523",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "11",

}

TY - JOUR

T1 - STATISTICAL ANALYSIS OF A HIGH RESOLUTION SPATIAL SPECTRUM ESTIMATOR UTILIZING AN AUGMENTED COVARIANCE MATRIX.

AU - Pillai, Unnikrishna

AU - Haber, Fred

PY - 1987/11

Y1 - 1987/11

N2 - Using an M-element array with elements arranged in a minimum-redundancy fashion and by augmenting the array output covariance matrix to create a covariance-type matrix of larger dimensions, the authors address the statistical properties and related issues of the augmented covariance matrix. They examine the case when the array output sample covariances are estimated from finite data using the maximum-likelihood method. Using a matrix factorization technique, the distribution of the sample Bartlett spatial spectrum estimator based on the augmented covariance matrix is shown to be a sum of weighted and dependent kappa **2-distributed random variables. The degradation in performance in making use of the augmented matrix is found in terms of the variance of the Bartlett estimator. This is shown to be on the order of twice the variance obtained with a uniform array of actual elements, the latter being equal in number to the dimension of the augmented array. To match the performance of the uniform array of actual elements using the augmented array would then require about twice the number of data samples.

AB - Using an M-element array with elements arranged in a minimum-redundancy fashion and by augmenting the array output covariance matrix to create a covariance-type matrix of larger dimensions, the authors address the statistical properties and related issues of the augmented covariance matrix. They examine the case when the array output sample covariances are estimated from finite data using the maximum-likelihood method. Using a matrix factorization technique, the distribution of the sample Bartlett spatial spectrum estimator based on the augmented covariance matrix is shown to be a sum of weighted and dependent kappa **2-distributed random variables. The degradation in performance in making use of the augmented matrix is found in terms of the variance of the Bartlett estimator. This is shown to be on the order of twice the variance obtained with a uniform array of actual elements, the latter being equal in number to the dimension of the augmented array. To match the performance of the uniform array of actual elements using the augmented array would then require about twice the number of data samples.

UR - http://www.scopus.com/inward/record.url?scp=0023455987&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023455987&partnerID=8YFLogxK

M3 - Article

VL - ASSP-35

SP - 1517

EP - 1523

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 11

ER -