A CLT on the SNR of Diagonally Loaded MVDR Filters

Author

Rubio, Francisco ; Mestre, Xavier ; Hachem, Walid

Volume

60

Issue

8

fYear

2012

Firstpage

4178

Lastpage

4195

Abstract

This paper studies the fluctuations of the signal-to-noise ratio (SNR) of minimum variance distorsionless response (MVDR) filters implementing diagonal loading in the estimation of the covariance matrix. Previous results in the signal processing literature are generalized and extended by considering both spatially as well as temporarily correlated samples. Specifically, a central limit theorem (CLT) is established for the fluctuations of the SNR of the diagonally loaded MVDR filter, under both supervised and unsupervised training settings in adaptive filtering applications. Our second-order analysis is based on the Nash-Poincare inequality and the integration by parts formula for Gaussian functionals, as well as classical tools from statistical asymptotic theory. Numerical evaluations validating the accuracy of the CLT confirm the asymptotic Gaussianity of the fluctuations of the SNR of the MVDR filter.

Keywords

covariance matrices; filtering theory; game theory; CLT; Gaussian functionals; Nash-Poincare inequality; SNR fluctuations; adaptive filtering; central limit theorem; covariance matrix; diagonally loaded MVDR filters; minimum variance distorsionless response filters; second-order analysis; signal-to-noise ratio fluctuations; statistical asymptotic theory; supervised training setting; unsupervised training setting; Arrays; Covariance matrix; Loading; Signal to noise ratio; Training; Vectors; Asymptotic theory; central limit theorem (CLT); linear filter; minimum variance estimation; performance analysis; random matrix theory; signal-to-noise ratio (SNR);

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2012.2197396

Filename

6193458