Title :
A CLT on the SNR of Diagonally Loaded MVDR Filters
Author :
Rubio, Francisco ; Mestre, Xavier ; Hachem, Walid
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);
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2012.2197396
