A CLT on the SNR of Diagonally Loaded MVDR Filters

TL;DR

This paper establishes a central limit theorem for the fluctuations of the SNR of diagonally loaded MVDR filters, considering correlated samples and different training settings, supported by numerical validation.

Contribution

It generalizes existing results by deriving a CLT for the SNR fluctuations of diagonally loaded MVDR filters with correlated samples in various training scenarios.

Findings

CLT confirms asymptotic Gaussianity of SNR fluctuations.

Numerical evaluations validate the theoretical CLT.

Results apply to both supervised and unsupervised training.

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-Poincar\'e 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.