Analysis of the SNR loss distribution with covariance mismatched training samples

TL;DR

This paper investigates the distribution of SNR loss in adaptive filters trained with mismatched covariance samples, proposing accurate approximations for different covariance relations to assess mismatch impact.

Contribution

It introduces a Pearson type approximation for the SNR loss distribution under covariance mismatch, covering both generalized eigenrelation and arbitrary cases.

Findings

The approximation accurately models the SNR loss distribution.

It enables straightforward assessment of covariance mismatch impact.

Numerical results confirm the effectiveness of the proposed method.

Abstract

We analyze the distribution of the signal to noise ratio (SNR) loss at the output of an adaptive filter which is trained with samples that do not share the same covariance matrix as the samples for which the filter is foreseen. Our objective is to find an accurate approximation of the distribution of the SNR loss which has a similar form as in the case of no mismatch. We successively consider the case where the two covariance matrices satisfy the so-called generalized eigenrelation and the case where they are arbitrary. In the former case, this amounts to approximate a central quadratic form in normal variables while the latter case entails approximating a non-central quadratic form in Student distributed variables. In order to obtain the approximate distribution, a Pearson type approach is advocated. A numerical study show that this approximation is rather accurate and enables one to assess, in a straightforward manner, the impact of covariance mismatch.