A short overview of adaptive multichannel filters SNR loss analysis

TL;DR

This paper reviews the performance analysis of adaptive multichannel filters, focusing on SNR loss when estimating noise covariance and considering different adaptive filter configurations.

Contribution

It provides a concise overview of existing literature on SNR loss analysis for adaptive multichannel filters, including various scenarios and filter types.

Findings

Analysis of SNR loss in different adaptive filter cases

Comparison of fully adaptive, partially adaptive, and regularized filters

Summary of key results from literature since the 1970s

Abstract

Many multichannel systems use a linear filter to retrieve a signal of interest corrupted by noise whose statistics are partly unknown. The optimal filter in Gaussian noise requires knowledge of the noise covariance matrix $\Sigma$ and in practice the latter is estimated from a set of training samples. An important issue concerns the characterization of the performance of such adaptive filters. This is generally achieved using as figure of merit the ratio of the signal to noise ratio (SNR) at the output of the adaptive filter to the SNR obtained with the clairvoyant -- known $\Sigma$ -- filter. This problem has been studied extensively since the seventies and this document presents a concise overview of results published in the literature. We consider various cases about the training samples covariance matrix and we investigate fully adaptive, partially adaptive and regularized filters.