Eigenvalue Estimates and Mutual Information for the Linear Time-Varying Channel

TL;DR

This paper provides rigorous eigenvalue estimates for linear time-varying channels with Gaussian noise and uses these estimates to derive mutual information bounds, offering theoretical justification for observed relationships in communication theory.

Contribution

It introduces a constructive method for estimating eigenvalues and mutual information in linear time-varying channels, bridging theory and observed empirical relationships.

Findings

Eigenvalue estimates are rigorously derived for a broad class of channels.

The mutual information of the channel can be estimated using these eigenvalues.

The approach balances operator diagonalization, signal dimension, and estimate accuracy.

Abstract

We consider linear time-varying channels with additive white Gaussian noise. For a large class of such channels we derive rigorous estimates of the eigenvalues of the correlation matrix of the effective channel in terms of the sampled time-varying transfer function and, thus, provide a theoretical justification for a relationship that has been frequently observed in the literature. We then use this eigenvalue estimate to derive an estimate of the mutual information of the channel. Our approach is constructive and is based on a careful balance of the trade-off between approximate operator diagonalization, signal dimension loss, and accuracy of eigenvalue estimates.