The Worst Case ISI channels and the Uniqueness of the Corresponding Minimum Eigenvalue

TL;DR

This paper investigates the impact of worst-case intersymbol interference (ISI) on communication channels, proving that increased ISI reduces the minimum Euclidean distance and establishing the uniqueness of the minimum eigenvalue in such scenarios.

Contribution

It demonstrates that the minimum Euclidean distance decreases with increasing ISI and proves the uniqueness of the minimum eigenvalue for worst case ISI channels.

Findings

Minimum Euclidean distance decreases as ISI increases.

The minimum eigenvalue of the worst case ISI channel is unique.

Worst case ISI scenarios lead to the most significant performance degradation.

Abstract

Intersymbol interference (ISI) is a major cause of degradation in the receiver performance of high-speed data communications systems. This arises mainly due to limited bandwidth available. The minimum Euclidean distance between any two symbol sequences is an important parameter in this case at moderate to high signal to noise ratios. It is proven here that as ISI increases the minimum distance strictly decreases when the worst case scenario is considered. From this it follows that the minimum eigenvalue of the worst case ISI channel of a given length is unique.