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

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.