A class of hopping patterns with minimal collisions

TL;DR

This paper introduces a new class of hopping patterns designed to minimize collisions in communication systems, achieving optimal bounds for both collision ratio and continual collisions.

Contribution

It provides a lower bound for the maximal collision ratio and constructs hopping patterns that meet the bounds for both collision metrics.

Findings

Hopping patterns with minimal collisions are achievable.

Theoretical bounds for collision metrics are established.

Constructed patterns meet the optimal bounds.

Abstract

In \cite{VTC} three metrics for hopping pattern performance evaluation is proposed: column period, maximal collision ratio, maximal continual collision number, a lower bound of maximal continual collision number is given also. In this paper we give a lower bound of maximal collision ratio, a class of hopping pattern whose both maximal collision ratio and maximal continual collision number fit the lower bounds is constructed also.