# A new family of one-coincidence sets of sequences with dispersed elements for frequency hopping CDMA systems

## TL;DR

This paper introduces a new family of one-coincidence sequence sets with dispersed elements for FH-CDMA systems, achieved by doubling the alphabet size of prime sequence sets, enhancing control and reducing crowdedness.

## Contribution

The paper proposes a novel method to generate dispersed one-coincidence sequence sets from prime sequences by increasing alphabet size, improving frequency hopping performance.

## Key findings

- New sequence sets with dispersed elements are derived from prime sequences.
- Doubling the alphabet size reduces crowdedness and improves control over sequence element spacing.
- Properties of the new sequence sets are analyzed and discussed.

## Abstract

We present a new family of one-coincidence sequence sets suitable for frequency hopping code division multiple access (FH-CDMA) systems with dispersed (low density) sequence elements. These sets are derived from one-coincidence prime sequence sets, such that for each one-coincidence prime sequence set there is a new one-coincidence set comprised of sequences with dispersed sequence elements, required in some circumstances, for FH-CDMA systems. Getting rid of crowdedness of sequence elements is achieved by doubling the size of the sequence element alphabet. In addition, this doubling process eases control over the distance between adjacent sequence elements. Properties of the new sets are discussed.