PPoL: A Periodic Channel Hopping Sequence with Nearly Full Rendezvous Diversity

TL;DR

This paper introduces PPoL, a novel periodic channel hopping sequence based on finite projective planes, achieving nearly full rendezvous diversity and significantly reducing maximum time-to-rendezvous in multichannel communication.

Contribution

PPoL is the first channel hopping sequence leveraging finite projective plane structures, providing nearly full rendezvous diversity and improved MTTR bounds.

Findings

PPoL achieves at least N-2 rendezvous channels for any nonzero clock drift.

The maximum time-to-rendezvous is bounded by N^2+3N+3, about 50% better than previous bounds.

PPoL's period is N^2-N+1 when N-1 is a prime power.

Abstract

We propose a periodic channel hopping (CH) sequence, called PPoL (Packing the Pencil of Lines in a finite projective plane), for the multichannel rendezvous problem. When $N-1$ is a prime power, its period is $N^2-N+1$, and the number of distinct rendezvous channels of PPoL is at least $N-2$ for any nonzero clock drift. By channel remapping, we construct CH sequences with the maximum time-to-rendezvous (MTTR) bounded by $N^2+3N+3$ if the number of commonly available channels is at least two. This achieves a roughly 50% reduction of the state-of-the-art MTTR bound in the literature.