Deterministic Collision-Resilient Channel Rendezvous: Theory and Algorithm

Abstract

We formulate and investigate the problem of distributed channel rendezvous in collision-prone wireless networks. Existing researches on this topic are mainly devoted to designing channel hopping sequences, each pair of which can overlap on a common channel within bounded delay. However, this overlap-based canonical rendezvous design does not take into account channel collision, which may render existing rendezvous algorithms fail to achieve bounded delay in collision-prone environment. Motivated by this observation, we formulate and investigate the collision-aware channel rendezvous problem in a generic scenario, where a collision occurs if more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> packets overlap in time on a same channel. Our generic formulation allows to model both the baseline single packet reception model with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C=1$ </tex-math></inline-formula> and the more sophisticated multiple packet reception model with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C &gt; 1$ </tex-math></inline-formula> . We further abstract the collision-aware rendezvous problem as the problem of constructing a robust rendezvous system. We establish the theoretical limit of the problem, guided by which we design a collision-resilient distributed rendezvous algorithm with truly bounded rendezvous delay. We then demonstrate the performance of our rendezvous algorithm both analytically and numerically.