On Topological Properties of Wireless Sensor Networks under the q-Composite Key Predistribution Scheme with On/Off Channels

TL;DR

This paper analyzes the topological properties of wireless sensor networks using the q-composite key predistribution scheme with unreliable on/off channels, providing new asymptotic results for node degrees and network connectivity.

Contribution

It extends prior work by deriving stronger asymptotic results for node degrees under the q-composite scheme for general q, including the case q=1.

Findings

Number of nodes with a certain degree converges to a Poisson distribution.

Asymptotic probability distribution for the minimum degree is derived.

Probability that the minimum degree exceeds a given value is asymptotically exact.

Abstract

The q-composite key predistribution scheme [1] is used prevalently for secure communications in large-scale wireless sensor networks (WSNs). Prior work [2]-[4] explores topological properties of WSNs employing the q-composite scheme for q = 1 with unreliable communication links modeled as independent on/off channels. In this paper, we investigate topological properties related to the node degree in WSNs operating under the q-composite scheme and the on/off channel model. Our results apply to general q and are stronger than those reported for the node degree in prior work even for the case of q being 1. Specifically, we show that the number of nodes with certain degree asymptotically converges in distribution to a Poisson random variable, present the asymptotic probability distribution for the minimum degree of the network, and establish the asymptotically exact probability for the property that the minimum degree is at least an arbitrary value. Numerical experiments confirm the validity of our analytical findings.