Connectivity of Wireless Sensor Networks Secured by Heterogeneous Key Predistribution Under an On/Off Channel Model

TL;DR

This paper analyzes the conditions for secure connectivity in wireless sensor networks using heterogeneous key predistribution and an on/off channel model, providing theoretical results supported by simulations for finite networks.

Contribution

It introduces a combined random graph model for secure WSN connectivity and derives scaling conditions for network connectivity and absence of isolated nodes.

Findings

Connectivity can be achieved with high probability under certain parameter scalings.

Simulation results confirm theoretical predictions for finite networks.

On/off channel model approximates more complex disk models effectively.

Abstract

We investigate the connectivity of a wireless sensor network secured by the heterogeneous key predistribution scheme under an independent on/off channel model. The heterogeneous scheme induces an inhomogeneous random key graph, denoted by $\mathbb{K}(n;\pmb{\mu},\pmb{K},P)$ and the on/off channel model induces an Erd\H{o}s-R\'enyi graph, denoted by $\mathbb{H}(n,\alpha)$. Hence, the overall random graph modeling the WSN is obtained by the intersection of $\mathbb{K}(n;\pmb{\mu},\pmb{K},P)$ and $\mathbb{H}(n,\alpha)$. We present conditions on how to scale the parameters of the intersecting graph with respect to the network size $n$ such that the graph i) has no isolated nodes and ii) is connected, both with high probability as the number of nodes gets large. Our results are supported by a simulation study demonstrating that i) despite their asymptotic nature, our results can in fact be useful in designing finite-node wireless sensor networks so that they achieve secure connectivity with high probability; and ii) despite the simplicity of the on/off communication model, the probability of connectivity in the resulting wireless sensor network approximates very well the case where the disk model is used.