Node Isolation of Secure Wireless Sensor Networks under a Heterogeneous Channel Model

TL;DR

This paper analyzes the secure connectivity of wireless sensor networks with heterogeneous key distribution and channel models, providing conditions for network connectivity with high probability as the network size grows.

Contribution

It introduces a zero-one law for the absence of isolated nodes in intersection graphs combining heterogeneous key predistribution and channel models.

Findings

Derived zero-one laws for network connectivity

Validated laws with numerical simulations

Applicable to large-scale heterogeneous sensor networks

Abstract

We investigate the secure connectivity of wireless sensor networks under a heterogeneous random key predistribution scheme and a heterogeneous channel model. In particular, we study a random graph formed by the intersection of an inhomogeneous random key graph with an inhomogeneous Erd\H{o}s-R\'enyi graph. The former graph is naturally induced by the heterogeneous random key predistribution scheme while the latter graph constitutes a heterogeneous on/off channel model; wherein, the wireless channel between a class-$i$ node and a class-$j$ node is on with probability $\alpha_{ij}$ independently. We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model so that it has no isolated node with high probability as the number of nodes gets large. We also present numerical results to support these zero-one laws in the finite-node regime.