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

We investigate the connectivity of a wireless sensor network (WSN) 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 H(n; μ, K, P ) and the on/off channel model induces an Erdos-Rényi graph, denoted by H(n, α). Hence, the overall random graph modeling the WSN is obtained by the intersection of H(n; μ, K, P ) and H(n, α). 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 (whp) 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 WSNs so that they achieve secure connectivity whp; and ii) despite the simplicity of the on/off communication model, the probability of connectivity in the resulting WSN approximates very well the case where the disk model is used.