Approximation Theory for Connectivity of Ad Hoc Wireless Networks With Node Faults

In this letter, we propose an approximation theory for connectivity of general random geometric graphs (RGGs) with stochastic node faults, which is regarded as an abstract model of ad hoc wireless sensor networks (WSNs) with unreliable nodes. In the model, each node in an RGG is independently at fault and the disconnection probability of a resulting survival network is evaluated. The proposed approximation formula for the probability is asymptotically correct and reveals the phase transition phenomena of connectivity in the model. In addition, we obtain phase transition thresholds of a practical Rayleigh single-input single-output (SISO) model and Rayleigh multiple-input multiple-output (MIMO) model, which shows the effectiveness of the MIMO system against attenuation and random node faults. The numerical results in Rayleigh MIMO model show that the approximation formula well estimates the connection probability even for finite graphs and that it provides useful information for design of WSN immune to node faults.