Connectivity and Transmission Delay in Large-Scale Cognitive Radio Ad Hoc Networks With Unreliable Secondary Links

In this paper, we investigate connectivity and transmission delay of secondary users in large-scale wireless cognitive radio (CR) ad hoc networks from a percolation-based perspective. Using the random connection model, we study the unreliability of wireless secondary links in CR ad hoc networks, which has not been well studied in the existing literature. By introducing two auxiliary random graphs and using continuum percolation theory, we study the impacts of key system parameters on connectivity and transmission delay in a CR network. We first characterize three behavioral regions of connectivity for a secondary network, i.e., disconnectivity, long-term connectivity and instantaneous connectivity regions. We show that the unreliability of secondary links does not affect the disconnectivity region, but affects the long-term connectivity and instantaneous connectivity regions. Using the ergodic theorem, we then study the scaling behavior of transmission delay with respect to the distance between two randomly chosen secondary users in a connected secondary network for two cases. Specifically, when propagation delay is negligible, we show that transmission delay scales linearly and sub-linearly with distance in the long-term connectivity and instantaneous connectivity regions, respectively. When propagation delay is considered, we show that transmission delay scales linearly with respect to distance in both the long-term connectivity and instantaneous connectivity regions.