Understanding topology dynamics in large-scale Cognitive Radio Networks under generic failures

Node failures are unavoidable in wireless networks and an initial failure may further trigger a sequence of related failures, incurring many holes in the network, which can easily result in devastating impact on network performance. To understand the size of these holes is very important to identify solutions to offset their adversarial effects. In this paper, we focus on the size of holes in Cognitive Radio Networks (CRNs) because of their phenomenal benefits in improving spectrum efficiency through opportunistic communications. Particularly, we first define two metrics, namely the failure occurrence probability p and failure connection function g(·), to characterize node failures and their spreading properties, respectively. Then we prove that each hole is exponentially bounded based on percolation theory. By mapping failure spreading using a branching process, we further derive an upper bound on the expected size of holes.