Phase Transition Analysis for Underlay Heterogeneous Cognitive Radio Networks with Applications

Characterizing the topology and therefore fundamental limit is a must to establish effective cognitive radio networking (CRN). However, there lacks complete understanding of the relationship among connectivity, interference, latency and other system parameters of the underlay CRN. To clarify this complication, by employing tools from both percolation theory and stochastic geometry, we provide a novel parametrization of underlay secondary ad hoc CRN wherein the secondary network is regarded as an operating point in the phase space in both cases with and without outage constraints on secondary links. Coexisting with a primary ad hoc network, the secondary network undergoes a phase transition due to avoiding interference to primary receivers, while being interfered by primary transmitters. Furthermore, transmit power allocation of secondary users is represented by a Pareto contour in the phase space, and the impact of interference on connectivity is captured by the latency-to-percolate. Based on this proposed framework, we develop and analyze many applications on underlay secondary network, such as benefits of importing avoidance regions, self-motivated cooperation scheme, delay minimizing routing, and data dissemination with epidemic broadcasting so that CRNs can successfully operate.