Phase Transition Diagram for Underlay Heterogeneous Cognitive Radio Networks

Characterizing the topology and therefore fundamental limits is a must to establish effective end-to-end cognitive radio networking (CRN). However, there lacks complete understanding of the relationship among connectivity, interference, latency and other system parameters of the CRN. To clarify this complication, by employing tools from both percolation theory and stochastic geometry, we thus provide a novel parametrization of underlay secondary ad hoc CRN wherein the secondary network is regarded as an operating point in the phase space. 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. Finally, with the cognitive capability of CR, performance improvement of importing an SU- avoidance region around primary receivers is analyzed, and CRNs can be therefore successfully supplied.