Node density and connectivity of multi-channel ad hoc cognitive radio networks

Node density and connectivity of large-scale multi-channel cognitive radio networks (CRNs) are studied in this paper. Current existing researches on connectivity of CRNs are mainly conducted under the assumption of one licensed channel and ignore the spectrum sensing errors. Thus, in this paper, practical assumptions such as spatially varying spectrum holes for secondary users (SUs), multiple channels licensed for the primary network, correct detection and false alarm probabilities (Pd and Pf) are considered to derive the diluted density of SUs in closed-form for the secondary network. The sensing errors of SUs and amount of licensed channels of primary users (PUs) are found to have a significant impact on the density of active SUs. Increasing density of PUs considerably reduces the node density of active SUs. Sequentially connectivity of the secondary network is investigated by applying percolation theory and complex network. The critical condition for percolation of the secondary network coexisting with primary network is then estimated analytically. We study the impacts of node density, protection radius, amount of licensed channels of the primary network on connectivity of the secondary network. It is shown that more licensed channels can loosen the condition for SUs percolation. Also, sensing errors significantly affect the connectivity of SUs. However, we found that more accurate sensing carried by SUs (larger Pd and smaller Pf) does not necessarily bring better connectivity of the secondary network.