In underlay cognitive radio networks (CRNs), the connectivity of secondary users (SUs) is difficult to be guaranteed due to the existence of primary users. Most prior studies only consider cognitive radio networks equipped with omni-directional antennas causing high interference at SUs. We name such CRNs with omni-directional antennas as Omn-CRNs. Compared with an omni-directional antenna, a directional antenna can concentrate the transmitting receiving capability at a certain direction, consequently resulting in the less interference. In this paper, we investigate the connectivity of SUs in CRNs with directional antennas (named as Dir-CRNs). In particular, we derive closed-form expressions of the connectivity of SUs of both Dir-CRNs and Omn-CRNs, thus enabling tractability. We show that the connectivity of SUs is mainly affected by two constraints: the spectrum availability of SUs and the topological connectivity of SUs. Extensive simulations validate the accuracy of our proposed models. Meanwhile, we also show that Dir-CRNs can have higher connectivity than Omn-CRNs mainly due to the lower interference, the higher spectrum availability, and the higher topological connectivity brought by directional antennas. Moreover, we also extend our analysis with considering transmission power efficiency. The simulation results show that Dir-CRNs require less transmission power to establish links than Omn-CRNs. We further investigate the throughput capacity of SUs, which is shown to heavily depend on the connectivity of SUs.
In underlay CRNs, connectivity is an important property depicting whether two nodes can establish a communication link. The connectivity of SUs in CRNs is more difficult to be ensured than that of PUs since SUs are susceptible to the existence of PUs having the higher priority to access to the spectrum than SUs. In this paper, we mainly consider the connectivity of SUs. Recently, a number of studies @cite_9 @cite_27 @cite_14 concentrate on analyzing the connectivity and delay of underlay CRNs. However, most of the studies only consider equipping both PUs and SUs with omni-directional antennas that can cause high interference due to the effect of radiating receiving signal equally in all directions. We call such CRNs equipped with omni-directional antennas only as . Take Fig. as an example. In this Omn-CRN, only one pair of SUs (i.e., SU @math and SU @math ) can establish a communication link while other SUs such as SU @math , SU @math , SU @math and SU @math cannot be active due to the existence of nearby PUs (note that the transmission region of a PU is represented by a shaded circle).
@cite_27 @cite_9 @cite_14
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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. We study the local connectivity, i.e., the node isolation probability of two coexisting wireless ad hoc networks (a primary network vs. a secondary network), where two users can communicate if the signal-to-interference ratio (SIR) at the receiver is larger than a threshold. Assuming the primary users are distributed as a Poisson point process (PPP) and the secondary users are distributed as a Matern cluster process (MCP), we investigate the impact of network parameters on the node isolation probability. Upper and lower bounds for the node isolation probability of the heterogeneous overlaid networks are presented. We also study the node isolation probability when the primary users are distributed as a MCP and the secondary users are distributed as a PPP. Numerical and simulation results indicate that the secondary users local connectivity has a performance degradation due to the heterogeneity of the secondary network, while the local connectivity is improved due to the heterogeneity of the primary network.