Understanding the tempo-spatial limits of information dissemination in multi-channel Cognitive Radio Networks

Cognitive Radio Networks (CRNs) have emerged to become promising network components for exploiting spectrum opportunistically in order that information can be delivered in circumstances otherwise impossible. Challenging yet open questions are how fast and how far a packet can be delivered in such networks, in temporal and spatial domains, respectively. The answers to these questions offer a straightforward interpretation of the potentials of CRNs for time-sensitive applications. To tackle these questions, we define two metrics, dissemination radius ∥ℒ(t)∥ and propagation speed S(d). The former is the maximum Euclidean distance that a packet can reach in time t, and the latter is the speed that a packet transmits between a source and destination at Euclidean distance d apart, which can be used to measure the transmission delay. Further, we determine the sufficient and necessary conditions under which there exist spatial and temporal limits of information dissemination in CRNs. We find that when information cannot be disseminated to the entire network, the limiting dissemination radius is statistically dominated by an exponential distribution, while the limiting information propagation speed approaches to zero. Otherwise, the dissemination radius approaches to infinity and the propagation speed S(d) is no lower than some constant k for large d. The results are validated through simulations.