| Cognitive Radio Networks (CRNs) are becoming an important supplementary technology to current communication systems. They offer dynamic spectrum opportunities for unlicensed users and greatly improve spectrum usage efficiency. However, CRNs confront many technical challenges that limit their full utilization. In such networks, the communication quality received by each unlicensed user depends highly on the cooperation of other unlicensed users and traffic of coexisting licensed users, which is constrained by many factors such as the opportunistic availability of radio spectrum, the heterogeneous communication capability of users, the mobility of users, the difficulty in user coordination, and the failure of user devices.;We intend to understand the performance and topology of wireless CRNs in this dissertation, which will help us to utilize CRNs effectively, efficiently and reliably. We identify four fundamental performance and topology aspects to investigate, namely, the communication capacity and spectrum sensing, the tempo-spatial limits, the node mobility, and the failure resilience. The study on the first two perspectives attempts to maximize the capacity and minimize the delay of CRNs, while the study on the last two perspectives evaluates and mitigates the impact of user mobility and failure on the network topology.;Specifically, we make the following contributions toward improving the utilization of CRNs. First, we have determined the maximum throughput capacity in large CRNs and designed a new sensing algorithm to achieve the maximum throughput in the order sense. Second, we have identified the sufficient and necessary conditions that a wireless CRN is connected and determined the fastest information dissemination for both connected and non-connected CRNs. Third, we have analyzed the distribution of information dissemination latency in finite CRNs, and its scaling law as the network size grows large, when the secondary users are mobile under a general mobility framework. Last, we have characterized the spread of user failures, identified the formation and structure of Blackholes (components of failed nodes) and suggested strategies to maintain global communications in large CRNs, in the face of node failures. The work in this dissertation improves our understanding and enhances the potential applications of wireless CRNs. |
