Experiments have demonstrated the temporal and spatial correlations of spectrum availability, which are of key importance in the design and analysis of cognitive radio networks. Motivated by the observation, this research applies the theory of random fields, which describes the behavior of multiple correlated random variables, to model the spectrum availabilities in time and space domains. For global spectrum activity, a homogeneous random field like Ising model is used to model the spatial correlation and analyze the performance. For local spectrum activities, Bayesian networks are used to describe the causality in spectrum and statistically infer the future spectrum situations. Furthermore, the model of controlled random fields is employed to design the networking protocols in cognitive radio networks. A low-cost spectrum sensor is designed to collect the real spectrum measurement in multiple locations simultaneously. The research promotes the understanding of frequency spectrum activities and enhances the design and analysis of the next generation cognitive radio networks. The research involves aspects of wireless communications, networking, artificial intelligence and imaging processing; thus the inter-disciplinary essence of the research also lends itself to cross-disciplinary education. Novel courses will be devised, which involve the topics of cognitive radio networks, machine learning and image processing. This project also expects to attract traditionally underrepresented groups, as well as outreach high school students.
Cognitive radio network can be considered as a society, in which each node can see (sense the spectrum), talk (communicate to neighbors) and think (compute). Hence, the cognitive radio network is modeled as a social network. The interactions among the nodes, in particular the exchange of spectrum knowledge, are analyzed. The knowledge of new good (or bad) spectrum channels is considered as epidemic propagated in the corresponding social network. The propagation procedure is modeled as random fields, either continuous time Markov process of interacting partciles or ordinary differential equations. Conclusions are obtained for the analysis and design of the knowledge propagation mechanism in cognitive radio networks. On the other hand, the emergence of primary users brings perturbations to the operation of the cognitive radio network. Then, the queuing dynamcis in the random field of cognitive radio nework will experience a transient period and then recover the equilibrium. In the project, the transient dynamcis of queuing after the perturbation of primary users are studied using the non-equilibrium statistical dynamics close to the equilibrium point. Expressions are obtained to describe how the queues in the cognitive radio nodes evolve, as well as the robustness of cognitive radio networks subject to perturbations of primary users. Finally, the futures market of spectrum is also studied for the ensemble of primar user activities, in which the spectrum market allows the purchase of future spectrum in terms of options. The dynamics of spectrum price are studied using real data traffic measurement at base stations and the volatility is tested. Option prices are obtained in closed forms.