Fueled by the rapid advancement in digital and wireless technologies, the ever-increasing capabilities of wireless devices have placed upon us a tremendous challenge - how to put all of this capability to effective use. Individually, wireless devices have outpaced the ability of users to optimally configure them. Collectively, the complexity is far more daunting. Research in cognitive networks seeks to provide a solution to the diffculty of effectively using the expanding capabilities of wireless networks by embedding greater degrees of intelligence within the network itself.

In this dissertation, we address some fundamental questions related to cognitive networks, such as "What is a cognitive network?" and "What methods may be used to design a cognitive network?" We relate cognitive networks to a common artificial intelligence (AI) framework, the multi-agent system (MAS). We also discuss the key elements of learning and reasoning, with the ability to learn being the primary differentiator for a cognitive network.

Having discussed some of the fundamentals, we proceed to further illustrate the cognitive networking principle by applying it to two problems: multichannel topology control for dynamic spectrum access (DSA) and routing in a mobile ad hoc network (MANET). The multichannel topology control problem involves confguring secondary network parameters to minimize the probability that the secondary network will cause an outage to a primary user in the future. This requires the secondary network to estimate an outage potential map, essentially a spatial map of predicted primary user density, which must be learned using prior observations of spectral occupancy made by secondary nodes. Due to the complexity of the objective function, we provide a suboptimal heuristic and compare its performance against heuristics targeting power-based and interference-based topology control objectives. We also develop a genetic algorithm to provide reference solutions since obtaining optimal solutions is impractical. We show how our approach to this problem qualifies as a cognitive network.

In presenting our second application, we address the role of network state observations in cognitive networking. Essentially, we need a way to quantify how much information is needed regarding the state of the network to achieve a desired level of performance. This question is applicable to networking in general, but becomes increasingly important in the cognitive network context because of the potential volume of information that may be desired for decision-making. In this case, the application is routing in MANETs. Current MANET routing protocols are largely adapted from routing algorithms developed for wired networks.

Although optimal routing in wired networks is grounded in dynamic programming, the critical assumption, static link costs and states, that enables the use of dynamic programming for wired networks need not apply to MANETs. We present a link-level model of a MANET, which models the network as a stochastically varying graph that possesses the Markov property. We present the Markov decision process as the appropriate framework for computing optimal routing policies for such networks. We then proceed to analyze the relationship between optimal policy and link state information as a function of minimum distance from the forwarding node.

The applications that we focus on are quite different, both in their models as well as their objectives. This difference is intentional and signficant because it disassociates the technology, i.e. cognitive networks, from the application of the technology. As a consequence, the versatility of the cognitive networks concept is demonstrated. Simultaneously, we are able to address two open problems and provide useful results, as well as new perspective, on both multichannel topology control and MANET routing.

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