Distributed optimization for cognitive radio networks using game theory

The focus of this thesis is to establish a game theoretic framework for cognitive radio (CR) wireless networks in which each user could adapt the parameters and operations according to the dynamic environment and its past experience to achieve optimal performance of itself as well as the equilibrium point of the whole network. By combining recent results in information theory, wireless network, control theory, and artificial intelligence, we establish a series of distributed learning algorithms for each user to improve its performance without causing adverse effects on others. We first introduce a simple distributed power control algorithm for the spatial spectrum sharing based multi-user CR network. In this network, maximizing the performance of the unlicensed users, called secondary users (SU), without violating the power constraints imposed by the licensed users, called primary users (PU), is a very important task. It is proved that, by using the proposed algorithm, each SU could iteratively improve its performance to approach a Nash equilibrium (NE). In addition, our setting does not require each SU to know the global channel state information as well as communicate with other SUs. It is proved that the proposed algorithm approaches to a $\epsilon$-NE at a rate of $T_\epsilon = O \left( \exp \left({1 \over \epsilon}\right)\right)$. To further improve the convergence speed, we also propose a sub-optimal algorithm which could approach a neighborhood of a NE at a speed of ${T_{\epsilon'} \over \log T_{\epsilon'}} = O \left( {1 \over \epsilon'} \right)$. We next investigate the performance of a general multi-user CR network when SUs are allowed to cooperate with each other. This work is motivated by the recent study which shows that the user cooperative network has a great potential to improve the performance of wireless networks. We derive the optimal power allocation methods for SUs under different assumptions and pricing functions. The conditions under which the optimal NE is obtained when all SUs use multi-hop relaying are discussed. Our results are extended into large multi-user CR networks with $K$ source-to-destination pairs. Two distributed algorithms are proposed. The first one is a sub-gradient based power allocation algorithm in which SUs can iteratively adjust their transmit powers to approach the payoff of a NE. The other one is a reenforcement learning based relay selection algorithm which enables each SU to iteratively search for a NE-achieving relaying scheme.DOCTOR OF PHILOSOPHY (EEE