In recent years, extensive research has been devoted to opportunistically exploiting spectrum in a distributed cognitive radio network. In such a network, autonomous secondary users (SUs) compete with each other for better channels without instructions from a centralized authority or explicit coordination among SUs. Channel selection relies on channel occupancy information observed by SUs, including whether a channel is occupied by a PU or an SU. Therefore, the SUs' performance depends on the quality of the information. Current research in this area often assumes that the SUs can distinguish a channel occupied by a PU from one occupied by another SU. This can potentially be achieved using advanced signal detection techniques but not by simple energy detection. However, energy detection is currently the primary detection technique proposed for use in cognitive radio networks. This creates a need to design a channel selection strategy under the assumption that, when SUs observe channel availability, they cannot distinguish between a channel occupied by a PU and one occupied by another SU. Also, as energy detection is simpler and less costly than more advanced signal detection techniques, it is worth understanding the value associated with better channel occupancy information.

The first part of this thesis investigates the impact of different types of imperfect information on the performance of secondary users (SUs) attempting to opportunistically exploit spectrum resources in a distributed manner in a channel environment where all the channels have the same PU duty cycle. We refer to this scenario as the homogeneous channel environment. We design channel selection strategies that leverage different levels of information about channel occupancy. We consider two sources of imperfect information: partial observability and sensing errors. Partial observability models SUs that are unable to distinguish the activity of PUs from SUs. Therefore, under the partial observability models, SUs can only observe whether a channel was occupied or not without further distinguishing it was occupied by a PU or by SUs. This type of imperfect information exists, as discussed above, when energy detection is adopted as the sensing technique. We propose two channel selection strategies under full and partial observability of channel activity and evaluate the performance of our proposed strategies through both theoretical and simulation results. We prove that both proposed strategies converge to a stable orthogonal channel allocation when the missed detection rate is zero. The simulation results validate the efficiency and robustness of our proposed strategies even with a non-zero probability of missed detection.

The second part of this thesis focuses on computing the probability distribution of the number of successful users in a multi-channel random access scheme. This probability distribution is commonly encountered in distributed multi-channel communication systems. An algorithm to calculate this distribution based on a recursive expression was previously proposed. We propose a non-recursive algorithm that has a lower execution time than the one previously proposed in the literature.

The third part of this thesis investigates secondary users (SUs) attempting to opportunistically exploit spectrum resources in a scenario where the channels have different duty cycles, which we refer to as the heterogeneous channel environment. In particular, we model the channel selection process as a one shot game. We prove the existence of a symmetric Nash equilibrium for the proposed static game and design a channel selection strategy that achieves this equilibrium. The simulation results compare the performance of the Nash equilibrium to two other strategies(the random and the proportional strategies) under different PU activity scenarios.