Dynamic channel selection in cognitive radio consists of two main phases. The first phase is spectrum sensing, during which the channels that are occupied by the primary users are detected. The second phase is channel selection, during which the state of the channel to be used by the secondary user is estimated. The existing cognitive radio channel selection literature assumes perfect spectrum sensing. However, this assumption becomes problematic as the noise in the channels increases, resulting in high probability of false alarm and high probability of missed detection. This thesis proposes a solution to this problem by incorporating the estimated state of channel occupancy into a selection cost function. The problem of optimal single-channel selection in cognitive radio is considered. A unique approach to the channel selection problem is proposed which consists of first using a particle filter to estimate the state of channel occupancy and then using the estimated state with a cost function to select a single channel for transmission. The selection cost function provides a means of assessing the various combinations of unoccupied channels in terms of desirability. By minimizing the expected selection cost function over all possible channel occupancy combinations, the optimal hypothesis which identifies the optimal single channel is obtained. Several variations of the proposed cost-based channel selection approach are discussed and simulated in a variety of environments, ranging from low to high number of primary user channels, low to high levels of signal-to-noise ratios, and low to high levels of primary user traffic.