Optimal and suboptimal policies for opportunistic spectrum access: A resource allocation approach

In recent years there has been significant research in increasing efficiency of using spectrum. This concept known as smart radios or Cognitive radio has received widespread attention by companies such as Google and Motorola looking for making contracts with FCC and designing smart radios which can effectively use the unused bandwidth and spectrum in order to transmit their signals without interference with signals of primary users. In this thesis, we study several problems related to resource allocation in wireless networks through modeling and studying them as game theory and stochastic control problems. In the first problem we looked at methods for designing optimal cognitive radios which use optimal and suboptimal sensing policies in order to maximize their long-term expected reward within a finite or infinite horizon. We proved in the case that channels are bursty and user can select only one channel and probe it, the optimal policy for the radio is to use a greedy policy in probing channels and select the channel at each moment that has the highest probability of being available for transmission. In second problem we modeled resource allocation as a congestion game and studied existence of Nash equilibrium for such game. In the last problem, we studied a more general case of the first problem where primary user can select multiple channels at a time in order to sense them. Again the goal of the cognitive radio in this case is to select those channels for sensing that provide him with the highest expected reward in the respective horizon where reward comes from successfully probing a channel and transmitting through it. We summarized all results in the conclusion chapter.