In this thesis, we have solved the problem considering power control and time allocation in CCRN scenario. We adopt a coalitional game to analyze the cooperative behavior of players. The proposed algorithm can solve the problem considering power control and time allocation iteratively in two steps. In the first step, we allocate the the time co-efficients and the problem can be simplified as a power optimization problem. Hence, each step of the proposed algorithm is guaranteed to be convex. The time coefficients are updated with the subgradient method, which guarantees to converge to an equilibrium.
However, there are still other methods to update time coefficients, which can be consid-ered in the future work. Alternative methods for updating time coefficients can speed up the convergence of the algorithm.
In the network scenario, we consider multiple PUs and SUs based on CDMA network.
When there are multiple users in the same channel, we use spreading codes to differentiate them. Whereas, the recent protocols, e.g. LTE, are all related to the OFDMA network.
Hence, the future work can apply OFDMA network to the CCRN scenario. The most important part is the channel’s scheduling for PU’s and SU’s usage. As in [24], the system model is CCRN based on OFDMA and authors also propose an algorithm to allocate the multi-channel cooperation. While, authors adopt a Nash Bargaining Game to model the problem in [24]. We have not seen any work applying OFDMA network to the CCRN with a coalitional game. Therefore, applying OFDMA network to the CCRN in a coalitional game approach is a practical direction for future work.
Another aspect for future work is to analyze the solution concept. The solution con-cepts of a coalitional game have been proposed in many years. However, few works discuss about the convergence region of the solution concept. In this thesis, we show that proposed algorithm converges to an equilibrium and examine that the equilibrium lies in the core. Future work can analyze the region of convergence (ROC) of the core. While, we have seen [25] discussion about the ROC of the core in a linear programming game.
However, in our work, many parameters influence the ROC of the core. Hence, we can set the power levels fixed and analyze the ROC of the core in time coefficients domain.
If we can find the ROC of the core, this helps us a lot to achieve the optimal point inside the ROC. As a result, we can analyze the solution concepts of a coalitional game in many perspectives. This can helps us know more properties about the solution concepts.
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