Centralized and Game Theoretical Solutions of Joint Source and Relay Power Allocation for AF Relay Based Network

Relaying is an emerging technique for 3G/4G high bandwidth networks in order to improve the capacity of edge nodes. As the deployment cost is high, there might be a few number of relay nodes in the cell which can help the edge nodes to transmit their data. From this perspective, one of the key problems in a relay equipped node is to make decision which edge nodes to be helped and how much power need to be disseminated among them in order to maximize the system capacity. This problem is formulated as an optimization problem given individual node and total available power constraints. The objective function of the formulated problem is non-convex, and we solve this using geometric programming (GP)-based method. Since the solution of this problem is computationally expensive, we propose a low complexity suboptimal solution. Having noticed the selfless nature of the sources in the centralized solution, we also provide a game theoretical solution. Two separate Stackelberg games are required to solve this power allocation problem. Moreover, given the total power constraint, a centralized entity is necessary to connect these two games. For assigning power among the sources, the centralized entity plays the buyer level game, whereas the sources act as power sellers. On the other hand, to disseminate relay power among the sources, roles of the players are just interchanged. Besides, before staring the game, the centralized entity determines, of total power, how much is for the transmit operation of the sources and how much is for their relay operation. We show that there is a unique Stackelberg Equilibrium (SE) for both games under certain convergence condition. Finally, the proposed game theoretical solution can achieve comparable performance in terms of resource allocation with the centralized optimal one.