Power allocation in parallel relay channels using a near-potential game theoretical approach

In this paper ¹, the problem of distributed power allocation in a two-hop relay network is solved using a game theoretical approach. We consider a scenario, where each source node sends its packets to its corresponding destination via a preassigned relay node using half-duplex Amplify-and-Forward (AF) relaying method. Each source-relay-destination triplet is considered a player in the proposed game that attempts to maximize the end-to-end transmission rate of a source-destination link by allocating the available power to the source and its designated relay. A relay network with an arbitrary number of parallel links is considered. To maximize the link throughput, a near-potential game model for distributed power allocation over the communications link is proposed. Utilizing the near-potential game approach not only reduces the complex joint optimization problem to a single multi-variable function-maximization problem, but also enables us to prove the existence and uniqueness of the equilibrium result for the general case of N parallel links. The numerical analysis demonstrates the performance of this method that approaches the cooperative solution benchmark.