Auction-Based Relay Power Allocation: Pareto Optimality, Fairness, and Convergence

It is well known that a cooperative communication technique can offer significant energy saving improvements. In particular, the efficient relay resource allocation makes energy saving practically appealing. In this work, we propose an auction-based relay power allocation scheme over multi-user relay networks from the energy-efficient perspective. In particular, during the relay resource allocation operation, three major design goals are considered: 1) efficient utilization of relay resources, in terms of Pareto optimal relay power allocation; 2) insurance of competitive fairness among competing users; and 3) guarantee of distributed implementation with relaxation of restrictions on complete private knowledge and accurate assessments of convergence. Specifically, we take full advantage of the auction mechanism, i.e., competitive fairness with the incomplete private information of other nodes, to model the interaction among the users as a multi-winner auction based on the optimal bidding decision. By treating the proposed auction mechanism as a non-cooperative game, we obtain the unique and Pareto optimal Nash equilibrium (NE), which yields the optimal bidding decision and allocation of the relay power. Moreover, we design a distributed algorithm based on best-response functions to reach the NE allocation. In particular, the convergence and the convergent rate of the algorithm are analyzed quantitatively to clarify the application scenarios.