Pricing mechanisms for multi-carrier wireless systems

Multi-carrier wireless schemes and systems such as Orthogonal Frequency Division Multiplexing (OFDM), cognitive radios, and femtocells play an important role for efficient power and spectrum utilization. In uplink transmissions of these systems, independent and autonomous mobile users may act selfishly in order to get a higher share of available resources, which is encountered by a pricing mechanism that penalizes the interference they create. Specifically, the mobile users strategically decide on their power levels to minimize their cost which is the difference between their utilities based on Shannon capacity and payments. The base station acts as a mechanism designer to ensure that certain global objectives are satisfied when allocating resources. In this paper, we consider two such objectives: one is sum of user utility maximization and the other one is operator revenue maximization based on the prices charged to users, which coincidentally acts as the coupling factor between user and designer optimization problems. We analyze first the single carrier case as a starting point, which we immediately extend to multi carriers. We next formulate the operator revenue maximization problem using the same framework. Numerical simulations illustrate the mechanism developed and show the convergence of power and price levels of the users.