Approach for power allocation in two-tier femtocell networks based on robust non-cooperative game

In this study, a power allocation scheme for two-tier femtocell networks is proposed to maximise the user utilities constrained with satisfactory quality of service, where femtocell users share the same frequency with macrocell users (MUEs). Since the environment changes and the channel gains cannot be assumed to be constants, a worst-case method is used to address the uncertainty of the power allocation problem. A non-cooperative game model is developed to maximise the utilities of femtocell users by letting the users competing the utilities with others. As the robustness can be affected by the changing gains of communication links, the robust Stackelberg game is proposed to model this hierarchical competition where the MUEs and femtocell users act as leaders and followers, respectively. Two effective pricing schemes are applied to maximise the utilities, when different user demands are required, where the uniqueness of Nash equilibrium is proved in the two schemes. Numerical results show the convergence of the Stackelberg game with uncertainty and also the results demonstrate the effectiveness of the power allocation algorithm.