A new power control game in two-tier femtocell networks

In this paper, the problem of distributed power control is investigated and analyzed for two-tiered femtocell networks that share the same frequency band with the central macrocell. Femtocell users are associated with a proper utility function via pricing, which represents the ratio of user's signal-to-interference-noise ratio (SINR) and the exponential price of power consumed. Assuming a femtocell user seeks selfishly to maximize its utility function under the imposed constraints, a femtocell non-cooperative power control game (FNPC) is formulated. We prove the existence and uniqueness of the Nash Equilibrium output for the game model of power control algorithm. Numerical results show the effectiveness of pricing parameters in the penalty function to the speed of convergence and power consumed.