https://hal.inria.fr/hal-01202403Ghosh, ArnobArnobGhoshUniversity of PennsylvaniaCottatellucci, LauraLauraCottatellucciEurecom [Sophia Antipolis]Altman, EitanEitanAltmanMAESTRO - Models for the performance analysis and the control of networks - CRISAM - Inria Sophia Antipolis - MÃ©diterranÃ©e - Inria - Institut National de Recherche en Informatique et en AutomatiqueNash Equilibrium for Femto-Cell Power Allocation in HetNets with channel uncertaintyHAL CCSD2015[INFO.INFO-GT] Computer Science [cs]/Computer Science and Game Theory [cs.GT]Altman, Eitan2015-09-23 10:53:202023-03-15 08:58:092015-09-25 16:47:56enConference papersapplication/pdf1We propose power allocation among femto-base stations (femto-BSs) in a heterogeneous network (HetNet) based on non cooperative games. A minimum level of quality of service has to be guaranteed at macro-user terminals (macro-UTs). Femto-BSs are unaware of the exact values of the channel parameters between them and macro-UTs because of the lack of cooperation and fading. First, we consider the design criterion where the outage probability has to be below a certain threshold at macro-UTs. The equilibrium concept is based on the Normalized Nash Equilibrium (NNE) since it caters to the distributed setting. NNE is unique only for a certain strictly concave utility functions in this case. We introduce the concept of Weakly Normalized Nash Equilibrium (WNNE) which keeps the most of the appealing features of NNE but can be extended to a wide class of utility functions and can be incorporated with low complexity. Finally, we consider the design criterion where the expected SINR at a macro-UT has to be greater than a threshold. In this case, the NNE is always unique for any strictly concave utility functions.