Normalized Nash Equilibrium for Power Allocation in Femto Base Stations in Heterogeneous Network
Résumé
We consider heterogeneous networks with multiple femtocells and macrocells.
Femto-base stations (femto-BS) are constrained to allocate transmitting
powers such that the total interference at each macro-user terminal
(macro-UT) is below a given threshold. We formulate a power allocation
problem as a concave game with femto-BSs as players and multiple macro-UTs
enforcing coupled constraints. Equilibrium selection is based on the
concept of normalized Nash equilibrium (NNE) . When the interference at a
femto-user terminal (femto-UT) from adjacent femto-BSs is negligible, for
any strictly concave nondecreasing utility the NNE is unique and the NNE is
the solution of a concave potential game. We also propose a distributed
algorithm which converges to the unique NNE. When the interference is not
negligible, an NNE may not be unique and the computation of NNE has
exponential complexity . We introduce the concept of weakly normalized Nash
equilibrium (WNNE) which keeps the most of NNEs' interesting properties
but, in contrast to the latter, the WNNE can be determined with low
complexity. We show the usefulness of the WNNE concept for the relevant
case of Shannon capacity as femto-BS's utility.
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