Power control under best response dynamics for interference mitigation in a two-tier femtocell network

Femtocell networks are about to be extensively deployed with the aim of providing substantial improvements to cellular coverage and capacity. However, their deployment is nontrivial because of the extra interference that the femtocell nodes cause to the macrocell nodes with which they share the same portion of the spectrum. This paper proposes a non-cooperative power control approach for interference mitigation in a two-tier femtocell network where the first tier is a conventional cellular network and the second tier is a set of (short-range) femtocells. We define objective functions that are different for Femtocell Mobile Nodes (FMNs) and macrocell Mobile Nodes (MNs). We then define a power control game, we prove the existence of a Nash Equilibrium (NE) for that game and we analyze the necessary and sufficient conditions so that the NE is unique. Based on the best response dynamics method, we propose a distributed iterative power control scheme that, starting from any initial power vector, converges to that NE. We simulate various scenarios that are based on realistic assumptions and topologies. Results show that, in many cases, in the NE, smooth coexistence of all entities of the topology is feasible.