  Smooth and green future extension/scalability (e.g., from sparse to dense,
from small-area dense to large-area dense, or from normal-dense to super-dense)
is an important issue in heterogeneous networks. In this paper, we study energy
efficiency of heterogeneous networks for both sparse and dense two-tier small
cell deployments. We formulate the problem as a hierarchical (Stackelberg) game
in which the macro cell is the leader whereas the small cell is the follower.
Both players want to strategically decide on their power allocation policies in
order to maximize the energy efficiency of their registered users. A backward
induction method has been used to obtain a closed-form expression of the
Stackelberg equilibrium. It is shown that the energy efficiency is maximized
when only one sub-band is exploited for the players of the game depending on
their fading channel gains. Simulation results are presented to show the
effectiveness of the proposed scheme.
