  In this paper, energy efficient power control for the uplink two-tier
networks where a macrocell tier with a massive multiple-input multiple-output
(MIMO) base station is overlaid with a small cell tier is investigated. We
propose a distributed energy efficient power control algorithm which allows
each user in the two-tier network taking individual decisions to optimize its
own energy efficiency (EE) for the multi-user and multi-cell scenario. The
distributed power control algorithm is implemented by decoupling the EE
optimization problem into two steps. In the first step, we propose to assign
the users on the same resource into the same group and each group can optimize
its own EE, respectively. In the second step, multiple power control games
based on evolutionary game theory (EGT) are formulated for each group, which
allows each user optimizing its own EE. In the EGT-based power control games,
each player selects a strategy giving a higher payoff than the average payoff,
which can improve the fairness among the users. The proposed algorithm has a
linear complexity with respect to the number of subcarriers and the number of
cells in comparison with the brute force approach which has an exponential
complexity. Simulation results show the remarkable improvements in terms of
fairness by using the proposed algorithm.
