  In this paper, we consider the problem of maximizing the energy efficiency
(EE) for multi-input multi-output (MIMO) interference channels, subject to the
per-link power constraint. To avoid extensive information exchange among all
links, the optimization problem is formulated as a noncooperative game, where
each link maximizes its own EE. We show that this game always admits a Nash
equilibrium (NE) and the sufficient condition for the uniqueness of the NE is
derived for the case of arbitrary channel matrices, which can be checked in
practice. To reach the NE of this game, we develop a totally distributed EE
algorithm, in which each link updates its own transmit covariance matrix in a
completely distributed and asynchronous way: Some players may update their
solutions more frequently than others or even use the outdated interference
information. The sufficient conditions that guarantee the global convergence of
the proposed algorithm to the NE of the game have been given as well. We also
study the impact of the circuit power consumption on the sum-EE performance of
the proposed algorithm in the case when the links are separated sufficiently
far away. Moreover, the tradeoff between the sum-EE and the sum-spectral
efficiency (SE) is investigated with the proposed algorithm under two special
cases: 1) low transmit power constraint regime; 2) high transmit power
constraint regime. Finally, extensive simulations are conducted to evaluate the
impact of various system parameters on the system performance.
