  A sum inverse energy efficiency (SIEE) minimization problem is solved.
Compared with conventional sum energy efficiency (EE) maximization problems,
minimizing SIEE achieves a better fairness. The paper begins by proposing a
framework for solving sum-fraction minimization (SFMin) problems, then uses a
novel transform to solve the SIEE minimization problem in a multiple base
station (BS) system. After the reformulation into a multi-convex problem, the
alternating direction method of multipliers (ADMM) is used to further simplify
the problem. Numerical results confirm the efficiency of the transform and the
fairness improvement of the SIEE minimization. Simulation results show that the
algorithm convergences fast and the ADMM method is efficient.
