  This paper studies the transmit power optimization in a multi-cell massive
multiple-input multiple-output (MIMO) system. To overcome the scalability issue
of network-wide max-min fairness (NW-MMF), we propose a novel power control
(PC) scheme. This scheme maximizes the geometric mean (GM) of the per-cell
max-min spectral efficiency (SE). To solve this new optimization problem, we
prove that it can be rewritten in a convex form and then solved using standard
tools. To provide a fair comparison with the available utility functions in the
literature, we solve the network-wide proportional fairness (NW-PF) PC as well.
The NW-PF focuses on maximizing the sum SE, thereby ignoring fairness, but
gives some extra attention to the weakest users. The simulation results
highlight the benefits of our model which is balancing between NW-PF and
NW-MMF.
