  Power control is becoming increasingly essential for the fifth-generation
(5G) and beyond systems. An example use-case, among others, is the
unmanned-aerial-vehicle (UAV) communications where the nearly line-of-sight
(LoS) radio channels may result in very low signal-to-interference-plus-noise
ratios (SINRs). Investigations in [1] proposed to efficiently and reliably
solve this kind of non-convex problem via a series of geometrical programmings
(GPs) using condensation approximation. However, it is only applicable for a
small-scale network with several communication pairs and practically infeasible
with more (e.g. tens of) nodes to be jointly optimized. We therefore in this
paper aim to provide new insights into this problem. By properly introducing
auxiliary variables, the problem is transformed to an equivalent form which is
simpler and more intuitive for condensation. A novel condensation method with
linear complexity is also proposed based on the form. The enhancements make the
GP-based power control feasible for both small-and especially large-scale
networks that are common in 5G and beyond. The algorithm is verified via
simulations. A preliminary case study of uplink UAV communications also shows
the potential of the algorithm.
