Powers Maximizing Proportional Fairness Among Poisson Bipoles
Nithin S. Ramesan, François Baccelli · 2019
This paper uses Poisson geometry to define a power control mechanism for large mobile ad hoc networks. It considers a homogeneous Poisson bipole network on the Euclidean plane. Bipoles, which represent transmitter-receiver pairs, adapt their power in a local and distributed way. The common aim of the bipoles is to maximize network wide proportional fairness. The mechanism is based on a heuristic which consists of simplifying the interference field seen by each receiver to its dominant term. This max-interference approximation decomposes the global (and infinite dimensional) optimization problem into a collection of finite problems involving the so called descending chains of the Poisson nearest neighbor graph. In addition, in the Rayleigh fading and interference limited case, the problem further factorizes into a collection of pairwise optimization problems with closed form solution. The properties of this power control mechanism are studied both analytically and by discrete event simulation. Significant performance gains are seen despite these approximations, for the motivating metric and other metrics.