Generalized geometry-based optimal power control in wireless networks

Geometry-based optimal power control was proposed in [14] to transform the power-control problem to a new geometrical problem on the position relationship between a line and some points. This scheme provides a novel visual perspective and lowers the complexity of optimization. We generalize this scheme to a larger class of power-control optimization problems so as to maximize the network utility with multiple average and peak power constraints in wireless networks. To facilitate the handling of the geometrical model, we define a subset of geometrical models with specified characteristics, called a regular geometrical model, and derive the type of power-control problems eligible for the regular geometrical model. For such a type of problems, two strategies are proposed for the construction of the regular geometrical model. Utilizing geometrical properties, we propose a novel geometry-based optimization scheme for the general power-control problem. Its computational complexity is significantly lower than the conventional algorithms. We also provide a further discussion on irregular geometrical model cases. Finally, we provide two examples of deploying the proposed geometry-based power-control scheme.