Maximizing lower bound of energy efficiency in multi-tier heterogeneous cellular network via stochastic geometry

Abstract

In this paper, an optimization method is proposed to maximize the lower bound of energy efficiency (EE) in the multi-tier heterogeneous cellular network (HCN) and resolved by adjusting Base Station (BS) density and BS transmit power. Firstly, we derive the mathematical formulation of network coverage probability and the average user rate. We prove that the network coverage probability and the average user rate monotonically increase with the cumulative sum of the product of BS density and BS transmit power. Then, the network coverage probability and the average user rate requirements are converted to the BS density and the BS transmit power constraints. An EE maximization problem is formulated. Nevertheless, the intractable problem is reformulated by maximizing the lower bound of EE since the coupled parameters are tight. The simplified optimization problem can be converted to a standard form of geometric programming (GP) by a convex approximation method. The problem in GP form can be further transformed into the traditional convex problem and can be fully solved using the interior point method. Numerical simulations show that the optimal solutions can be determined with fast convergence, while the network EE is significantly improved. The gap between the approximate and the original solutions is analyzed through simulations.