Energy-Efficient Transmit Power Control for Multi-tier MIMO HetNets

In this paper, we study energy-efficient transmit power control for multi-tier multi-antenna (MIMO) heterogeneous cellular networks (HetNets), where each tier operates in closed-access policy and base stations (BSs) in each tier are distributed as a stationary Poisson point process (PPP). Each BS serves multiple users at a fixed distance away from it. We first study noncooperative energy-efficient power control, where each tier selfishly chooses its transmit power to maximize its network energy efficiency (EE). This is modeled by a noncooperative power control game. We prove the existence and the uniqueness of the Nash equilibrium of the game. Moreover, we analyze the effects of circuit power and BS densities of the tiers on their transmit power at the Nash equilibrium. Then, we investigate cooperative energy-efficient power control, where all the tiers cooperatively choose their transmit power to optimize their network EE. This cooperative power control is formulated as a multiobjective problem. To obtain Pareto-optimal solutions of the problem, we develop an algorithm that alternately updates the transmit power of the tiers. In addition to the transmit power, the circuit power consumption of the operating BSs and their active antennas affects the network EE. Due to the circuit power, activating all the BSs and turning on all the antennas may not be optimal in maximizing the network EE. Motivated by this observation, we also develop energy-efficient BS activation control and antenna activation control schemes. Finally, we extend the analysis to the highest signal-to-interference-plus-noise ratio (SINR) association, where each user connects to the BS that offers the highest SINR among the BSs in its tier. Simulation results show that the proposed energy-efficient designs significantly improve the network EE at the cost of small spectral efficiency loss compared with the spectral-efficient designs.