Age-Based Utility Maximization for Wireless Powered Networks: A Stackelberg Game Approach

Abstract

This paper investigates the efficient cooperation in wireless-powered communication networks, where an access point (AP) and multiple helpers first together charge up a sensor via radio-frequency (RF)-based wireless power transfer (WPT), and then the sensor uses the harvested energy to transmit real-time status updates to the AP. Due to the selfishness of the helpers, payment is provided as an incentive to them by the sensor-AP communication pair. For such a system, a Stackelberg game approach is designed to establish efficient cooperation between the helpers and the sensor-AP communication pair. An Age of Information (AoI)-based utility and a profit-based utility are defined for the sensor-AP pair and the helpers, respectively. Optimization problems are formulated to maximize their utilities. An explicit expression of the optimal transmit power of the helper is derived, with which a Dinkelbach's Programming (DP)-based algorithm is designed to jointly find the optimal payment price and transmit power at the AP, and at the same time, the Stackelberg equilibrium (SE) is achieved. Moreover, a closed-form expression of the minimum AoI of the system is also presented. Numerical results show that the more helpers there exist, the higher payment price the AP should fix, and meanwhile, the lower AoI of the sensor-AP communication pair can be achieved. Besides, it is shown that by increasing the transmit power at the AP, the optimal average AoI could not be reduced evidently.