Delay-Optimal Scheduling in WPTNs with Adaptive Transmission over Fading Channels

Wireless power transfer (WPT) is an effective approach to enhance sustainability of mobile devices. In this context, we consider a system composed of a hybrid access point (HAP) that powers a wireless device (WD), provisioned with a finite energy storage and data butter. The WD uses the harvested energy to perform data transmission. We assume that both HAP and WD can perform power adaptation to save energy. Unlike most existing works, we focus on delay minimization in transmitting an arbitrary data arrival packets over wireless fading channels, which is extremely important for time-sensitive applications. Previous works mainly focused on slot-oriented optimization, where the harvested energy is consumed in the same slot, without considering the possibility of storing energy for future use. In contrast, we consider a long-term average delay minimization under average power consumption constraint at the HAP. This requires to consider the data arrival process, data and energy queue evolution, and the channel state statistics, thus, greatly increasing the optimization complexity. Our goal is to determine the optimal delay-power tradeoff and its corresponding scheduling strategy to decide the operations, e.g., data transmission by the WD and power transfer by the HAP, for arbitrary i.i.d arrival process and adaptive transmissions. Through two-dimensional Markov chain modeling and linear programming, we provide the optimal scheduling strategy. We corroborate the theoretical analysis by simulation results.