Weighted-Sum Average Age of Information in Unilaterally Powered Two-Way Data Exchanging Systems

This paper considers a two-way data exchanging system with a constant powered access point and an energy-harvesting powered smart device. The access point simultaneously transmits information and energy to the smart device with fixed powers $\bar{\rho }{P}_{\text{t}}$ and $\rho P_{\text{t}}$, respectively. Upon collecting enough energy, the smart device performs one block of transmission immediately. We investigate the timeless of the two-way data exchange in terms of age of information (AoI). Specifically, we investigate the trade-off between downlink timeliness and uplink timeliness by optimizing the weighted-sum average AoI. Moreover, we provide a gradient based method to compute this ratio numerically. Our numerical results show that power-splitting based systems outperform time-splitting based systems in terms of timeliness in general.