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

## TL;DR

This paper analyzes the age of information in a two-way data exchange system with energy harvesting, optimizing the weighted average AoI to improve timeliness, and compares power-splitting and time-splitting methods.

## Contribution

It introduces a weighted-sum AoI optimization framework for energy-harvesting two-way systems and provides a numerical method for ratio computation.

## Key findings

- Power-splitting systems outperform time-splitting in timeliness.
- Gradient-based method effectively computes the optimal AoI ratio.
- Trade-off between downlink and uplink timeliness is characterized.

## Abstract

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.