A Stochastic Geometry Analysis of Energy-Age Tradeoff in Wireless IoT Network

We investigate an internet of things (IoT) network where the IoT devices first leverage the received power from the transmitters for harvesting energy, and then employ the harvested energy to decode the data packets. In particular, we propose a slot division scheme based on a parameter ε wherein the first phase of the slot is dedicated for energy harvesting (EH), while the second phase of the slot is dedicated for data transmission. We define a metric called the joint success probability (JSP) that jointly takes into account the event that the harvested energy exceeds an energy threshold and that the received signal to interference ratio (SIR) exceeds an SIR threshold. Deriving an exact expression for the JSP is challenging, and accordingly, we provide lower and upper bounds for the same. Based on this framework, we derive the peak age-of-information (PAoI) of the data packets. The higher the slot interval dedicated for EH, the lower will be the data transmission time, thereby requiring employment of a higher rate for a link. On the contrary, a lower slot interval allotted for the EH phase will result in the IoT devices not having sufficient energy to decode the packets successfully. We demonstrate that the optimal slot partitioning factor may be different for maximizing the JSP as compared to minimizing the PAoI. Accordingly, for different transmit powers and deployment areas, we recommend the optimal slot partitioning factor for the above two metrics.