Age of Information for Partial Earliest Relay Aided Short Packet Status Update With Energy Harvesting

Abstract

This paper focuses on the timely delivery of status updates for a multi-relay assisted energy harvesting (EH) Internet of Things system with short packet communications (SPC), where an EH-powered source transmits status updates to a destination with the aid of multiple EH-powered relays. To improve the energy efficiency and information freshness, an earliest-ℓ partial relay selection scheme is proposed, in which the earliest ℓ relays that successfully receive the status update from the source will be selected to forward the status update to the destination, and the selection combining (SC) and maximal-ratio combining (MRC) schemes are used at the destination. Firstly, we investigate the update packet delivery schemes of source-relay (S-R) and relay-destination (R-D) links, and present the packet error probabilities under the SC and MRC schemes based on SPC theory. Secondly, after characterizing the full charge time durations of both the source and relay, we investigate the statistical description of the number of the packet transmission attempts from the source to relay as well as the one from the relay to destination by using order statistics. With the analysis of the evolution of the instantaneous age of information (AoI), the expression for average AoI is derived. Finally, we investigate the average AoI minimization, which is formulated as a coupled triplet problem of the packet lengths at the source and relays and the value of ℓ. To overcome the coupling, we present the convexity approximation of the average AoI as well as the concise proof. Then, an efficient gradient-based two-step optimal search algorithm is proposed to solve the optimization problem, which searches the local optimal packet lengths for S-R and R-D links by iteratively updating the value of ℓ until the global optimal objective parameters are found. Numerical analyses give the effect of the key parameters on the average AoI, and the comparison demonstrates that the proposed gradient-based method converges quickly than the conventional greedy search method.