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Consider an energy harvesting (EH) sensor that continuously monitors a systemand sends time-stamped status update to a destination. The sensor harvestsenergy from nature and uses it to power its updating operations. Thedestination keeps track of the system status through the successfully receivedupdates. With the recently introduced information freshness metric "Age ofInformation" (AoI), our objective is to design optimal online status updatingpolicy to minimize the long-term average AoI at the destination, subject to theenergy causality constraint at the sensor. Due to the noisy channel between thesensor and the destination, each transmitted update may be erased with a fixedprobability, and the AoI at the destination will be reset to zero only when anupdate is successfully received. We first consider status updating withoutfeedback available to the sensor and show that the Best-effort Uniform updating(BU) policy is optimal. We then investigate status updating with perfectfeedback to the sensor and prove the optimality of the Best-effort Uniformupdating with Retransmission (BUR) policy. In order to prove the optimality ofthe proposed policies, for each case, we first identify a lower bound on thelong-term average AoI among a broad class of online policies, and thenconstruct a sequence of virtual policies to approach the lower boundasymptotically. Since those virtual policies are sub-optimal to the originalpolicy, the original policy is thus optimal.

Age of Information Minimization for an Energy Harvesting Source with Updating Erasures: With and Without Feedback