Optimal status updating for an energy harvesting sensor with a noisy channel

Consider an energy harvesting sensor continuously monitors a system and sends time-stamped status update to a destination. The destination keeps track of the system status through the received updates. Under the energy causality constraint at the sensor, our objective is to design an optimal online status updating policy to minimize the long-term average Age of Information (AoI) at the destination. We focus on the scenario where the the channel between the source and the destination is noisy, and each transmitted update may fail independently with a constant probability. We assume there is no channel state information or transmission feedback available to the sensor. We prove that within a broadly defined class of online policies, the best-effort uniform updating policy, which was shown to be optimal when the channel is perfect, is still optimal in the presence of update failures. Our proof relies on tools from Martingale processes, and the construction of a sequence of virtual policies.