Optimal online strategies for an energy harvesting system with Bernoulli energy recharges

We consider an energy harvesting system where the fixed size battery of the transmitter is recharged with certain probability at each channel use. For this setup, we explicitly characterize the optimal online energy management strategy for maximizing the long-term throughput under different assumptions on the availability of channel state information. We show that in the case of no fading, the amount of energy allocated to each channel use decreases exponentially with time since the last battery recharge and in the case of fading, the optimal solution has a discounted water-filling structure. Our results reveal that the structure of the optimal energy management strategy in the online case with finite battery is significantly different from the infinite battery and offline cases characterized in the literature.