Optimal scheduling for energy harvesting transmitters with hybrid energy storage

We consider data transmission with an energy harvesting transmitter which has a hybrid energy storage unit composed of a perfectly efficient super-capacitor (SC) and an inefficient battery. The SC has finite space for energy storage while the battery has unlimited space. The transmitter can choose to store the harvested energy in the SC or in the battery. The energy is drained from the SC and the battery simultaneously. In this setting, we consider the offline throughput maximization problem by a deadline over a point-to-point channel. In contrast to previous works, the hybrid energy storage model with finite and unlimited storage capacities imposes a generalized set of constraints on the transmission policy. As such, we show that the solution generalizes that for a single battery and is obtained by applying directional water-filling algorithm multiple times.