  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.
