Optimal and Near-Optimal Online Strategies for Energy Harvesting Broadcast Channels

We consider an energy harvesting broadcast channel where a transmitter powered by energy harvested from the environment serves data to two receivers on the downlink. Energy harvests occur randomly over time as an independent and identically distributed (i.i.d.) random process; the battery at the transmitter in which the harvested energy is stored is of finite size. We focus on online transmission schemes where the transmitter knows the energy arrivals only causally as they happen. We first consider the case where the energy arrivals follow a Bernoulli distribution, where the incoming energy is either zero or it fills the battery completely. For this case, we determine the optimum online strategy that allocates power over time and between users optimally. We note that the optimum total transmit power is not equal to the optimum single-user transmit power as it depends on the receiver noise variance; this is unlike the offline problem, where the optimum total transmit power in the broadcast channel equals the optimum single-user transmit power. We then consider the case of general i.i.d. energy arrivals, and propose a sub-optimum strategy coined fractional power constant cut-off (FPCC) policy. We develop a lower bound for the performance of the proposed FPCC policy. In addition, we develop a universal upper bound for the broadcast channel capacity region that depends only on the average recharge rate. We show that the FPCC policy is near-optimal in that it yields rates that are within a constant gap from the developed upper bound, and therefore, from the actual capacity region, for all system parameters.