Online policies for multiple access channel with common energy harvesting source

We consider online transmission policies for the two-user multiple access channel, where both users harvest energy from a common source. The transmitters are equipped with arbitrary but finite-sized batteries. The energy harvests are independent and identically distributed (i.i.d.) over time, and synchronized at the two users due to their common source. The transmitters know the energy arrivals only causally. We first consider the special case of Bernoulli energy arrivals. For this case, we determine the optimal policies that achieve the boundary of the capacity region. We show that the optimal power allocation decreases in time, and that the capacity region is a pentagon. We then consider general i.i.d. energy arrivals, and propose a distributed fractional power (DFP) policy. We develop lower and upper bounds on the performance of the proposed DFP policy for general i.i.d. energy arrivals, and show that the proposed DFP is near-optimal in that it yields rates which are within a constant gap of the derived lower and upper bounds.