Energy Harvesting Multiple Access Channels: Optimal and Near-Optimal Online Policies

We consider online transmission policies for a two-user multiple access channel, where both users harvest energy from nature. The energy harvests are independent and identically distributed (i.i.d.) over time, but can be arbitrarily correlated between the two users. The transmitters are equipped with arbitrary but finite-sized batteries. We focus on the online case where the transmitters know the energy arrivals only causally as they happen. The users do not know the probability distribution of the energy arrivals; each user knows only its own average recharge rate. We consider the most general case of arbitrarily distributed energy arrivals with arbitrary correlation between the users. In order to study this general case, we first study a special case for the energy arrivals, namely, we first consider the special case of synchronized (i.e., fully-correlated) Bernoulli energy arrivals at the two users. Even though the energy arrivals are fully-correlated, average recharge rates at the users are different due to the different battery sizes. For this case, we determine the exactly optimal policies that achieve the boundary of the long-term average capacity region. We show that the optimal power allocation policy is decreasing within the renewal interval, and that the long-term average capacity region is a single pentagon. We then propose a distributed fractional power (DFP) policy, which users implement distributedly with no knowledge of the other user's energy arrival or battery state. We develop a lower bound on the performance of the DFP for synchronized Bernoulli energy arrivals. We then consider the case of two arbitrarily correlated asynchronous Bernoulli energy arrivals under the assumption of equal normalized average recharge rates. We show that extreme correlation between the energy sources hurts the achievable rate by showing that the throughput with asynchronous Bernoulli energy arrivals is larger than the throughput with the corresponding perfectly synchronized Bernoulli energy arrivals. We then show that under the DFP policy, the performance of Bernoulli energy arrivals forms a lower bound on the performance of any arbitrary energy arrivals. We also develop a universal upper bound on the performance of all online policies, 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, and hence, of the optimal policy, for all system parameters.