Capacity of the Energy-Harvesting Channel With a Finite Battery
We consider an energy harvesting channel, in which the transmitter is powered by an exogenous stochastic energy harvesting process Et, such that 0 ≤ Et ≤ E̅, which can be stored in a battery of finite size B̅. We provide a simple and insightful formula for the approximate capacity of this channel with bounded guarantee on the approximation gap, independent of system parameters. This approximate characterization of the capacity identifies two qualitatively different operating regimes for this channel: in the large battery regime, when B̅ ≥ E̅, the capacity is approximately equal to that of an additive white Gaussian noise channel with an average power constraint equal to the average energy harvesting rate, i.e., it depends only on the mean of Et and is (almost) independent of the distribution of Et and the exact value of B̅. In particular, this suggests that a battery size B̅ ≈ E̅ is approximately sufficient to extract the infinite battery capacity of the system. In the small battery regime, when B̅ <; E̅, we clarify the dependence of the capacity on the distribution of Et and the value of B̅. There are three steps to proving this result, which can be of interest in their own right: 1) we characterize the capacity of this channel as an n-letter mutual information rate under various assumptions on the availability of energy arrival information: causal and noncausal knowledge of the energy arrivals at the transmitter with and without knowledge at the receiver; 2) we characterize the approximately optimal online power control policy that maximizes the long-term average throughput of the system; and 3) we show that the information-theoretic capacity of this channel is equal, within a constant gap, to its long-term average throughput. This last result provides a connection between the information- and communication-theoretic formulations of the energy harvesting communication problem that have been so far studied in isolation.