Capacity of the Energy Harvesting Channel with a Finite Battery

TL;DR

This paper derives an approximate capacity formula for energy harvesting channels with finite batteries, revealing different regimes based on battery size and providing insights into optimal power control and the relation between capacity and throughput.

Contribution

It offers a simple capacity approximation for finite battery energy harvesting channels and characterizes the regimes where capacity depends on battery size and energy distribution.

Findings

Capacity approximates an AWGN channel with average power constraint in large batteries.

Battery size of about the energy harvesting maximum is sufficient for near-infinite capacity.

Capacity is within a constant gap of the long-term average throughput.

Abstract

We consider an energy harvesting channel, in which the transmitter is powered by an exogenous stochastic energy harvesting process $E_t$, such that $0\leq E_t\leq\bar{E}$, which can be stored in a battery of finite size $\bar{B}$. 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 $\bar{B}\geq \bar{E}$, the capacity is approximately equal to that of an AWGN channel with an average power constraint equal to the average energy harvesting rate, i.e. it depends only on the mean of $E_t$ and is (almost) independent of the distribution of $E_t$ and the exact value of $\bar{B}$. In particular, this suggests that a battery size $\bar{B}\approx\bar{E}$ is approximately sufficient to extract the infinite battery capacity of the system. In the small battery regime, when $\bar{B}<\bar{E}$, we clarify the dependence of the capacity on the distribution of $E_t$ and the value of $\bar{B}$. 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; 2) we characterize the approximately optimal online power control policy that maximizes the long-term average throughput of the system; 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.