  We study the problem of online power control for energy harvesting
communication nodes with random energy arrivals and a finite battery. We assume
a block i.i.d. stochastic model for the energy arrivals, in which the energy
arrivals are constant for a fixed duration $T$, but are independent across
different blocks, drawn from an arbitrary distribution. This model serves as a
simple approximation to a random process with coherence time $T$. We propose a
simple online power control policy, and prove that its performance gap to the
optimal throughput is bounded by a constant which is independent of the
parameters of the problem. This also yields a simple formula for the
approximately optimal long-term average throughput, which sheds some light on
the qualitative behavior of the throughput and how it depends on the coherence
time of the energy arrival process. Our results show that, perhaps
counter-intuitively, for a fixed mean energy arrival rate the throughput
decreases with increasing coherence time $T$ of the energy arrival process. In
particular, the battery size needed to approach the AWGN capacity of the
channel increases linearly with the coherence time of the process. Finally, we
show that our results can provide an approximation to the information-theoretic
capacity of the same channel.
