# Online Power Control for Block i.i.d. Energy Harvesting Channels

## TL;DR

This paper introduces an online power control policy for energy harvesting channels with block i.i.d. energy arrivals, providing bounds on performance and insights into how coherence time affects throughput and capacity approximation.

## Contribution

It proposes a simple online power control policy with a performance gap independent of parameters and analyzes the impact of energy arrival coherence time on throughput.

## Key findings

- Performance gap to optimal throughput is bounded by a constant.
- Throughput decreases as the coherence time of energy arrivals increases.
- Battery size needed to approach capacity grows linearly with coherence time.

## Abstract

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.