Online Fixed Fraction Policies in Energy Harvesting Communication Systems

We consider power scheduling policies for single-user energy harvesting communication systems, where the goal is to characterize online policies that maximize the long term average utility, for general concave and monotonically increasing utility functions. The transmitter relies on energy harvested from nature to send its messages to the receiver, and is equipped with a finite-sized battery to store its harvested energy. Energy packets are independent and identically distributed (i.i.d.) over time slots, and are revealed causally to the transmitter. We first characterize the optimal solution for the case of Bernoulli arrivals. Then, for general i.i.d. arrivals, we first show that fixed fraction policies, in which a fixed fraction of the battery state is consumed in each time slot, are within a constant multiplicative gap from the optimal solution for all energy arrivals and battery sizes. We then derive a set of sufficient conditions on the utility function to guarantee that fixed fraction policies are within a constant additive gap as well from the optimal solution. We then apply these results to a specific scenario where a sensor node collects samples from a Gaussian source and sends them to a destination node over a Gaussian channel, and the goal is to minimize the long term average distortion of the source samples received at the destination. We study two problem settings for this case: the first is when sampling is cost-free, and the second is when there is a sampling cost incurred whenever samples are collected. For the problem with sampling costs, the transmission policy can be bursty; the sensor may collect samples and transmit for only a portion of the time. Finally, we present an alternative analysis approach that is more tailored to these distortion problems to show that fixed fraction policies achieve an additive gap that is independent of the sampling cost.