Approximate capacity of energy harvesting communication with finite battery

We consider an energy-harvesting communication system where a transmitter powered by an exogenous energy arrival process and equipped with a finite battery communicates over a discrete-time AWGN channel. Assuming that the energy arrival process is i.i.d. Bernoulli, we provide a simple approximation to the capacity of this channel and bound the approximation gap by a constant independent of all system parameters. Our result reveals two qualitatively different regimes for the channel: in the large battery regime, the capacity depends critically on the average energy arrival rate and not so much on the exact value of the battery size; while in the small-battery regime, the capacity depends on the peakiness of the energy arrival process and is logarithmically increasing in the battery size.