On the capacity of a communication system with energy harvesting and a limited battery

We consider the problem of determining the capacity of an energy-harvesting transmitter with finite battery communicating over a discrete memoryless channel. When the battery is unlimited, or zero, the capacity has been determined, but it remains unknown for a finite non-zero battery. In this paper we assume that the harvested energy at each time, the total battery storage, and the transmitter signal energy at each time can be quantized to the same unit (i.e., the same energy interval). Under this assumption, we show that the capacity can be described using the Verdú-Han general framework. If we further assume that the transmitted symbol at each time depends only on the energy currently available, and not on the entire past history of energy harvests and symbols transmitted, then we show that the system reduces to a finite state channel (FSC) with the required ergodic and Markov properties so that lower bounds on the capacity can be readily numerically computed. We conjecture that our numerical bounds are tight. Our numerical results indicate that even the minimal possible battery storage can reap a significant fraction of the infinite battery capacity.