Fundamental limits of energy harvesting and remotely powered communication systems
Keywords: Electrical Engineering.

Energy harvesting is quickly becoming a game-changing technology for many wireless systems. The promise of self-sustaining perpetual operation opens exciting possibilities for a wide range of applications, from powering base stations in rural areas with renewable energy sources (e.g. wind or sun), to building in-body wireless networks powered by body heat or motion. However, communication with energy harvesting devices introduces a new paradigm -- energy dynamics -- into communication system design. While energy is central to the design of any engineering system, its associated dynamics so far have had minimal impact on the design of communication schemes for wireless systems. This is because conventionally, the battery and the encoder operate at two drastically different time scales, and communication can be accurately modeled as constrained only in terms of average power. In contrast, in a harvesting system, energy is continuously generated and consumed, and it is desirable for the wireless device to operate in an energy-neutral fashion where the incoming and outgoing energy processes are matched with minimal buffering in between. Moreover, due to inherent randomness in the harvesting process, the amount of energy available to the device at any given time becomes a random quantity. The communication system should now be designed by taking these random energy dynamics into account. In this thesis, we present two different formulations for studying a communication system operating under such random energy dynamics. The first formulation leads to a power control problem. It is relevant when the energy expenditure rate of the communication system needs to be adjusted over a time scale of the order of the codeword length. The optimal power control policy aims to maximize throughput under random energy availability when the transmitter is equipped with a finite energy buffer (or battery). In particular, available energy should not be consumed too fast, or transmission can be interrupted in the future due to an energy outage; on the other hand, if the energy consumption is too slow, it can result in the wasting of the harvested energy and missed recharging opportunities in the future due to an overflow in the battery capacity. This leads to an interesting online decision problem, which is in general hard to solve and requires perfect knowledge of the statistical distribution of the energy process. Instead of finding the optimal policy, we propose a simple near-optimal policy, which requires minimal information of the energy arrival statistics, and prove that its performance is universally close to optimal for all values of the problem parameters. This result also allows us to approximate the optimal performance of the system with a simple formula, which sheds some light on its qualitative behavior. Next, we extend this policy to the case where the energy arrivals process has memory, specifically a block i.i.d. structure. These results give important insights on how the throughput depends on the coherence time of the process, as well as on the other parameters. The second formulation we present is an information-theoretic model for an energy harvesting transmitter operating under random energy availability. It replaces the classical average power constraint on the encoder for an additive white Gaussian noise channel with a dynamic and random energy constraint. This leads to a peculiar state dependent channel with memory, where the state is causally known only at the transmitter. We discuss the capacity and optimal schemes for this channel, and show that the information-theoretic model is in fact closely related to the power control problem mentioned earlier. Finally, we present a novel information-theoretic model for analyzing communication systems in which the transmitter is powered remotely via wireless energy transfer. These systems differ from passive energy harvesting systems in that, in addition to designing energy-adaptive transmitter coding schemes, we must also design an efficient charging scheme for a remote charger. We derive capacity expressions for these systems, and show how they can be computed for two important special cases.