Finite-horizon optimal transmission policies for energy harvesting sensors

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In this paper, we derive optimal transmission poli- cies for energy harvesting sensors to maximize the utility obtained over a finite horizon. First, we consider a single energy harvesting sensor, with discrete energy arrival process, and a discrete energy consumption policy. Under this model, we show that the optimal finite horizon policy is a threshold policy, and explicitly characterize the thresholds, and the threshold sc an be precomputed using a recursion. Next, we address the case of multiple sensors, with only one of them allowed to transmit at any given time to avoid interference, and derive an explicit optimal policy for this scenario as well. I. INTRODUCTION the throughput obtained is concave in the energy spent. For the special case when the throughput obtained in linear in the energy spent, the authors derive a closed-form optimal policy. For the energy harvesting case, maximizing a time-average utility function over an infinite horizon is considered in (4). Under a Bernoulli energy arrival, and binary energy expendi- ture model, the authors show that the optimal policy is of the threshold form, with the threshold values being monotonically decreasing in the energy available. However, an explicit char- acterisation of the thresholds was not possible. In a closely related paper (5), the authors derive structural propertie ss uch as monotonicity for an infinite horizon discounted reward Markov decision process. Similar properties are established for the finite horizon case in (6). Another recent paper (7) proposes computationally simple control policies based on heuristics that achieve near-optimal performance in the finite- horizon case with a finite battery. Finally, (8), (9) take a queue stability view of energy harvesting networks, using Lyapunov optimization techniques. Contributions: In the present paper, we derive optimal transmission policies for energy harvesting nodes to maximize au tility function over a fi nite horizon. The utility function is assumed to be a monotonic increasing function of the energy used by the node. First we consider a single node case, where the node is allowed to transmit any discrete quantum of available energy, under a general energy burst arrival model. We show that the optimal transmission policy is of the threshold form, and we also explicitly characterize the threshold values, where the thresholds can be computed using ar ecursion. Next, we show that for ac ase with more than one energy harvesting node, the same results can be derived, although the structure becomes more cumbersome.