Optimal Power Management for Remote Estimation with an Energy Harvesting Sensor

This paper studies the design of an estimation system where a remotely observed source sequence is to be communicated through a noisy channel to an estimator. The remote node is assumed to have the capability of harvesting, and, subject to a capacity limit, storing energy from its ambient environment. The focus is on various transmit power-allocation strategies that minimize the mean square error at the estimator for such an energy harvesting estimation system as the fluctuation of harvested energy presents a unique challenge compared with a traditional battery powered system. We first establish the optimality of uncoded transmission for such a system. Two types of side information (SI) at the transmitter are then considered in this paper: noncausal SI (energy harvested in the past, present, and future) and causal SI (energy harvested in the past). For the case where noncausal SI is available and battery storage is unlimited, it is shown that the optimal power allocation amounts to a simple "staircase-climbing" procedure, where the power level follows a nondecreasing staircase function. For the case where battery storage has a finite capacity, the optimal power-allocation policy can also be obtained via standard convex optimization techniques. Dynamic programming (DP) is used to optimize the allocation policy when only causal SI is available. The issue of unknown transmit power at the receiver is also addressed for both the causal and noncausal SI cases. Finally, to make the proposed solutions practically more meaningful, two heuristic schemes are proposed; these schemes are largely motivated by the structure of the solution to the DP formulation but with much reduced computational complexity. Numerical examples are provided to examine the complexity-performance tradeoff of various power-allocation strategies.