[Paper Review] Optimum Transmission Policies for Battery Limited Energy Harvesting Nodes

Kaya Tutuncuoglu, Aylin Yener|arXiv (Cornell University)|Oct 29, 2010

Energy Harvesting in Wireless Networks20 citations

TL;DR

This paper proposes optimal transmission policies for energy harvesting nodes with finite battery capacity, maximizing short-term throughput under energy causality and storage constraints. It derives an algorithm that determines the optimal power allocation to either maximize data transmitted by a deadline or minimize transmission completion time, showing equivalence between the two problems under the same constraints and proving optimality via convex optimization and dynamic programming principles.

ABSTRACT

Wireless networks with energy harvesting battery powered nodes are quickly emerging as a viable option for future wireless networks with extended lifetime. Equally important to their counterpart in the design of energy harvesting radios are the design principles that this new networking paradigm calls for. In particular, unlike wireless networks considered up to date, the energy replenishment process and the storage constraints of the rechargeable batteries need to be taken into account in designing efficient transmission strategies. In this work, we consider such transmission policies for rechargeable nodes, and identify the optimum solution for two related problems. Specifically, the transmission policy that maximizes the short term throughput, i.e., the amount of data transmitted in a finite time horizon is found. In addition, we show the relation of this optimization problem to another, namely, the minimization of the transmission completion time for a given amount of data, and solve that as well. The transmission policies are identified under the constraints on energy causality, i.e., energy replenishment process, as well as the energy storage, i.e., battery capacity. The power-rate relationship for this problem is assumed to be an increasing concave function, as dictated by information theory. For battery replenishment, a model with discrete packets of energy arrivals is considered. We derive the necessary conditions that the throughput-optimal allocation satisfies, and then provide the algorithm that finds the optimal transmission policy with respect to the short-term throughput and the minimum transmission completion time. Numerical results are presented to confirm the analytical findings.

Motivation & Objective

• To design optimal transmission policies for energy harvesting nodes constrained by finite battery capacity and energy causality.
• To maximize short-term throughput—i.e., the amount of data transmitted within a finite deadline—under energy and storage constraints.
• To establish the equivalence between throughput maximization and transmission completion time minimization under the same system parameters.
• To develop an offline algorithm that computes the optimal power allocation policy for both problems using convex optimization and dynamic programming.
• To validate the theoretical findings through numerical simulations comparing the optimal policy against greedy and traditional transmission strategies.

Proposed method

• Formulates a continuous-time transmission model with variable power control under known energy arrival times and discrete energy packets.
• Derives necessary optimality conditions using convex optimization, identifying that the optimal power allocation lies within an energy-feasible tunnel defined by cumulative energy availability and battery capacity.
• Applies dynamic programming to solve the throughput maximization problem by iteratively shifting the time horizon and checking feasibility of constant power transmission.
• Introduces a backward recursion algorithm to determine the optimal power allocation that maximizes data delivery by a deadline, ensuring energy causality and battery capacity constraints are satisfied.
• Demonstrates equivalence between throughput maximization and completion time minimization by showing identical optimal power allocation policies under dual formulations.
• Validates the algorithm numerically using synthetic energy arrival traces with uniform packet sizes and exponential inter-arrival times, comparing performance against on-off and idealized constant-power policies.

Experimental results

Research questions

• RQ1 What is the optimal power allocation policy that maximizes the amount of data transmitted by a given deadline in an energy harvesting node with finite battery capacity?
• RQ2 How does the optimal solution for throughput maximization relate to the problem of minimizing transmission completion time for a fixed data size?
• RQ3 Under what conditions does the optimal power allocation policy remain feasible when energy arrivals are discrete and battery capacity is limited?
• RQ4 Can the optimal policy be computed efficiently using dynamic programming and convex optimization techniques?
• RQ5 How does the performance of the optimal offline policy compare to simpler heuristic policies like on-off transmission under realistic energy arrival statistics?

Key findings

• The optimal transmission policy for maximizing short-term throughput under energy causality and finite battery capacity is derived using convex optimization and dynamic programming, with the solution lying within an energy-feasible tunnel defined by cumulative energy availability and storage limits.
• The optimal power allocation policy that maximizes data delivery by a deadline is identical to the policy that minimizes transmission completion time for the same data size, establishing a duality between the two problems.
• Numerical results confirm that the proposed offline algorithm significantly outperforms a greedy on-off transmission policy, especially under high variability in energy arrivals or limited battery capacity.
• The performance gap between the optimal policy and a traditional constant-power transmitter (with perpetual energy) is substantial, but the optimal algorithm recovers a major portion of this loss by leveraging knowledge of future energy arrivals.
• The algorithm achieves optimal performance by iteratively checking feasibility of constant power transmission in shifted time windows, terminating when a feasible constant power solution is found.
• The study demonstrates that optimal power allocation is most beneficial in systems with small battery capacity or large fluctuations in energy packet sizes, where simple policies fail to exploit energy availability efficiently.