Optimum Transmission Policies for Battery Limited Energy Harvesting Nodes (1010.6280v2)

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.

• The paper introduces optimal transmission strategies that maximize short-term throughput while ensuring energy is used efficiently within battery limits.
• It establishes a duality between maximizing throughput and minimizing transmission time for transferring a fixed data amount.
• An iterative algorithm is developed to prevent battery overflow and underutilization, significantly enhancing wireless network performance.

Optimum Transmission Policies for Battery-Limited Energy Harvesting Nodes

Introduction

The paper "Optimum Transmission Policies for Battery-Limited Energy Harvesting Nodes" by Kaya Tutuncuoglu and Aylin Yener presents a comprehensive exploration of transmission strategies for wireless networks equipped with energy harvesting capabilities and battery storage constraints. Specifically, the paper addresses the need for efficient transmission policies that consider both the intermittent nature of energy availability and the finite capacity of storage in rechargeable batteries. This work is critical in the context of next-generation wireless networks aiming for extended or perpetual operation through the utilization of renewable energy sources.

Core Contributions

The main contributions of this paper are twofold:

1. Short-Term Throughput Maximization: The authors identify the optimal transmission policy that maximizes data throughput within a finite time horizon.
2. Transmission Completion Time Minimization: A relationship is established between the aforementioned problem and the problem of minimizing the time required to transmit a given amount of data. The same methodology to solve the former can be applied to achieve optimal solutions for the latter.

Both problems were solved under the constraints of energy causality—energy cannot be used before being harvested—and battery capacity, where any excess energy harvest that exceeds the battery's capacity is lost.

Detailed Analysis

System Model and Problem Definition

The paper models a single-link continuous time system where the transmission power can be varied dynamically. The harvested energy arrives in discrete packets, and the storage is capped at a maximum capacity $E_{max}$. The transmission rate is modeled as a strictly concave, non-negative function of the transmission power, aligned with conventional power-rate functions, such as for the AWGN channel.

Throughput Maximization

The paper's first problem is to maximize the throughput given a deadline $T$. The strategy hinges on identifying feasible power levels that ensure the battery does not overflow or deplete prematurely. This involves maintaining the power level constant between energy arrivals, as theoretical analysis shows that constant-power transmission is optimal for any given consumed energy.

The authors present several lemmas that underpin the necessary conditions for an optimal policy:

• Constant power transmission within each time interval maximizes throughput.
• Battery overflow at any time instant is suboptimal.
• Transmission power should remain stable unless the battery is full or empty.
• Power level adjustments must respect energy causality constraints.
• All harvested energy must be expended by the deadline.

Combining these principles, the authors develop an iterative algorithm (A1) that calculates the longest feasible constant-power transmission interval, ensuring optimal energy utilization.

Completion Time Minimization

The second problem is to minimize the transmission completion time for a given amount of data $B$. Interestingly, the optimal solution for this problem mirrors that of the throughput maximization problem. Specifically, the paper proves that if one knows the throughput-maximizing policy for time interval $[0, T]$ that sends $B$ bits, it will also be the optimal policy for completing $B$ bits in the minimum time $T$. Conversely, the minimum-time policy for $B$ bits will transmit exactly within the interval $[0, T]$.

Numerical Results

The numerical results corroborate the analytical findings. For example, simulations show the optimal transmission policy for various deadline constraints and data sizes, verifying that the proposed algorithms match perfectly for equivalent constraints across the throughput maximization and completion time minimization problems.

In longer simulations with randomly generated energy arrivals, the optimal policy's performance was compared to simpler policies like constant power transmission and traditional (non-energy-constrained) transmission. The results illustrate that while energy constraints cause performance degradation compared to a traditional unlimited energy source, the optimal policy significantly outperforms simple heuristics like on-off transmission based on average energy harvesting rates.

Practical and Theoretical Implications

The practical implications of this research are profound for the deployment of energy-harvesting wireless systems. Efficient power control policies, as developed in this paper, can significantly extend network lifetime while maximizing data throughput, particularly important for IoT and sensor networks in remote or critical applications.

Theoretically, the paper's methodology provides a robust framework for addressing more complex multi-terminal systems. The insights obtained from the single-node model can be extended to optimize power allocations in larger network scenarios, potentially involving multiple nodes and varying energy harvesting profiles.

Future Directions

Future research could focus on developing online algorithms that accommodate stochastic energy arrivals and data demands. Furthermore, extending these models to multi-terminal or collaborative networks would be a logical next step. Such networks might include cooperative nodes, relays, and more sophisticated energy-sharing mechanisms, providing a richer field of paper.

Conclusion

This paper offers a comprehensive approach to optimizing transmission policies for energy-harvesting wireless nodes, addressing both short-term throughput maximization and transmission completion time minimization within constrained energy storage environments. The provided algorithms are shown to be optimal and significantly enhance system performance within defined constraints, laying a strong foundation for future exploration in energy-efficient wireless communications.