[Paper Review] Finite-horizon Online Transmission Rate and Power Adaptation on a Communication Link with Markovian Energy Harvesting

Baran Tan Bacinoglu, Elif Uysal‐Biyikoglu|arXiv (Cornell University)|May 20, 2013

Energy Harvesting in Wireless Networks8 references5 citations

TL;DR

This paper proposes a low-complexity online transmission rate and power adaptation policy for energy harvesting communication systems with finite horizons and Markovian energy arrivals. By leveraging expected threshold computation based on dynamic programming insights, the policy achieves near-optimal throughput—outperforming infinite-horizon optimal policies in terms of delay-limited performance—while remaining computationally feasible for real-time implementation.

ABSTRACT

As energy harvesting communication systems emerge, there is a need for transmission schemes that dynamically adapt to the energy harvesting process. In this paper, after exhibiting a finite-horizon online throughput-maximizing scheduling problem formulation and the structure of its optimal solution within a dynamic programming formulation, a low complexity online scheduling policy is proposed. The policy exploits the existence of thresholds for choosing rate and power levels as a function of stored energy, harvest state and time until the end of the horizon. The policy, which is based on computing an expected threshold, performs close to optimal on a wide range of example energy harvest patterns. Moreover, it achieves higher throughput values for a given delay, than throughput-optimal online policies developed based on infinite-horizon formulations in recent literature. The solution is extended to include ergodic time-varying (fading) channels, and a corresponding low complexity policy is proposed and evaluated for this case as well.

Motivation & Objective

• Address the challenge of dynamic transmission rate and power adaptation in energy harvesting systems with unpredictable, time-varying energy availability.
• Formulate a finite-horizon online throughput-maximization problem under discrete power/rate adaptation and Markovian energy harvesting.
• Develop a low-complexity heuristic policy that approximates the optimal dynamic programming solution with minimal computational overhead.
• Demonstrate that the proposed policy outperforms existing infinite-horizon optimal policies in delay-constrained scenarios.
• Extend the framework to time-varying (fading) channels by introducing a dynamic expected water level computation for rate adaptation.

Proposed method

• Formulate the problem as a Markov decision process (MDP) with state space defined by stored energy, harvest state, and time-to-horizon end.
• Derive the structure of the optimal solution via dynamic programming, revealing threshold-based decision rules for rate and power selection.
• Propose an Expected Threshold (ET) policy that computes a time-varying threshold based on expected future energy and channel conditions.
• Use a water-filling-inspired approximation to compute the expected water level, which guides transmission power and rate adaptation.
• Introduce a simplified expression for the expected water level that depends on prior energy harvest expectations and channel gains.
• Extend the policy to fading channels by dynamically computing an expected water level that accounts for time-varying channel states.

Experimental results

Research questions

• RQ1 How can online transmission rate and power adaptation be optimized in a finite-horizon energy harvesting system with Markovian energy arrivals?
• RQ2 What is the structure of the optimal online policy for discrete-rate, convex power-rate functions under energy constraints?
• RQ3 Can a low-complexity heuristic closely approximate the performance of the optimal dynamic programming solution?
• RQ4 How does the performance of the proposed policy compare to infinite-horizon optimal policies in terms of throughput and delay?
• RQ5 Can the framework be extended to time-varying (fading) channels with dynamic water-level computation?

Key findings

• The proposed Expected Threshold (ET) policy achieves throughputs close to the optimal dynamic programming solution across a wide range of energy harvest patterns.
• The ET policy significantly outperforms constant-rate and greedy policies, especially when energy harvesting processes deviate from stationarity.
• For any given mean delay, the ET policy achieves higher throughput than the infinite-horizon throughput-optimal (TO) policy from prior work.
• The performance gap between the ET policy and the optimal solution remains small, even for short horizon lengths, validating its effectiveness in delay-sensitive applications.
• The expected water level approximation provides a computationally efficient way to estimate optimal transmission levels without solving the full dynamic program.
• The extension to fading channels via dynamic expected water level computation maintains strong performance, demonstrating the policy’s adaptability to time-varying conditions.