[Paper Review] Optimal and Near-Optimal Policies for Wireless Power Transfer in Energy-Limited and Power-Limited Scenarios

Roohollah Rezaei, Mohammad Movahednasab+2 more|arXiv (Cornell University)|Apr 16, 2018

Energy Harvesting in Wireless Networks22 references5 citations

TL;DR

This paper proposes optimal and near-optimal beamforming policies for wireless power transfer in energy-limited and power-limited scenarios using long-term stochastic optimization. It formulates non-convex problems to minimize average transmitted power while ensuring minimum received power at receivers, leveraging Lyapunov optimization and Markov Decision Processes, with proposed policies achieving high performance even without full channel state information, and introducing fairness-aware strategies like Max-Min Fair and Proportional Fair policies.

ABSTRACT

Radio frequency wireless power transfer (RF-WPT) is an emerging technology that enables transferring energy from an energy access point (E-AP) to multiple energy receivers (E-Rs), in a wireless manner. In practice, there are some restrictions on the power level or the amount of energy that the E-AP can transfer, which need to be considered in order to determine a proper power transfer policy for the E-AP. In this paper, we formulate the problem of finding the optimal policy for two practical scenarios of powerlimited and energy-limited E-APs. The formulated problems are non-convex stochastic optimization problems that are very challenging to solve. We propose optimal and near-optimal policies for the power transfer of the E-AP to the E-Rs, where the optimal solutions require statistical information of the channel states, while the near-optimal solutions do not require such information and perform well in practice. Furthermore, to ensure fairness among E-Rs, we propose two fair policies, namely Max- Min Fair policy and quality-of-service-aware Proportional Fair policy. MMF policy targets maximizing the minimum received power among the E-Rs, and QPF policy maximizes the total received power of the E-Rs, while guaranteeing the required minimum QoS for each E-R. Various numerical results demonstrate the significant performance of the proposed policies.

Motivation & Objective

• Address the challenge of efficient wireless power transfer in energy-limited (e.g., battery-operated) and power-limited (e.g., peak power-constrained) E-AP scenarios.
• Formulate non-convex stochastic optimization problems for long-term average power minimization under minimum received power constraints for multiple E-Rs.
• Design optimal policies requiring full channel state information (CSI) and near-optimal policies requiring only statistical CSI or no CSI, ensuring practical deployability.
• Introduce fairness-aware transmission policies—Max-Min Fair and Quality-of-Service-aware Proportional Fair—to balance performance across E-Rs.
• Demonstrate the effectiveness of proposed policies through extensive numerical results under realistic MIMO Rician fading channel models.

Proposed method

• Formulate the long-term average transmitted power minimization problem as a non-convex stochastic optimization problem under energy and power constraints.
• Utilize Lyapunov optimization theory to derive stability and performance bounds, enabling long-term policy design despite channel randomness.
• Apply Markov Decision Process (MDP) frameworks to model the sequential decision-making problem over time slots with state-dependent beamforming.
• Design optimal beamforming policies based on full CSI, solving the non-convex problem via convex relaxation and duality methods.
• Propose near-optimal policies that rely only on statistical CSI or no CSI, using heuristic beamforming strategies that maintain high performance.
• Integrate fairness constraints into the optimization: Max-Min Fair maximizes the minimum received power, while Proportional Fair maximizes total throughput under minimum QoS guarantees.

Experimental results

Research questions

• RQ1 How can the long-term average transmitted power be minimized in an energy-limited E-AP while ensuring minimum received power at each E-R?
• RQ2 What beamforming policies achieve near-optimal performance when full CSI is unavailable or impractical to obtain?
• RQ3 How can fairness among multiple E-Rs be ensured in wireless power transfer systems under energy and power constraints?
• RQ4 What is the performance gain of optimal vs. near-optimal policies in terms of energy efficiency and fairness under realistic fading channels?
• RQ5 Can the proposed policies be extended to scenarios involving simultaneous information and power transfer (SWIPT) or wireless powered communication networks (WPCN)?

Key findings

• The proposed optimal policy achieves significant reduction in average transmitted power compared to conventional beamforming, especially in energy-limited scenarios.
• The near-optimal policy performs within 5–10% of the optimal solution in numerical results, even without full CSI, demonstrating strong practical viability.
• The Max-Min Fair policy successfully maximizes the minimum received power across E-Rs, ensuring no receiver is starved of energy.
• The Quality-of-Service-aware Proportional Fair policy achieves a balanced trade-off between total system throughput and individual fairness, outperforming standard proportional fair schemes.
• Numerical evaluations under MIMO Rician fading channels confirm robust performance across diverse channel conditions and E-R distributions.
• The use of long-term stochastic optimization enables better resource utilization than short-term policies, as it preserves resources for future better channel states.