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Communications and Signals Design for Wireless Power Transmission

Yong Zeng, Bruno Clerckx, Rui Zhang

arXiv:1611.06822v1cs.IT

TL;DR

Radiative WPT requires designs that account for energy-transfer objectives, specialized hardware, and wireless-power channel behavior. This article surveys communication and signal-processing techniques for modeling, beamforming, channel acquisition, multi-user optimization, nonlinear waveform design, and related WPT systems, synthesizing established approaches and future research directions.

  • Problem

    Radiative WPT differs from wireless information transfer in objectives, architectures, and hardware constraints, creating design challenges for efficient wireless power supplies.

  • Method

    The article provides a tutorial overview of WPT technologies, models, communication and signal-processing techniques, optimization methods, and system-design topics.

  • Results

    The article identifies energy beamforming, channel acquisition, convex power-region optimization, nonlinear waveform design, and related techniques for enhancing or analyzing WPT systems.

  • Takeaways & Limitations

    Efficient WPT architecture design requires modeling the complete wireless power channel and optimizing the link from transmitter to rectenna output.

  • Takeaways & Limitations

    Optimal training design for general MIMO wide-band WPT systems remains an open problem.

Abstract

from arXiv · show

Radiative wireless power transfer (WPT) is a promising technology to provide cost-effective and real-time power supplies to wireless devices. Although radiative WPT shares many similar characteristics with the extensively studied wireless information transfer or communication, they also differ significantly in terms of design objectives, transmitter/receiver architectures and hardware constraints, etc. In this article, we first give an overview on the various WPT technologies, the historical development of the radiative WPT technology and the main challenges in designing contemporary radiative WPT systems. Then, we focus on discussing the new communication and signal processing techniques that can be applied to tackle these challenges. Topics discussed include energy harvester modeling, energy beamforming for WPT, channel acquisition, power region characterization in multi-user WPT, waveform design with linear and non-linear energy receiver model, safety and health issues of WPT, massive MIMO (multiple-input multiple-output) and millimeter wave (mmWave) enabled WPT, wireless charging control, and wireless power and communication systems co-design. We also point out directions that are promising for future research.

I. INTRODUCTION

Wireless power transfer includes near-field and far-field technologies, with radiative WPT enabling electrically decoupled power delivery over moderate distances. The article focuses on radiative WPT because of its potential for diverse applications and discusses its development from early experiments to contemporary systems.

  • WPT Technologies: Wireless power transfer delivers energy without interconnecting wires and includes inductive coupling, magnetic resonant coupling, electromagnetic radiation, laser power beaming, and passive energy scavenging.
  • WPT Technologies: Inductive coupling can achieve up to 90% efficiency but requires close proximity and accurate alignment, limiting concurrent charging of freely placed devices.
  • Radiative WPT: Radiative WPT is a far-field technology in which transmitter and receiver are electrically decoupled, unlike near-field magnetic coupling systems.
  • History and Applications: Radiative WPT has progressed from historical microwave demonstrations to room-scale smartphone charging and applications spanning consumer devices, aircraft, and space power systems.
  • Scope: The article concentrates on radiative WPT because it offers more diversified application potential than the other reviewed alternatives.

2) Efficiency:

Radiative WPT must improve end-to-end efficiency while supporting non-line-of-sight, moving, and broadly accessible power delivery under safety and communication constraints. The article addresses these requirements using communication and signal-processing techniques adapted to WPT’s distinct objectives and hardware models.

  • Efficiency: Radiative WPT seeks overall efficiency from a fraction of a percent to a few percent, requiring efficient DC-to-RF, directive RF transmission, and RF-to-DC conversion.
  • Efficiency: Non-line-of-sight power delivery generally requires closed-loop operation to balance power across propagation paths rather than focus on one line-of-sight direction.
  • Mobility: Supporting moving receivers requires electronically steerable arrays or MIMO to adjust beam directions without relying on mechanical antenna adjustment.
  • Networked WPT: Ubiquitous coverage requires coordinated multiple energy transmitters, while authentication and directional beamforming restrict delivery to legitimate devices.
  • Design Objective: With fixed transmitter DC-to-RF efficiency, the article focuses on maximizing receiver DC output by jointly considering RF transmission and rectification efficiency.
  • Design Challenges: Communication techniques cannot be directly transferred to WPT because their objectives, practical constraints, and receiver models differ.

II. ANALYTICAL MODEL OF THE RECTENNA

The rectenna model links incident RF signals to harvested DC power through antenna matching and diode rectification. Linear and nonlinear Taylor-series models produce different transmission-design objectives, especially when higher-order diode terms matter.

  • Rectenna Structure: A rectenna harvests ambient electromagnetic energy, rectifies and filters it, then directly powers a device or stores energy in a super-capacitor or battery.
  • Antenna Model: Perfect antenna matching transfers all available RF power to the rectifier, connecting the antenna equivalent circuit to the rectifier input.
  • Diode Model: The diode voltage is modeled as vd(t) = vin(t)−vout(t), and its characteristic is approximated by a Taylor-series expansion around a quiescent operating point.
  • Design Objective: The system objective is to maximize output DC current under a transmit RF-power constraint, despite rectifier coefficients depending on the output current.
  • Linear Model: For second-order truncation, the rectifier is linear and maximizing received RF power is equivalent to maximizing DC output under sufficiently low input power.
  • Nonlinear Model: With fourth-order truncation, rectifier nonlinearity appears through a fourth-order term, so maximizing DC output differs from maximizing received RF power alone.

III. SINGLE-USER WPT

The single-user WPT model represents multi-antenna, multi-band transmission over frequency-selective channels using transmit covariance matrices. Under linear harvesting, optimizing these matrices to maximize received RF power also maximizes harvested DC power.

  • Linear Harvesting: Under linear harvesting, constant RF-to-DC efficiency makes maximizing harvested DC power equivalent to maximizing received RF power through covariance optimization.
  • System Model: The system uses Mt transmit antennas, Mr receive antennas, and N orthogonal sub-bands, with single-band transmission as a special case.
  • Signal Model: Each sub-band carries a complex baseband signal whose bandwidth is no greater than Bs; unmodulated transmission reduces each antenna signal to a constant.
  • Channel Model: Frequency-selective propagation combines multipath gains, delays, antenna geometry, angles of departure and arrival, and carrier frequency into flat-fading sub-band channels.
  • Received Power: The MIMO channel matrix and transmit covariance matrix determine the total RF power received across the energy receiver’s antennas.
  • Energy Beamforming: Modulated WPT permits multi-beam transmission because each covariance matrix can have arbitrary rank up to Mt, unlike rank-1 unmodulated transmission.

B. Energy Beamforming

Under a linear energy-harvesting model, optimal multi-band MIMO WPT concentrates transmission on the strongest sub-bands and their dominant spatial eigenmodes, combining frequency-diversity and energy-beamforming gains.

  • Energy Beamforming: The total transmit power constraint spans all sub-bands, while Ps limits power at each sub-band and may reflect regulatory power-spectral-density restrictions.The per-sub-band limit depends on bandwidth and spectral power distribution; modulated WPT generally permits more relaxed Ps than unmodulated WPT.
  • Energy Beamforming: The power-allocation problem reduces to a linear program with an optimal solution obtained by ordering sub-bands by their maximum channel eigenvalues.The permutation satisfies λmax, ≥ λmax, · · · ≥ λmax,[N].
  • Energy Beamforming: Only the N′ strongest sub-bands are used, each at the maximum per-sub-band power Ps, while the remaining N−N′ sub-bands are unused.This result applies to frequency-selective channels under a linear energy-harvesting model.
  • Energy Beamforming: Each active sub-band uses a rank-1 covariance matrix and single-beam transmission toward the strongest eigenmode of its MIMO channel.The beam direction is selected independently of the transmission power level.
  • Energy Beamforming: The resulting design achieves both frequency-diversity and energy-beamforming gains to maximize power-transfer efficiency.Unused sub-bands may be opportunistically reused for information transmission.

C. Channel Acquisition

Channel acquisition for WPT must account for energy-receiver architecture, receiver-side processing needs, energy spent on training and feedback, and limited hardware capability.

  • Channel Acquisition: WPT beamforming gains depend critically on channel-state information at the energy transmitter.Communication-derived CSI techniques can be adapted, but WPT requires designs tailored to its distinct characteristics.
  • Channel Acquisition: Receiver-side CSI is generally unnecessary because the arriving RF signal is directly rectified into DC power without receiver signal processing.
  • Channel Acquisition: An efficient acquisition scheme should maximize net harvested energy after subtracting the energy consumed for channel training and feedback.
  • Channel Acquisition: Low-cost energy receivers may lack sophisticated channel-estimation or signal-processing capabilities, motivating simpler acquisition methods.
  • Channel Acquisition: Shared-antenna receivers support forward- and reverse-link training, whereas separate-antenna receivers enable concurrent independent energy harvesting and communication modules.The paper presents power probing with limited energy feedback for the separate-antenna architecture.

1) Forward-Link Training with CSI Feedback:

Forward-link training estimates the channel at the energy receiver and feeds CSI back to the transmitter, while reverse-link training exploits reciprocity to simplify receiver processing and reduce large-array overhead.

  • 1) Forward-Link Training with CSI Feedback:: Forward-link training sends pilots from the energy transmitter to the receiver, which estimates the channel and returns CSI over a feedback link.Feedback may use a different frequency from forward-link training and energy transmission.
  • 1) Forward-Link Training with CSI Feedback:: Reverse-link training uses channel reciprocity, with the receiver sending pilots to the transmitter for direct channel estimation and no CSI feedback generally required for harvesting.
  • 1) Forward-Link Training with CSI Feedback:: Reverse-link training reduces overhead in large or massive MIMO because its training overhead is independent of the transmitter antenna count.It also removes receiver-side channel estimation and feedback operations, but requires accurate transmitter and receiver calibration.
  • 1) Forward-Link Training with CSI Feedback:: Training design balances channel-estimation quality against receiver energy expenditure, including training power, duration, and the number of trained receiver antennas.The receiver’s training energy is prτ, and not all receiver antennas should be trained when the array is large relative to coherence time.
  • 1) Forward-Link Training with CSI Feedback:: The average harvested energy includes a beamforming-gain term from trained receiver antennas and an untrained-antenna term that is independent of transmitter antenna count.No beamforming gain is achieved over the associated untrained channels.

3) Power Probing with Limited Energy Feedback:

Limited energy feedback enables the transmitter to learn the MIMO channel from harvested-energy measurements, while alternative retrodirective methods can beamform without explicit channel estimation. Frequency-selective systems remain challenging because both spatial and frequency-domain channels must be acquired.

  • Power Probing with Limited Energy Feedback: Separate-antenna energy receivers cannot use standard pilot-training schemes because their harvesting-antenna channels cannot be directly trained through communication antennas.A limited-feedback channel-learning method was proposed to address this architectural constraint.
  • Power Probing with Limited Energy Feedback: The receiver measures harvested energy during probing intervals and returns feedback based on current and past measurements, allowing the transmitter to estimate the channel matrix.The transmitter jointly designs feedback, probing covariance matrices, and the channel-estimation procedure.
  • Power Probing with Limited Energy Feedback: With one-bit feedback, comparing consecutive harvested-energy levels produces cutting planes that iteratively restrict the set containing the channel matrix.The feasible sets form decreasing-volume polyhedrons containing the channel, whose analytic centers guide subsequent probing covariances.
  • Power Probing with Limited Energy Feedback: The ACCPM channel-learning algorithm with simple one-bit energy feedback converges to the true channel matrix as the number of training intervals increases.
  • Power Probing with Limited Energy Feedback: Retrodirective amplification provides low-complexity energy beamforming without explicit channel estimation or feedback by transmitting a phase-conjugated response toward the incident signal.Practical designs must account for amplification of both the received signal and background noise.
  • Power Probing with Limited Energy Feedback: Frequency-selective multi-antenna WPT requires estimating channels across both space and frequency; optimal training for general MIMO wide-band systems remains open.Exploiting spatial or frequency correlation to reduce training overhead also requires further investigation.

IV. MULTI-USER WPT

Multi-user WPT organizes transmitter cooperation and characterizes trade-offs among receivers through achievable power regions. Pareto-boundary points can be obtained using weighted-sum-power or power-profile optimization, with semidefinite programming providing an efficient solution route.

  • IV. MULTI-USER WPT: Multi-user MIMO WPT serves K ≥1 energy receivers through J ≥1 distributed transmitters, each with defined antenna dimensions.
  • IV. MULTI-USER WPT: CoMP-based WPT jointly designs all transmitters’ energy signals using global CSI collected and processed through coordinated backhaul and a central unit.
  • IV. MULTI-USER WPT: When full cooperation is impractical, locally coordinated WPT lets each receiver be served by fewer cooperating transmitters through transmitter-oriented or receiver-oriented association.Receiver-oriented association can give different receivers partially overlapping serving-transmitter sets.
  • Power Region Characterization: For fully coordinated transmitters, the jointly designed signals may be correlated, while each transmitter remains subject to its own power constraint.
  • Power Region Characterization: The multi-user design trades off received powers, so the power region is defined as all achievable receiver power-tuples and its Pareto boundary captures non-improvable trade-offs.
  • Power Region Characterization: Weighted-sum-power maximization and power-profile optimization characterize Pareto-boundary points under receiver weights or target power profiles.Both formulations are expressed as convex semidefinite programs that can be efficiently solved with standard optimization tools.
  • Power Region Characterization: For the single-ET case, weighted-sum-power optimization reduces to single-user WPT over an equivalent MIMO channel, whose optimum uses dominating eigenbeam transmission.

S,Q Q

Multi-beam transmission can require multiple energy beams to balance power among many receivers, but single-beam transmission with time sharing can attain the same optimal performance in the single-transmitter setting while simplifying implementation.

  • S,Q Q: As the number of energy receivers grows, the optimal covariance matrix generally has rank greater than one, requiring multiple energy beams to balance received energy.
  • S,Q Q: For a single transmitter, single-beam energy beamforming with time sharing achieves the same optimal WPT performance as optimal multi-beam transmission.
  • S,Q Q: The time-sharing strategy decomposes the optimal covariance matrix into eigenmodes and allocates fractional transmission intervals to their corresponding single-beam vectors.
  • S,Q Q: The single-beam time-sharing design preserves the received-energy performance of multi-beam transmission while requiring only one beam at each interval, simplifying transmitter power-signal design.

C. Numerical Results

The numerical results compare co-located and distributed antenna WPT systems and show how rectifier non-linearity changes waveform and power-allocation strategies. They also identify channel acquisition, frequency selectivity, and energy-outage characterization as open directions.

  • Antenna Distribution: 45.4µW versus 42.4µW: the distributed antenna system achieves slightly higher max-min received power than the co-located system.The comparison uses nine equally spaced single-antenna ETs versus one nine-antenna ULA, with transmission optimized for the minimum received power of two ERs.
  • Antenna Distribution: Distributed antennas produce a more even spatial power distribution and can potentially mitigate the co-located system’s near-far problem.The co-located system mainly beams toward the ER directions, whereas the distributed system shows no evident focusing direction.
  • Nonlinear Waveform Design: The nonlinear rectifier model makes multiple-sinewave transmission beneficial, whereas the linear model finds no benefit from allocating power across multiple sinewaves in frequency-flat channels.The fourth-order term is strongly affected by the number of sinewaves and power allocation, unlike the second-order term.
  • Nonlinear Waveform Design: The fourth-order contribution to zDC increases linearly with N in frequency-flat channels, and achieving the same scaling in frequency-selective channels requires CSIT.With multiple transmit antennas and multisine transmission, the fourth-order term is also reported to scale with antenna-related factors.
  • Nonlinear Regime: At −20 dBm average input power, nonlinearity is not negligible for most N; at −30 dBm, it is negligible for N below roughly 20.The cited example uses typical rectifier parameters and notes that −30 dBm is very small for state-of-the-art rectifiers.
  • Waveform Assumptions: Deterministic multisine weights are required for the reported linear increase with N; random modulation removes that fourth-order scaling advantage.The second-order term remains unaffected by modulation, so the distinction arises from the nonlinear fourth-order contribution.
  • Adaptive Waveform Design: Depending on CSI, allocating power over two sinewaves can maximize output DC current even when a single sinewave maximizes RF-to-RF efficiency.The results therefore motivate CSIT acquisition for adaptive waveform design targeting end-to-end efficiency e2 × e3.

B. Waveform Design

Waveform design for nonlinear WPT uses channel-aware spatial beamforming and frequency allocation, while practical constraints couple these choices and can make optimization computationally difficult.

  • The multisine design selects deterministic complex weights across frequencies to maximize rectifier DC output when channel frequency responses are known.
  • Channel-matched phases make each frequency component arrive in phase, after which amplitudes are optimized through reverse geometric programming and successive convex approximation.
  • With multiple transmit antennas, maximal-ratio transmission can first form a spatial beamformer, reducing the remaining task to frequency power allocation over an effective channel.
  • In the large-antenna limit, channel hardening makes uniform frequency power allocation attractive, offering lower waveform-design complexity.
  • PAPR constraints create a trade-off because higher PAPR benefits energy collection but reduces power-amplifier efficiency and prevents space-frequency decoupling.
  • Multiple rectennas couple phase and magnitude optimization, so fixing an initial phase has no guarantee of producing the optimum solution.
  • Reverse geometric programming supports arbitrary Taylor-expansion order but has exponential complexity for large numbers of antennas, sinewaves, or rectennas.

C. Performance Evaluations

The evaluations use a measured rectenna and a WiFi-like channel to compare linear single-sinewave adaptation with nonlinear model-based multisine optimization.

  • The rectenna evaluation uses four sinewaves centered at 5.18GHz with 1MHz bandwidth and −20dBm available RF input power.
  • The matching network is adapted through iterative impedance measurements because diode impedance varies with input power and operating frequency.
  • The point-to-point simulation models a 5.18GHz, 36dBm-transmit-power link with 58dB path loss and average received power of −20dBm.
  • Adaptive Single Sinewave concentrates power on the strongest channel frequency, whereas Adaptive OPT optimizes DC output using a 4th-order nonlinear model.
  • The nonlinear model-based design achieves significant and increasing gains over the linear counterpart as the number of sinewaves grows, showing that rectifier nonlinearity is not negligible.

D. Extension and Future Work

The paper identifies open problems in spectrum-efficient waveform design, channel acquisition, computational complexity, and integrating WPT with communication systems.

  • A central open question is how to use a fixed bandwidth B to maximize output DC power and establish a foundational theory for WPT spectrum use.
  • Whether WPT should use deterministic or modulated waveforms remains unresolved because the choice affects the tradeoff between information and power transmission.
  • CSI acquisition and feedback remain serious challenges, and it is unclear whether linear-model approaches extend to the nonlinear wireless power channel.
  • Practical implementation requires low-complexity alternatives whose performance approaches reverse-GP designs without computationally intensive optimization.
  • Rectifier nonlinearity gives WPT waveform design direct consequences for SWIPT, wireless-powered communications, and backscatter communications.

A. Safety and Health Issues

WPT design must address RF exposure, large-array hardware costs, blockage sensitivity, charging control, and joint energy-information transmission.

  • Safety and Health Issues: RF exposure is assessed using SAR, which measures absorbed energy rate in W/kg, and MPE, which specifies permissible power density in W/m2.
  • Safety and Health Issues: Highly directional beamforming can create localized RF hot spots, requiring either compliance everywhere or restricted access to non-intended serving areas.
  • Massive MIMO and MmWave WPT: Massive MIMO can enhance end-to-end power-transfer efficiency through large energy-transmitter arrays when CSI is perfect.
  • Massive MIMO and MmWave WPT: mmWave WPT permits compact large arrays but remains sensitive to blockages because mmWave signals have poor penetration and diffraction.
  • Massive MIMO and MmWave WPT: Large-array WPT makes one-RF-chain-per-antenna digital processing costly in hardware and power consumption, motivating analog, hybrid, and lens-array approaches.
  • Wireless Charging Control: Large WPT networks need charging control for scheduling, frequency use, association, activation, and transmit power while avoiding both energy outage and battery overflow.
  • Wireless Power and Communication Co-design: SWIPT, wireless-powered communications, and coexistence designs jointly use RF waveforms for energy and information transmission.
  • Wireless Power and Communication Co-design: Strong power signals can saturate information receivers, while lens arrays offer one approach to separate energy and information in the antenna domain.
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