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Fundamentals of Wireless Information and Power Transfer: From RF Energy Harvester Models to Signal and System Designs

Bruno Clerckx, Rui Zhang, Robert Schober, Derrick Wing Kwan Ng, Dong In Kim, H. Vincent Poor

arXiv:1803.07123v1cs.ITeess.SP

TL;DR

Wireless information and power transmission requires signal and system designs that account for energy-harvester behavior, but integrating communication and power introduces broad unresolved challenges. This tutorial compares linear and nonlinear harvester models and shows that the underlying model determines WIPT rate-energy regions and designs. Its central conclusion is that WIPT performance depends crucially on exploiting the appropriate energy-harvester model.

  • Problem

    Integrating wireless communication and power creates unresolved cross-disciplinary challenges in designing networks that convey information and energy together.

  • Method

    The paper characterizes linear and nonlinear energy-harvester models and reviews their implications for WIPT architectures, waveforms, modulation, beamforming, distributions, and resource allocation.

  • Results

    WIPT rate-energy regions and signal designs differ across harvester models, with properly exploiting diode nonlinearity enlarging the achievable region over a linear-model design.

  • Takeaways & Limitations

    WIPT design should be tied to the underlying energy-harvester model because harvester nonlinearity can create rate-energy tradeoffs and improve performance when exploited.

  • Takeaways & Limitations

    Accurate harvester modeling remains scope-limited because dynamic input power and signal variation can prevent guaranteed impedance matching.

Abstract

from arXiv · show

Radio waves carry both energy and information simultaneously. Nevertheless, Radio-Frequency (RF) transmission of these quantities have traditionally been treated separately. Currently, we are experiencing a paradigm shift in wireless network design, namely unifying wireless transmission of information and power so as to make the best use of the RF spectrum and radiations as well as the network infrastructure for the dual purpose of communicating and energizing. In this paper, we review and discuss recent progress on laying the foundations of the envisioned dual purpose networks by establishing a signal theory and design for Wireless Information and Power Transmission (WIPT) and identifying the fundamental tradeoff between conveying information and power wirelessly. We start with an overview of WIPT challenges and technologies, namely Simultaneous Wireless Information and Power Transfer (SWIPT),Wirelessly Powered Communication Network (WPCN), and Wirelessly Powered Backscatter Communication (WPBC). We then characterize energy harvesters and show how WIPT signal and system designs crucially revolve around the underlying energy harvester model. To that end, we highlight three different energy harvester models, namely one linear model and two nonlinear models, and show how WIPT designs differ for each of them in single-user and multi-user deployments. Topics discussed include rate-energy region characterization, transmitter and receiver architecture, waveform design, modulation, beamforming and input distribution optimizations, resource allocation, and RF spectrum use. We discuss and check the validity of the different energy harvester models and the resulting signal theory and design based on circuit simulations, prototyping and experimentation. We also point out numerous directions that are promising for future research.

I. INTRODUCTION … C. The Crucial Role of Energy Harvester Modeling

WIPT unifies wireless information and power transmission, motivated by the shared RF medium and the need to balance communication and energy delivery. The paper surveys WIPT architectures and shows that signal and system designs fundamentally depend on whether the energy harvester is modeled linearly or nonlinearly.

  • I. INTRODUCTION: WIPT combines communication and power delivery over the same RF spectrum and infrastructure, bridging the communication-only and power-only extremes.This integration creates challenges spanning communication, information, circuit, RF, signal-processing, protocol, optimization, prototyping, and experimental disciplines.
  • A. Overview of WIPT Challenges and Technologies: WIPT systems must address range, efficiency, and line-of-sight or non-line-of-sight operation while delivering power over practical 5–100 m distances.The broader engineering requirements include multiple additional network and implementation challenges discussed in the paper.
  • A. Overview of WIPT Challenges and Technologies: The paper distinguishes SWIPT, WPCN, and WPBC according to downlink/uplink roles, receiver organization, and whether backscatter modulation supplies the uplink transmission.WPBC tags avoid carrier-generating oscillators and therefore can consume orders of magnitude less power than conventional radios.
  • B. Objectives and Organization: The paper systematically characterizes the fundamental rate-energy tradeoff and develops signal and system designs for jointly conveying information and energy wirelessly.Its scope covers transmitter and receiver architectures, waveform and modulation design, beamforming, input distributions, resource allocation, and RF spectrum use.
  • B. Objectives and Organization: WIPT designs revolve around the energy harvester model: the paper compares one linear and two nonlinear models and shows that changing the model radically changes the resulting designs.The article emphasizes this modeling dependence because earlier WIPT reviews largely rested on an unexamined linear harvester assumption.
  • C. The Crucial Role of Energy Harvester Modeling: Earlier WIPT analyses treated RF-to-DC conversion as constant and optimized separable DC-to-RF, RF-to-RF, and RF-to-DC stages, thereby decoupling RF and signal design.Those assumptions included unit DC-to-RF efficiency and a linear relation between input RF power and output DC power.
  • C. The Crucial Role of Energy Harvester Modeling: Circuit simulations and measurements show that RF-to-DC efficiency depends nonlinearly on input signal power and shape, so maximizing each transfer stage separately need not maximize end-to-end efficiency.This motivates nonlinear harvester models and signal designs that account directly for waveform-dependent energy conversion.

II. ANALYTICAL MODELS FOR THE RECTENNA · A. Rectenna Behavior · B. The Antenna Model

The rectenna converts captured RF energy into DC power, but its efficiency depends strongly on rectifier design, received power, and waveform shape because circuit nonlinearities and practical losses complicate modeling. The antenna model assumes a lossless, perfectly matched interface that transfers available RF power to the rectifier while neglecting harvestable antenna noise.

  • II. ANALYTICAL MODELS FOR THE RECTENNA: Rectennas combine an antenna, rectifier, low-pass filter, and power-management unit to convert RF energy into usable or stored DC power.Recovered power can directly supply low-power devices, charge batteries or supercapacitors, or pass through a DC-to-DC converter.
  • A. Rectenna Behavior: Rectifier efficiency decreases with distance and input power, reaching 50% at 1m, 25% at 10m, and about 5% at 30m under the stated 915MHz conditions.Reported efficiency also falls from 80% at 10 mW to 2% at 1 µW because diodes become difficult to turn on at low input power,.
  • A. Rectenna Behavior: For a simulated single-series rectifier, efficiency is about 2% at 1µW, 15% at 10µW, and 35% at 100µW, then drops sharply beyond 1mW as DC output saturates.The diode becomes reverse biased at 2V, while multiple-diode rectifiers are preferred above 1mW to avoid saturation,,.
  • A. Rectenna Behavior: RF-to-DC efficiency depends on signal shape as well as average power: high-PAPR multisine waveforms create larger peaks and can improve charge-pump efficiency and RFID-reader range [41],.This dependence makes waveform design relevant to energy-harvesting performance rather than treating the rectifier as a constant-efficiency device.
  • A. Rectenna Behavior: Rectenna modeling is challenging because resistors, capacitors, and diodes introduce nonlinearities, while threshold and reverse-breakdown voltages, parasitics, impedance mismatch, and harmonics cause implementation losses,,,.Detailed multistage circuit models can become analytically intractable for signal and resource-allocation optimization.
  • A. Rectenna Behavior: The analytical framework therefore introduces diode linear and nonlinear models driven by diode physics, while recognizing that exact circuit input-output descriptions may be too complex for tractable optimization.The model choice determines how rectenna behavior can be represented in subsequent signal and resource-allocation designs.
  • B. The Antenna Model: The antenna is modeled as a voltage source v_s(t) with series resistance R_ant; under perfect matching, available RF power is transferred to and absorbed by the rectifier, with antenna noise neglected.The simplified treatment assumes R_in = R_ant and X_in = 0; a more general resistance model is noted in.

C. The Diode Linear and Nonlinear Models

The section develops linear and nonlinear diode-based rectifier models by Taylor-expanding the diode characteristic and shows that WIPT signal optimization depends on whether higher-order terms are negligible. The linear model is appropriate in the square-law regime, whereas the nonlinear model captures waveform-, power-, and modulation-dependent RF-to-DC efficiency in the transition regime.

  • Model formulation: A Taylor expansion around the diode’s quiescent operating point yields a tractable rectifier model whose averaged diode current captures both DC output and randomness from modulated RF inputs.The model starts from a single series diode, low-pass filter, and load, but also applies to more general multi-diode rectifiers.
  • Linear model: The diode linear model truncates at second order, making optimal transmit design equivalent to maximizing average RF input power because conversion efficiency is constant and signal-independent.This model was introduced in and adopted in early WIPT works, with higher-order terms assumed negligible.
  • Operating regimes: The linear model applies in the square-law regime below -20dBm for continuous waves, but multisine inputs shift its validity toward below -30dBm, where higher-order terms remain negligible,,.Such very low power levels are also below the operating range of state-of-the-art rectifiers.
  • Nonlinear model: The nonlinear model retains fourth- or higher-order terms, so maximizing harvested DC power is no longer equivalent to maximizing average RF input power and efficiency depends on waveform shape, power, and modulation format,.The model is a memoryless polynomial form used in WPT, –, SWIPT, –, and WPBC,.
  • Model limitations: The Taylor-series model is valid only in the diode’s nonlinear operating region; at large input amplitudes, series resistance dominates and the diode behaves linearly in region R3.The transition region for the nonlinear model spans approximately −20 to 0 dBm for continuous waves and can shift to [−30, −10]dBm for multisine inputs.

D. The Saturation Nonlinear Model

The saturation nonlinear model captures rectifier output-power saturation caused by diode breakdown and represents harvested power with a tractable, measurement-fitted sigmoid of received RF power. It matches practical circuits in the high-power regime, while both it and the conventional linear model show discrepancies at low power.

  • D. The Saturation Nonlinear Model: The model describes output DC-power saturation beyond a threshold when excessive input RF power drives the rectifier toward diode breakdown.Breakdown occurs under reverse bias above the voltage VBR and causes a sudden opposite-direction current; rectifiers should avoid this operating region.
  • D. The Saturation Nonlinear Model: A tractable parametric model proposed in fits practical energy-harvesting measurements for a predefined waveform using only average received RF power.This formulation separates SWIPT resource allocation from circuit-specific implementation and waveform-distribution details.
  • D. The Saturation Nonlinear Model: The harvested-power response is modeled as a sigmoid whose PSat is the saturation ceiling, while a controls charging steepness and b sets the minimum turn-on voltage.Parameters a, b, and PSat can be obtained by curve fitting measurements from a given hardware circuit and adopted waveform.
  • D. The Saturation Nonlinear Model: In the high-power regime Prf ≥ −10 dBm = 10−1 mW, the model closely matches measurements from two practical circuits, unlike the conventional linear model.Fig. 8 compares the proposed model with continuous-wave measurement data from and.
  • D. The Saturation Nonlinear Model: At low received RF power, both the conventional linear model and the saturation nonlinear model exhibit discrepancies with practical energy-harvesting behavior.The saturation model has nevertheless been widely adopted for resource-allocation algorithm design, including –.

E. Comparisons of The Rectenna Models … A. Signal and System Model

The paper compares rectenna models, finding the diode nonlinear model more accurate in practical low-power regimes, and identifies broader modeling challenges for WIPT design. It then formulates single-user MIMO SWIPT over multipath, multicarrier channels with receiver architectures that route received RF signals to information and energy processing.

  • E. Comparisons of The Rectenna Models: Circuit simulations show that the diode nonlinear rectenna model more accurately characterizes behavior in the practical low-power regime than the diode linear model.Further comparisons of diode linear and nonlinear models are reported in,,.
  • F. Extension and Future Work: Accurate yet tractable energy-harvester models remain a central challenge because software models are too slow for signal design, while simple models can be oversimplified.Software-based models remain useful for validating analytical models.
  • F. Extension and Future Work: Future work includes combined diode–saturation models, improved low-power modeling, non-continuous-waveform designs, and accounting for impedance mismatch and rectifier output harmonics.Alternative models have emerged in, –, but more work is needed beyond the continuous-wave inputs assumed by existing models.
  • F. Extension and Future Work: Jointly modeling transmitter power-amplifier and receiver energy-harvester nonlinearities creates a tradeoff between low-PAPR transmit signals and high-PAPR signals preferred at the harvester input.A design in maximizes harvested DC power under average-power and transmit-PAPR constraints.
  • III. SINGLE-USER WIPT: The single-user WIPT analysis characterizes rate–energy regions and signal designs across three energy-harvester models, alongside receiver architectures and their optimization problems.The section covers the signal model, receiver architectures, and rate–energy-region maximization.
  • A. Signal and System Model: The system is a single-user point-to-point MIMO SWIPT link with Mt transmit and Mr receive antennas, using N orthogonal subbands and independent information symbols on multicarrier waveforms.The transmitted signals propagate through a general L-path multipath channel, with narrowband signaling assumed within each subband.
  • A. Signal and System Model: Each received RF signal is routed wholly or partly to an energy receiver for direct harvesting and to an information receiver for downconversion and filtering.The considered receiver architectures include ideal, time-switching, and power-splitting designs, as shown in Fig. 9.
  • A. Signal and System Model: The baseband model uses additive white Gaussian noise, positive-semidefinite per-subband input covariance matrices, total average transmit-power constraints, and perfect CSIT and CSIR.The subband transmit power is Pn = Tr(Qn).

B. Receiver Architectures · C. Rate-Energy Region and Problem Formulation

The paper characterizes rate-energy tradeoffs and signaling strategies across receiver architectures and linear or nonlinear energy-harvester models. It defines the rate-energy region through achievable rate and harvested-energy constraints, emphasizing a worst-case processing-noise setting for practical power-splitting receivers.

  • B. Receiver Architectures: An ideal receiver decodes information and harvests energy from the same signal, with transmit-signal design controlling the resulting R-E tradeoff,.This architecture is not yet realizable with practical circuits.
  • B. Receiver Architectures: A time-switching receiver alternates between energy harvesting and information decoding in orthogonal slots, with slot length and transmit signals determining the R-E tradeoff,,.Its co-located ID and EH components operate periodically across the two transmission phases.
  • B. Receiver Architectures: A power-splitting receiver divides the received signal between EH and ID using ratio ρ and jointly optimized transmit signals, thereby controlling the R-E tradeoff,,.The EH and ID components are the same as those in a time-switching receiver.
  • C. Rate-Energy Region and Problem Formulation: The paper characterizes the R-E tradeoff and signaling strategies for ideal, time-switching, and power-splitting receivers under linear and nonlinear EH models.The R-E region is the set of simultaneously achievable communication rates and harvested energies.
  • C. Rate-Energy Region and Problem Formulation: The R-E region is formed from input distributions satisfying an average transmit constraint and simultaneous rate and harvested-energy requirements.Capacity is obtained by optimizing mutual information over input distributions subject to covariance, power, and minimum-energy constraints.
  • C. Rate-Energy Region and Problem Formulation: For diode models, the harvested-energy constraint is conveniently expressed using zdc because delivered DC power directly relates to the output current and zdc.The target harvested energy is represented by the constraint zdc(x0, ..., xN−1) ≥ Ē.
  • C. Rate-Energy Region and Problem Formulation: The worst-case processing-noise setting yields an R-E region that serves as a performance lower bound for practical PS receivers.In the opposite noise extreme, PS can achieve the same boxlike R-E region as the ideal receiver.

D. Rate-Energy Tradeoff with The Diode Linear Model · 1) Single-Subband Transmission:

The diode linear model is analyzed through rate-energy tradeoffs, beginning with SISO single-subband transmission and extending to broader transmission settings. In the single-subband case, the transmit signal need not create a rate-energy tradeoff; receiver architecture determines it.

  • D. Rate-Energy Tradeoff with The Diode Linear Model: The diode linear-model analysis begins with SISO single-subband transmission before extending to multi-subband and multi-antenna settings.
  • 1) Single-Subband Transmission:: For an ideal SISO receiver, CSCG signaling x ∼ CN(0, P) is optimal, and the rate-energy region is a rectangle with no rate-energy tradeoff.
  • 1) Single-Subband Transmission:: With time switching, CSCG signaling remains optimal and produces a triangular rate-energy region parameterized by the energy-harvesting time fraction τ.
  • 1) Single-Subband Transmission:: With power splitting, CSCG signaling remains optimal and produces a concave rate-energy region parameterized by the power-splitting ratio ρ.
  • 1) Single-Subband Transmission:: Thus, in single-subband transmission, the diode linear model’s rate-energy tradeoff is induced by receiver architecture rather than the transmit signal.
  • 1) Single-Subband Transmission:: The ideal receiver outperforms power splitting, while power splitting outperforms time switching in the considered rate-energy regions.

2) Multi-Subband Transmission: · 3) Multi-Antenna Transmission:

Under the diode linear model, multi-subband transmission creates an additional rate-energy tradeoff through transmitter power allocation, while multi-antenna transmission realizes the tradeoff through covariance selection and modified water-filling. Uniform power splitting is no worse than time switching, and in the MISO case maximum-ratio transmission simultaneously maximizes rate and energy, eliminating the tradeoff.

  • 2) Multi-Subband Transmission:: Multi-subband rate-energy optimization balances energy-seeking concentration on the strongest subband against rate-seeking water-filling across multiple subbands.The resulting optimum is a modified water-filling allocation that incorporates the total harvested-energy constraint.
  • 2) Multi-Subband Transmission:: When the energy constraint is inactive, allocation reduces to conventional water-filling; when tight, stronger subbands receive higher water levels and more aggressively concentrated power.This makes the allocation more greedy toward strong channels under binding harvesting requirements.
  • 2) Multi-Subband Transmission:: Multi-subband systems therefore face a transmitter power-allocation tradeoff in addition to the receiver-architecture tradeoff, while uniform power splitting achieves an R-E region no smaller than time switching.Time switching alternates conventional water-filling with strongest-subband transmission, whereas power splitting jointly optimizes a common splitting ratio and subband allocations.
  • 3) Multi-Antenna Transmission:: Multi-antenna rate-energy regions arise from the input covariance choice under a total harvested-energy constraint, with power splitting jointly optimizing the precoder and receive-antenna splitting ratios.Time switching instead alternates eigenmode transmission for rate with a single energy beam aligned to the strongest channel eigenvector.
  • 3) Multi-Antenna Transmission:: In multi-antenna transmission, energy maximization beamforms along the dominant channel eigenvector, whereas rate maximization uses multiple eigenmodes with conventional water-filling.The rate-energy optimum retains multiple-eigenmode transmission but replaces conventional with modified water-filling; the diagonal-channel SISO multi-subband case is a special case.
  • 3) Multi-Antenna Transmission:: For MISO transmission, maximum-ratio transmission maximizes both rate and energy, so the rate-energy region is a rectangle enlarged by beamforming gain.The optimal covariance is aligned with the normalized channel, and the same channel-norm replacement applies to time-switching and power-splitting regions.
  • 3) Multi-Antenna Transmission:: Under the diode linear model, CSCG inputs achieve rate-energy boundaries, while any average-power input, including continuous waves, is equally suitable for energy maximization alone.Thus time switching can use CSCG signals for information transmission and continuous waves for power transmission.

E. Rate-Energy Tradeoff with The Diode Nonlinear Model · 1) Single-Subband Transmission:

Diode nonlinearity can improve wireless information-and-power transfer when exploited through suitable signal and input-distribution designs,. In single-subband SISO transmission, it creates a rate-energy tradeoff, enlarges the achievable region, and makes higher-order input statistics and receiver architecture central design considerations.

  • E. Rate-Energy Tradeoff with The Diode Nonlinear Model: Diode-nonlinearity-aware signals outperform linear-model designs by exploiting nonlinearity together with beamforming and channel frequency diversity gains,.
  • E. Rate-Energy Tradeoff with The Diode Nonlinear Model: Modulated signals can improve energy transfer over deterministic continuous-wave inputs, showing that modulation and input randomness matter under the diode nonlinear model.
  • 1) Single-Subband Transmission:: Higher-order moments make zero-mean asymmetric Gaussian inputs optimal within the considered Gaussian family, rather than conventional circularly symmetric Gaussian inputs [64].The nonlinear energy metric depends on moments through order four, including real and imaginary input components.
  • 1) Single-Subband Transmission:: In SISO single-subband transmission, the nonlinear model produces a rate-energy tradeoff because harvested energy depends on fourth-order received-signal moments.The resulting nonlinear-model region is larger than the region obtained with the linear-model-motivated input distribution.
  • 1) Single-Subband Transmission:: Under average transmit-power and delivered-power constraints, AWGN capacity remains unchanged up to the Gaussian input’s delivered energy, while higher requirements are approached through time sharing [67].The time-sharing distributions combine information-rich Gaussian inputs with power-rich, low-probability high-amplitude flash signaling.
  • 1) Single-Subband Transmission:: The nonlinear model favors non-Gaussian distributions that boost higher-order moments, and flash signaling can exceed the fourth-order moments of real Gaussian and circularly symmetric Gaussian inputs.
  • 1) Single-Subband Transmission:: Time sharing makes time-switching, power-splitting, and ideal receivers achieve the same optimal rate-energy region, although ideal and power-splitting receivers can differ for fixed distributions.The practical optimum may require high-amplitude flash signals, and the Taylor expansion model fails when amplitudes enter the diode’s resistive zone.

2) Multi-Subband Transmission:

In multi-subband WIPT, non-zero-mean inputs and deterministic multisine power waveforms enlarge the rate-energy region by exploiting diode nonlinearity, unlike CSCG-only signaling. The section also develops corresponding receiver architectures and finite-constellation modulation designs, while noting that capacity-achieving input distributions remain unresolved.

  • Multi-Subband Transmission: Unmodulated multisine waveforms exploit diode nonlinearity more efficiently than modulated multi-carrier CSCG waveforms, with zdc scaling linearly with the number of sinewaves N [46],.This mechanism explains why deterministic power symbols improve wireless power delivery relative to zero-mean inputs.
  • Multi-Subband Transmission: The resulting SWIPT architecture superposes deterministic power symbols and CSCG information symbols, achieving the same rate with or without explicit power-waveform cancellation.Without cancellation, the receiver decodes translated baseband symbols; with cancellation, it subtracts the known power waveform after down-conversion and ADC.
  • Multi-Subband Transmission: The non-zero-mean Gaussian R-E boundary is convex at low rates and concave at high rates, allowing time switching to outperform power splitting for the diode nonlinear model.At the minimum-energy/maximum-rate extreme, deterministic power allocation is zero and information power follows standard water-filling; other allocations are obtained through a reversed geometric program.
  • Multi-Subband Transmission: Non-zero-mean Gaussian inputs significantly enlarge the R-E region over CSCG inputs by superposing a deterministic multisine power waveform on modulated information waveforms,.Fig. 13 shows this enlargement for a PS receiver with N = 16, fixed received power of -20 dBm, and 20 dB SNR per subband.
  • Multi-Subband Transmission: Asymmetric PSK constellations with optimized probability masses yield a larger R-E region than conventional symmetric PSK, extending nonlinear SWIPT design beyond Gaussian inputs.The constellation points have equal magnitude and are uniformly distributed over [−δ, δ], with δ ≤π, before probability optimization.

3) Multi-Antenna Transmission: … 2) Multi-Subband Transmission:

The section shows that nonlinear energy-harvester models substantially reshape WIPT design: MRT remains optimal for MISO, whereas multi-band MIMO requires joint spatial-frequency optimization. For saturation nonlinearities, resource allocation can be reformulated convexly, but capacity modeling depends on the assumed waveform.

  • 3) Multi-Antenna Transmission:: MRT in each subband is optimal for general multi-band MISO transmission, with symbols combining the channel direction and a SISO-optimal diode-nonlinear input distribution.
  • 3) Multi-Antenna Transmission:: Multi-band MIMO remains open because maximizing harvested energy couples spatial beamforming and frequency allocation, making sequential domain decoupling suboptimal.
  • 3) Multi-Antenna Transmission:: Under the diode nonlinear model, maximizing RF received power does not maximize DC power, CSCG inputs cannot attain optimal rate-energy boundaries, and diode nonlinearity benefits overall performance.
  • 3) Multi-Antenna Transmission:: The diode nonlinear model changes WIPT input distributions and therefore modulation, waveform, spectrum use, resource allocation, and receiver architecture, despite identical point-to-point MISO beamforming via MRT.
  • F. Rate-Energy Tradeoff with The Saturation Nonlinear Model: For the saturation nonlinear model, the rate-energy tradeoff is studied with CSCG information signals and an ideal receiver, requiring parameters a, b, and P_Sat fitted for CSCG inputs.
  • 1) Single-Subband Transmission: : In single-subband saturation-model SWIPT with CSCG inputs, allocating all available transmit power to the carrier maximizes rate and harvested power, yielding a rectangular rate-energy region.
  • 2) Multi-Subband Transmission:: The saturation model’s predefined waveform parameters may prevent explicit capacity definition; although PS may outperform TS by analogy with the linear model, this remains unverified.
  • 2) Multi-Subband Transmission:: Multi-subband saturation-model allocation is efficiently solvable through convex constraints, with an auxiliary variable capturing maximal received power and a water level controlled by saturation-aware dual variables.

3) Multi-Antenna Transmission: … A. Rate-Energy Tradeoff with The Linear Model

The paper shows that multi-antenna and multi-user WIPT designs depend fundamentally on the energy-harvester model, with nonlinear saturation imposing performance and signaling constraints. In multi-user SWIPT under the diode linear model, jointly optimized beamforming characterizes the rate-energy tradeoff and establishes the advantages of power splitting over time switching.

  • 3) Multi-Antenna Transmission:: For the saturation nonlinear model, generalized multiple-eigenmode transmission remains optimal after introducing an auxiliary allocation variable, and its rate-energy tradeoff resembles the diode linear model.The saturation nonlinearity is nevertheless detrimental because the optimization becomes the diode-linear problem with an additional constraint.
  • 3) Multi-Antenna Transmission:: Saturation nonlinearity preserves RF-to-DC power-maximizing strategies but prevents CSCG inputs from generally attaining optimal rate-energy boundaries, while power splitting outperforms time switching.These conclusions parallel the corresponding diode-linear and diode-nonlinear observations.
  • G. Extension and Future Work: Future WIPT research must address imperfect CSIT, since limited terminal energy complicates channel acquisition and nonlinear-model waveform design with limited feedback can outperform linear-model designs relying on perfect CSIT.The cited work reports this advantage for diode nonlinear waveform design with limited feedback.
  • G. Extension and Future Work: Open directions include practical modulation, coding, input distributions, secure SWIPT, and WPCN/WPBC designs tailored to nonlinear harvesters, including multisine waveforms that improve WPBC reader SNR and tag harvested energy.Optimal nonlinear input distributions remain largely open beyond single-subband, single-antenna settings, while secure SWIPT for the diode nonlinear model has no existing work in the cited discussion.
  • IV. MULTI-USER WIPT: The multi-user SWIPT downlink comprises an M_t-antenna transmitter serving K information receivers and J energy receivers, exploiting wireless broadcast for one-to-many charging.The system is introduced as SWIPT with separated information and energy receivers and illustrated in Fig. 14.
  • A. Rate-Energy Tradeoff with The Linear Model: Under the diode linear model, information and energy beams are transmitted to separated receivers, with beamforming designed under transmit-power and information-receiver SINR constraints to maximize harvested energy.The optimization can be solved using semidefinite relaxation or uplink-downlink duality; zero-forcing initialization provides a more practical alternative.
  • A. Rate-Energy Tradeoff with The Linear Model: In multi-user SWIPT, maximizing total received RF power maximizes total harvested DC power, CSCG information inputs suffice for rate-energy boundaries, and power splitting outperforms time switching.These properties carry over from the diode-linear single-user model; dedicated energy signals are unnecessary for the optimal tradeoff when their interference cannot be canceled.

B. Rate-Energy Tradeoff with The Nonlinear Models

In multi-user SWIPT, saturation and diode nonlinear energy-harvesting models produce different rate-energy tradeoffs and beamforming designs. Saturation makes maximizing received RF power insufficient for maximizing harvested DC power, while saturation-aware dual variables avoid over-targeting already saturated receivers.

  • B. Rate-Energy Tradeoff with The Nonlinear Models: The saturation-model resource-allocation problem has a sum-of-ratios objective, which is transformed into an equivalent subtractive form to enable an efficient iterative optimal resource-allocation algorithm [47].The optimization remains subject to the stated rate and power constraints.
  • B. Rate-Energy Tradeoff with The Nonlinear Models: With orthogonal energy-receiver channels and zero information-rate requirements, saturation-aware beamforming uses the maximum eigenmode of Σ_j g_jg_j^H rather than diode-linear maximum-ratio transmission toward the strongest receiver.For the diode-linear model, all transmit power is allocated toward the receiver with the largest channel norm; saturation instead changes the optimal direction to the maximum eigenmode.
  • B. Rate-Energy Tradeoff with The Nonlinear Models: Dual variables weighting each receiver’s received-power constraint decrease as that receiver enters saturation, preventing excessive power allocation toward saturated receivers.These weights determine the beamforming direction in the saturation nonlinear design.
  • B. Rate-Energy Tradeoff with The Nonlinear Models: Saturation nonlinear modeling changes the multi-user rate-energy tradeoff relative to a diode-linear baseline, as illustrated for one information receiver and five energy receivers.The comparison uses the same simulation parameters as, with the baseline optimized for total harvested power under the diode-linear model.
  • B. Rate-Energy Tradeoff with The Nonlinear Models: Unlike the single-user case, maximizing total received RF power across users does not maximize total harvested DC power under the saturation nonlinear model.The resulting beamforming direction generally differs from that obtained with the diode-linear formulation and depends on the operating regime.
  • B. Rate-Energy Tradeoff with The Nonlinear Models: Single-user observations for the diode nonlinear model are expected to extend to multi-user SWIPT, whereas saturation-model observations do not all carry over.Reference [67] is described as applicable to a two-receiver setting with one information receiver and one energy receiver despite using a point-to-point ideal-receiver model.

C. Extension and Future Work · V. PROTOTYPING, EXPERIMENTATION, AND VALIDATION · A. Single-Subband Transmission

Experiments validate diode-nonlinear signal design by showing that real Gaussian inputs harvest more DC power than CSCG inputs and continuous waves at equal received RF power. Future work targets nonlinear multi-user WIPT designs, broader architectures, larger networks, rate-splitting, and real-time closed-loop prototyping.

  • C. Extension and Future Work: Multi-user SWIPT under the diode nonlinear model remains largely unexplored, motivating new input-distribution, modulation, and waveform designs for broadcast and interference channels.The multi-user WPT waveform optimization framework in is suggested as a starting point.
  • C. Extension and Future Work: Nonlinearity motivates rethinking SWIPT architectures for broadcast, multiple-access, interference, and relay channels, both with and without secrecy constraints, alongside analysis of large networks.These directions concern nonlinear energy-harvester models.
  • C. Extension and Future Work: Diode nonlinearity is expected to affect multi-user WPCN and WPBC, where waveform design must address interference while maximizing reader SINR and harvested energy at each tag.Recent work studied nonlinear multi-user waveform design for WPBC.
  • C. Extension and Future Work: Rate-splitting could improve the multi-user SWIPT framework by partially decoding interference and partially treating it as noise instead of treating all residual interference as noise.The baseline model assumes linearly precoded transmission with residual multi-user interference fully treated as noise; rate-splitting has outperformed conventional linear precoding across varied network loads.
  • V. PROTOTYPING, EXPERIMENTATION, AND VALIDATION: Validating WIPT signal theory experimentally remains challenging because it requires closed-loop real-time over-the-air operation that switches between channel acquisition and wireless power-and-information transfer.Channel acquisition must occur at the millisecond level.
  • A. Single-Subband Transmission: Pdc,N ≥ Pdc,CN ≥ Pdc,CW in simulations and experiments, validating diode-nonlinear theory and showing real Gaussian inputs outperform CSCG inputs and continuous waves for harvested DC power.These measurements also invalidate the equal-DC-power prediction of the linear diode model for equal average RF power.

B. Multi-Subband Transmission … VI. CONCLUSIONS

Experiments show that nonlinear, channel-adaptive waveform designs can substantially increase harvested DC power, while multi-antenna beamforming improves wireless power transfer. The paper concludes that WIPT design depends fundamentally on the energy-harvester model, with prototyping and validation remaining important research needs.

  • B. Multi-Subband Transmission: The measurements confirm that maximizing received RF power does not necessarily maximize harvested DC power, validating the importance of modeling diode nonlinearity.Multipath and channel frequency selectivity also significantly affect waveform design and harvested energy, consistent with theoretical, circuit-simulation, and independent measurement results.
  • B. Multi-Subband Transmission: Measurements show that diode-nonlinear, channel-adaptive multisine design yields significantly higher harvested DC power than diode-linear design and non-adaptive waveforms.The nonlinear design sacrifices RF input power to exploit rectifier nonlinearity and channel frequency diversity, maximizing harvested DC power instead.
  • C. Multi-Antenna Transmission: A real-life multi-antenna wireless-powered sensor-network testbed validates receive-power-based channel estimation, energy beamforming, and adaptive duty-cycle control for energy-neutral operation.The benefit of multi-antenna beamforming is linked to increasing RF-to-DC conversion efficiency as average rectifier input power rises.
  • C. Multi-Antenna Transmission: Distributed power beacons can improve coverage probability compared with a single beacon using many co-located antennas, according to reported experimental results.These distributed RF power-transfer designs were developed to address low end-to-end power-transfer efficiency.
  • D. Extension and Future Work: Future WPT research needs further prototyping of modulation, waveform, and beamforming designs, multi-user systems, and reconfigurable rectifiers.Serial rectifier configurations target higher efficiency at low RF input power, whereas parallel configurations target high RF input power.
  • D. Extension and Future Work: SWIPT prototyping remains at an early stage, with no experimental setup yet validating the discussed rate-energy regions and signal designs.Circuit simulations have validated some emerging SWIPT designs,,,, while further transceiver efforts are ongoing.
  • VI. CONCLUSIONS: The paper’s central conclusion is that WIPT signal and system designs crucially depend on the underlying energy-harvester model.The tutorial presents three energy-harvester models and aims to support future development of efficient WIPT systems.
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