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Wireless Information and Power Transfer: Architecture Design and Rate-Energy Tradeoff

Xun Zhou, Rui Zhang, Chin Keong Ho

arXiv:1205.0618v3cs.IT

TL;DR

SWIPT promises simultaneous wireless information and power transfer, but practical harvesting circuits cannot directly decode carried information. This paper introduces DPS and separated or integrated receiver architectures, then characterizes their rate-energy tradeoffs. OPS is optimal with receiver circuit power consumption, whereas SPS is optimal when that consumption is negligible.

  • Problem

    Practical energy-harvesting circuits cannot directly decode information from received radio signals, so ideal simultaneous decoding and harvesting assumptions do not describe practical receiver hardware.

  • Method

    The paper generalizes receiver operation through DPS and proposes separated and integrated information-and-energy receiver architectures, characterizing their rate-energy regions.

  • Results

    OPS is optimal for both receivers with receiver circuit power consumption, while SPS is optimal for both when receiver circuit power consumption is negligible.

  • Takeaways & Limitations

    The results provide design guidance for practical SWIPT receivers by comparing separated and integrated architectures under circuit-power and realistic-modulation settings.

Abstract

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Simultaneous information and power transfer over the wireless channels potentially offers great convenience to mobile users. Yet practical receiver designs impose technical constraints on its hardware realization, as practical circuits for harvesting energy from radio signals are not yet able to decode the carried information directly. To make theoretical progress, we propose a general receiver operation, namely, dynamic power splitting (DPS), which splits the received signal with adjustable power ratio for energy harvesting and information decoding, separately. Three special cases of DPS, namely, time switching (TS), static power splitting (SPS) and on-off power splitting (OPS) are investigated. The TS and SPS schemes can be treated as special cases of OPS. Moreover, we propose two types of practical receiver architectures, namely, separated versus integrated information and energy receivers. The integrated receiver integrates the front-end components of the separated receiver, thus achieving a smaller form factor. The rate-energy tradeoff for the two architectures are characterized by a so-called rate-energy (R-E) region. The optimal transmission strategy is derived to achieve different rate-energy tradeoffs. With receiver circuit power consumption taken into account, it is shown that the OPS scheme is optimal for both receivers. For the ideal case when the receiver circuit does not consume power, the SPS scheme is optimal for both receivers. In addition, we study the performance for the two types of receivers under a realistic system setup that employs practical modulation. Our results provide useful insights to the optimal practical receiver design for simultaneous wireless information and power transfer (SWIPT).

I. INTRODUCTION

SWIPT is attractive for using RF signals simultaneously for wireless information and power transfer, but practical receiver hardware cannot directly decode information from harvested signals. The paper develops DPS-based receiver architectures and characterizes their rate-energy performance.

  • Motivation: Practical harvesting circuits cannot directly decode information from radio signals, making ideal simultaneous decoding and harvesting assumptions optimistic.The paper identifies practical receiver implementation as a central challenge for SWIPT.
  • Proposed approach: Dynamic power splitting (DPS) generalizes time switching and static power splitting by dynamically dividing the received signal with an arbitrary power ratio over time.On-off power splitting is also studied, with TS and SPS treated as special cases of OPS.
  • Receiver architectures: The paper proposes separated and integrated information-and-energy receiver architectures for point-to-point SWIPT links.The separated architecture feeds split RF streams to distinct energy and information receivers, while the integrated architecture combines front-end components.
  • Performance analysis: The two receiver architectures are evaluated through rate-energy regions and optimal transmission strategies under practical receiver constraints.The analysis explicitly accounts for receiver circuit power consumption.
  • Main findings: With receiver circuit power consumption, OPS is optimal for both receivers; when circuit consumption is negligible, SPS is optimal for both.A realistic practical-modulation setup further compares the receiver architectures.
  • Practical comparison: For zero-net-energy consumption, the integrated receiver achieves more rate than the separated receiver at sufficiently small transmission distance.This comparison is reported for a realistic system using practical modulation.

C. Energy Receiver

The energy receiver converts the received RF signal into DC power through a rectenna and stores it with an assumed linear conversion efficiency. These models support upper bounds on simultaneous information-rate and harvested-energy performance.

  • Energy receiver: The energy receiver converts the received RF signal directly into a DC signal using a rectenna comprising a Schottky diode and passive low-pass filter.The filtered DC output is used to charge a battery and store harvested energy.
  • Rectifier model: The diode output is modeled through a Taylor expansion, and higher-order terms are ignored because γy(t) is assumed practically small.The resulting rectifier model retains the lower-order contribution used for subsequent analysis.
  • Energy storage: The stored harvested energy is assumed linearly proportional to the rectifier output current, with conversion efficiency 0 < ζ ≤ 1.Energy contributed by noise is treated as a small constant and ignored.
  • Joint operation: The joint SWIPT objective is to maximize decoded information rate R and harvested energy Q from the same received signal.The paper uses separate information and energy receiver models to derive a performance bound.
  • Performance upper bound: Q ≤ hP limits harvested energy, while R ≤ log2(1 + hP/σ2_A) limits information rate for practical receiver architectures.These bounds define an outer rate-energy performance region.

III. RECEIVER ARCHITECTURE FOR WIRELESS INFORMATION AND POWER TRANSFER

The paper introduces dynamic power splitting (DPS) and uses it to design separated and integrated receivers for simultaneous wireless information and power transfer. TS and SPS are special cases of OPS, while the integrated architecture places splitting within the energy receiver.

  • Dynamic Power Splitting: The block-based DPS model uses symbol-specific splitting ratios ρ_k and permits the information receiver to switch off for fraction α of each transmission block.The receiver is off for αT and on for (1 − α)T.
  • Special Cases of DPS: TS uses all signal power alternately for harvesting and decoding, whereas SPS remains on throughout with a constant splitting ratio.TS and SPS correspond to distinct DPS operating patterns.
  • Special Cases of DPS: OPS combines an initial full-harvesting period with constant-ratio splitting during the remaining symbols, making TS and SPS special cases.TS follows by setting ρ = 0, and SPS by setting α = 0.
  • Separated Receiver: The separated receiver splits the antenna signal in the RF band before feeding separate energy and information receivers.The two streams are separately used for energy harvesting and information decoding.
  • Integrated Receiver: The integrated receiver splits the rectifier output, integrating RF band-to-baseband conversion into the energy receiver.This architecture is motivated by encoding information through time-varying energy-signal power without degrading power-transfer efficiency.

IV. RATE-ENERGY TRADEOFF FOR SEPARATED INFORMATION AND ENERGY RECEIVER

The separated receiver’s achievable rate-energy region is characterized for DPS and its TS and SPS special cases. SPS is optimal for the separated receiver, while processing-noise conditions affect the resulting tradeoff and the comparison with TS.

  • DPS Rate-Energy Region: The separated receiver’s DPS operation yields an achievable rate-energy region characterized through the symbol-dependent information-receiver SNR τ(ρ_k).The analysis studies the region generated by DPS and then specializes it to TS and SPS.
  • Rate-Energy Boundary: The outer-bound rate-energy boundary is a straight line connecting the maximum-rate and maximum-energy operating points.The boundary connects (R̂_max, 0) and (0, Q̂_max) as α varies.
  • Optimal Scheme: Proposition 4.1 establishes that SPS is the optimal DPS scheme for the separated information and energy receiver.The result identifies SPS as sufficient for the optimal separated-receiver rate-energy tradeoff.
  • Noise Effects: When processing noise dominates antenna noise, the information-receiver SNR approaches (1 − ρ)hP/σ2_cov, and the optimal tradeoff uses ρ approaching 1.The cited result further states that with ζ = 1 this reaches the R-E tradeoff outer bound.
  • TS versus SPS: For the separated receiver, SPS achieves larger rate-energy pairs than TS under the plotted noise-power setups.The comparison uses h = 1, P = 100, ζ = 1, and antenna-noise power σ2_A = 1.
  • Noise Effects: As processing-noise power σ2_cov increases, the gap between the SPS and TS regions decreases.The cited discussion also states that the SPS region enlarges toward the rate-energy upper bound in the corresponding limiting condition.

V. RATE-ENERGY TRADEOFF FOR INTEGRATED INFORMATION AND ENERGY RECEIVER

The integrated receiver has a nonlinear equivalent baseband channel because rectifier conversion precedes decoding. Its achievable rate-energy region depends on power splitting and processing noise, with integrated performance varying relative to separated reception across noise regimes.

  • Channel model: The integrated receiver’s rectifier makes its equivalent baseband channel nonlinear, unlike the separated receiver’s linear channel.Information is encoded in transmitted signal power rather than phase.
  • Power splitting: With ρk approaching 1 for every symbol, DPS becomes SPS that sends infinitesimal power to information decoding while maximizing harvested power.The average SNR remains independent of ρk when ρk < 1.
  • Capacity bounds: 2 log2 P is the stated high-power asymptotic upper-bound behavior for channel (29), which is tighter than channel (26) for channel (25).The comparison applies at high SNR.
  • Rate-energy region: The integrated receiver’s achievable R-E region is characterized using the nonlinear-channel capacity subject to nonnegative input and an average-input constraint.A central chi-square input distribution provides an achievable lower bound for numerical results.
  • Receiver comparison: When processing noise equals antenna noise, integrated reception has lower achievable rate than separated reception because it uses noncoherent rather than coherent modulation.When processing noise is much larger, the integrated region becomes superior because rectifier noise occurs before power splitting.
  • ADC noise: Nonzero ADC noise lowers the integrated receiver’s achievable rate, especially when more harvested energy is desired.The corresponding R-E regions are no longer boxes.

VI. RATE-ENERGY TRADEOFF WITH RECEIVER CIRCUIT POWER CONSUMPTION

The analysis incorporates information-decoding circuit power into harvested-energy accounting. Separated and integrated receivers consume different circuit powers because the separated design includes an RF mixer, whereas the integrated design uses only an ADC.

  • Circuit-power model: Receiver circuit power is excluded from earlier harvested-energy characterization because the energy receiver’s Schottky diode and low-pass filter are passive.Additional control-circuit consumption is included in conversion efficiency ζ.
  • Circuit-power model: The separated receiver consumes PS = Pm + PADC, while the integrated receiver consumes PI = PADC for information decoding.The separated receiver’s RF-band mixer contributes additional circuit power.
  • Circuit-power model: PS is generally much greater than PI because the RF-band mixer consumes substantial power.

A. Separated Receiver with PS > 0

For the separated receiver with positive circuit power, OPS is the optimal DPS scheme for the rate-energy tradeoff. SPS can be competitive at low harvested energy but becomes inefficient when more energy is required.

  • Optimal scheme: OPS is the optimal DPS scheme for the separated receiver when PS > 0.The result holds for all transmission powers P ≥ 0.
  • Optimal scheme: Each boundary point of the separated receiver’s OPS R-E region is achieved by a unique power-splitting pair (α*, ρ*).The optimal pair is obtained through the stated optimization over α and ρ.
  • Scheme comparison: SPS achieves the R-E boundary only in the low harvested-energy region.Its performance becomes worse, even than TS, when more harvested energy is desired.
  • Scheme comparison: Keeping the information receiver continuously active is energy-inefficient when greater harvested energy is desired.This explains why SPS degrades at high harvested-energy requirements.

B. Integrated Receiver with PI > 0

For the integrated receiver with positive circuit power, OPS with ρ approaching 1 is optimal. Compared with separated reception, integrated reception is favored at higher harvested energy and under sufficiently high circuit-power costs.

  • Optimal scheme: OPS with ρ approaching 1 is the optimal DPS scheme for the integrated receiver when PI > 0.The rate is independent of ρk, so the information-decoding split is minimized.
  • R-E boundary: When PI ≥ ζhP, the integrated receiver’s OPS boundary is a straight line between (ζhPCNL/PI, 0) and (0, ζhP).
  • Receiver comparison: With low circuit power PS = 25 and PI = 10, integrated reception is superior when more energy is harvested, while separated reception is superior for no more than 37 energy units.
  • Receiver comparison: With high circuit power PS = 200 and PI = 80, integrated reception is always superior because separated reception needs more harvesting time to offset information-decoding power.

VII. PRACTICAL MODULATION

The practical-modulation analysis optimizes rate under symbol-error and harvested-energy constraints for separated and integrated receivers. As transmission distance increases, modulation size and information-decoder operating time jointly determine achievable rate, producing distance-dependent receiver advantages.

  • Modulation model: Practical modulation uses constellation size M = 2^l, with integer l ≥ 1 and maximum supported rate l ≤ 10 bits/channel use.The symbol error rate is approximated for QAM, while the integrated receiver uses pulse energy modulation with equispaced positive constellation points.
  • Optimization formulation: The maximum-rate problems optimize modulation size M and information-decoder off-time α subject to symbol-error and minimum harvested-energy constraints.For the separated receiver, the optimization also includes power-splitting ratio ρ; for the integrated receiver, ρ → 1 is optimal.
  • Optimization formulation: As received signal power decreases, M decreases to satisfy the modulation constraint and α increases to satisfy harvested energy, reducing achievable rate.The rate is jointly determined by modulation size and the fraction of time the information decoder operates in off mode.
  • Receiver comparison: With PS > PI > 0, the separated receiver requires at least as much information-decoder off-time as the integrated receiver; if M*_1 ≤ M*_2, then R*_1 ≤ R*_2.At sufficiently small transmission distances, both receivers support M*_1 = M*_2 = 2^10, so the integrated receiver outperforms the separated receiver.
  • Receiver comparison: Numerically, IntRx outperforms SepRx through log10 d ≤ 1, SepRx performs better for 1.1 ≤ log10 d ≤ 1.5, and IntRx cannot support modulation at log10 d = 1.5.SepRx can support higher-order constellations over part of the intermediate-distance range, but its larger α lowers average rate; IntRx generally uses smaller M.

VIII. CONCLUSION

The paper proposes separated and integrated receiver architectures for practical SWIPT and characterizes their rate-energy performance with circuit power consumption included. The conclusion reports numerical performance comparisons and identifies modulation and decoder off-time as practical design factors.

  • VIII. CONCLUSION: The separated receiver splits the antenna signal into RF streams for separate energy harvesting and information decoding, whereas the integrated receiver incorporates RF-to-baseband conversion into the energy receiver through the rectifier.The integrated architecture is presented as integrating part of the information-decoding implementation into the energy receiver.
  • VIII. CONCLUSION: The practical comparison varies modulation size M and information-receiver off-time percentage α across transmission distance.These quantities are reported for separated and integrated receivers in the associated modulation results.
  • VIII. CONCLUSION: Both receiver architectures are evaluated through rate-energy performance characterization that accounts for receiver circuit power consumption.

APPENDIX A PROOF OF PROPOSITION 4.1

The appendix proves that static and on-off power splitting are special cases of dynamic power splitting and establishes their rate-energy relationships. It uses concavity and optimization properties to show the corresponding region inclusions.

  • Proof of Proposition 4.1: SPS is a special case of DPS obtained by setting ρ_k = ρ for every time index k.
  • Proof of Proposition 4.1: The proof uses concavity of f(ρ) = log2(...) over ρ ∈ [0, 1] and Jensen’s inequality to establish the relevant rate-energy relation.
  • Proof of Proposition 6.1: OPS is a special case of DPS obtained by setting ρ_k = ρ over the designated off-mode indices.
  • Proof of Proposition 6.1: For OPS, the power-splitting variables are optimized at ρ_k = 1 over the initial αN indices, yielding the stated rate-energy-region relationship.
  • Auxiliary lemma: The appendix analyzes the sign of the second derivative of R(s) through the factor bc − ad and the associated affine function f_2(s).The derivative expressions are used to complete the proof of the stated lemma.

APPENDIX D PROOF OF PROPOSITION 7.1

The proof compares optimal decoder off-times and modulation sizes under positive circuit-power assumptions. These inequalities yield the sufficient condition under which the integrated receiver’s maximum rate is no smaller.

  • Proof of Proposition 7.1: For 0 ≤ Qreq ≤ ζhP and PS > PI, the optimal off-time satisfies α*_1 ≥ α*_2 for separated and integrated receivers.
  • Proof of Proposition 7.1: If M*_1 ≤ M*_2, then the separated receiver’s maximum achievable rate satisfies R*_1 ≤ R*_2.The result follows because achievable rate is proportional to (1 − α) log2 M under the compared solutions.
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