PaperlayerView exact revision on arXiv

Source-linked AI summary

Sensitive and Nonlinear Far Field RF Energy Harvesting in Wireless Communications

Panos N. Alevizos, Aggelos Bletsas

arXiv:1707.07041v3cs.ITmath.IT

TL;DR

Far-field SWIPT research often omits the harvester’s finite sensitivity, despite its substantial gap from communication-receiver sensitivity. The paper models realistic nonlinear harvesting and derives harvested-power statistics from rectifier datapoints and channel fading. Its approximation matches the realistic model across the studied metrics, whereas common alternatives can deviate from it.

  • Problem

    SWIPT studies often use linear harvesting models or omit finite harvester sensitivity, which is substantially worse than communication-receiver sensitivity.

    Source: §I · p. 2

  • Method

    The paper represents harvested power as an arbitrary nonlinear, continuous, non-decreasing function and uses a piecewise-linear approximation to derive harvested-power statistics from datapoints and fading distributions.

    Source: §I · pp. 2–3

  • Results

    The approximation matches the realistic model across all studied metrics; linear models can be off by an order of magnitude, while unlimited-sensitivity nonlinear models deviate at low input power.

    Source: §I · p. 3

  • Takeaways & Limitations

    The conclusion is that SWIPT analysis should account for both actual harvesting nonlinearity and limited harvester sensitivity.

    Source: §VI · p. 12

Abstract

from arXiv · show

This work studies both limited sensitivity and nonlinearity of far field RF energy harvesting observed in reality and quantifies their effect, attempting to fill a major hole in the simultaneous wireless information and power transfer (SWIPT) literature. RF harvested power is modeled as an arbitrary nonlinear, continuous, and non-decreasing function of received power, taking into account limited sensitivity and saturation effects. RF harvester's sensitivity may be several dBs worse than communications receiver's sensitivity, potentially rendering RF information signals useless for energy harvesting purposes. Given finite number of datapoint pairs of harvested (output) power and corresponding input power, a piecewise linear approximation is applied and the statistics of the harvested power are offered, as a function of the wireless channel fading statistics. Limited number of datapoints are needed and accuracy analysis is also provided. Case studies include duty-cycled (non-continuous), as well as continuous SWIPT, comparing with industry-level, RF harvesting. The proposed approximation, even though simple, offers accurate performance for all studied metrics. On the other hand, linear models or nonlinear-unlimited sensitivity harvesting models deviate from reality, especially in the low input power regime. The proposed methodology can be utilized in current and future SWIPT research.

I. INTRODUCTION

Far-field RF harvesting combines nonlinear rectifier behavior with a sensitivity threshold that can lie far above communication-receiver sensitivity. The paper models these effects and evaluates their consequences under fading using a piecewise-linear approximation.

I. INTRODUCTION

  • A harvester produces zero output below its sensitivity, rises nonlinearly between sensitivity and saturation, and saturates above that threshold.The rectifier’s diodes impose the nonlinear power conversion.Source: §I · p. 1
  • Communication signals near receiver sensitivity may be decodable but unusable for harvesting, because harvester sensitivity is roughly 55–120 dB worse.Communication sensitivity ranges from −140 dBm to −85 dBm, while state-of-the-art harvesting sensitivity is around −30 dBm.Source: §I · p. 2
  • The paper models harvested power as an arbitrary nonlinear, continuous, non-decreasing function that includes limited sensitivity and saturation.Saturation is generally uncommon at nominal levels but may be approached or exceeded in ultra-small-range RFID applications.Source: §I · p. 2
  • Given rectifier input-output datapoints and a fading density, a piecewise-linear approximation yields the harvested-power PDF and CDF.The methodology also provides an approximation-accuracy analysis.Source: §I · p. 3
  • The proposed approximation matches the realistic harvester across all three studied metrics, while linear models can be off by an order of magnitude and unlimited-sensitivity nonlinear models deviate at low input power.The metrics are expected harvested energy, expected charging time, and passive-RFID successful-reception probability.Source: §I · p. 3

II. WIRELESS SYSTEM MODEL

  • The system model considers narrowband transmission over quasi-static flat fading, with the channel changing independently across coherence blocks.Nakagami fading is used for numerical results and can represent small-scale LoS and NLoS fading.Source: §II · pp. 3–4

III. FUNDAMENTALS OF FAR FIELD RF ENERGY HARVESTING

Far-field RF harvesting uses a nonlinear rectenna whose sensitivity and saturation constrain the relationship between received and harvested power. The paper models this relationship from measured data and evaluates a realistic harvesting function for two rectenna designs.

III. FUNDAMENTALS OF FAR FIELD RF ENERGY HARVESTING

  • The rectenna converts incoming RF to DC through nonlinear diode operation; adding diodes usually improves efficiency at the expense of sensitivity.A boost converter may also follow the rectifier because its output is a nonlinear function of input power.Source: §III · p. 4

A. Realistic Far Field RF Energy Harvesting Model

  • The harvesting function is continuous and non-decreasing, with zero output below sensitivity and constant output beyond saturation.Between those thresholds, the function captures the rectifier’s input-output behavior.Source: A. Realistic Far Field RF Energy… · p. 4
  • The ground-truth harvesting efficiency is fitted as a high-order polynomial on the dBm scale using measured efficiency data.The polynomial coefficients are fitted to measured data using convex optimization techniques.Source: A. Realistic Far Field RF Energy… · p. 4
  • The ground-truth function is used to evaluate a simpler piecewise-linear approximation based on input-output datapoint pairs.This parametrization uses the dBm scale to provide higher granularity at very small input powers.Source: A. Realistic Far Field RF Energy… · p. 4
  • The evaluated data comprise 118 points for rectenna and 53 for PowerCast, across their respective input-power ranges.Rectenna spans 10^-4.25 to 10^1.6 mWatt; PowerCast spans 10^-1.2 to 10 mWatt.Source: A. Realistic Far Field RF Energy… · p. 4
  • Harvested power is a nonlinear function of input power for both studied rectennas, and the PowerCast module.Fig. 3 shows efficiency versus input power and harvested power versus input power for the two devices.Source: A. Realistic Far Field RF Energy… · p. 5, Figure 3 · p. 5

B. Impact of Harvester’s Sensitivity in RF Energy Harvesting

Harvester sensitivity determines when RF input is sufficient to produce energy, but prior harvesting models make different simplifications about sensitivity, efficiency, and saturation. The reported outage examples vary substantially by harvester and transmission setting.

B. Impact of Harvester’s Sensitivity in RF Energy Harvesting

  • The outage metric is the probability that channel-dependent input power falls below harvester sensitivity, or the fraction of time the rectenna cannot harvest.The probability is considered as a function of harvester sensitivity.Source: B. Impact of Harvester’s Sensitivity… · p. 5
  • For PowerCast, outage is almost 1 at 20 dBm beyond 4 meters, but falls to 10% at 35 dBm and 4 meters; rectenna is almost 0 across studied scenarios.The scenarios use path-loss exponent ν = 2.1 and Nakagami parameter m = 5.Source: B. Impact of Harvester’s Sensitivity… · p. 5, Figure 4 · p. 5

1) Linear (L) Energy Harvesting Model:

  • The linear model ignores input-dependent efficiency, the sensitivity threshold, and saturation.Its harvested power is proportional to received power under a constant efficiency ηL.Source: 1) Linear (L) Energy Harvesting Model · p. 5

2) Constant-Linear (CL) Energy Harvesting Model: (

  • The constant-linear model accounts for zero harvesting below sensitivity but ignores input-dependent efficiency and saturation.It uses a constant efficiency ηCL above the sensitivity threshold.Source: 2) Constant-Linear (CL) Energy… · pp. 5–6

3) Constant-Linear-Constant (CLC) Energy Harvesting Model:

The CLC baseline includes a saturation region but retains constant efficiency. The paper then approximates a general harvesting function piecewise-linearly and derives its harvested-power statistics and an approximation-error result.

3) Constant-Linear-Constant (CLC) Energy Harvesting Model:

  • The CLC model includes sensitivity and saturation but ignores the dependence of harvesting efficiency on input power.Its constant efficiency is selected empirically to minimize mismatch against the realistic model in the simulation scenarios.Source: 3) Constant-Linear-Constant (CLC)… · p. 6

IV. STATISTICS OF HARVESTED POWER

  • The proposed approximation uses M + 1 support points and linearly interpolates the harvesting function between adjacent input-power breakpoints.It sets output to zero below the first breakpoint and to the final output value at and above the last breakpoint.Source: §IV · p. 6
  • The piecewise-linear approximation supports direct interpolation from measured input-output datapoints without requiring the exact harvesting-function form.Its evaluation cost is O(M), compared with O(1) for the listed baseline models and nonlinear prior-art functions.Source: §IV · p. 6
  • The section derives the PDF and CDF of harvested power from the input-power distribution induced by channel fading.The derivation treats the saturation output separately because the inverse function does not exist there.Source: §IV · pp. 6–7
  • With continuously differentiable harvesting function and uniformly spaced support points, approximation error decays quadratically with the number of points.The stated bound depends on the maximum absolute second derivative of the harvesting function over the input range.Source: §IV · p. 7

A. Baseline Comparison: Average Harvested Energy

Average-energy comparisons show the proposed piecewise-linear approximation matching the true harvesting model, while baseline and prior nonlinear models deviate. The time-switching analysis estimates accumulated-energy distributions to assess charging before communication.

1) Numerical Results:

  • For the second harvesting module, the linear model is highly inaccurate, and the other linear baselines retain non-negligible slope mismatch.The comparisons use 221 approximation points at a distance of 3 m.Source: 1) Numerical Results · p. 8, Figure 6 · p. 8
  • The sigmoid prior-art model overestimates harvested power at low input levels, while the polynomial can predict negative power near sensitivity.The proposed ground-truth model fits the measured data; the polynomial’s negative values occur below −10 dBm.Source: 1) Numerical Results · p. 8
  • The proposed piecewise-linear approximation matches the exact model’s expected harvested energy across the studied distances.It interpolates measured harvested-power data directly, without fitting.Source: 1) Numerical Results · pp. 8–9
  • The model in underestimates expected harvested energy, reaching negative values for d > 3.5, and is more accurate than for d ≤ 3.5.Source: 1) Numerical Results · p. 9

B. Time-Switching RF Energy Harvesting Scenario: Expected Charging Time

  • The charging-time framework estimates accumulated harvested energy by combining independent per-period random variables to obtain its distribution.That distribution supports evaluating the expected number of coherence periods needed to reach the charging threshold.Source: B. Time-Switching RF Energy Harvesting… · p. 9
  • For one, 20, and 50 coherence periods, the estimated accumulated-energy PDFs match the actual histograms under the stated rectenna and channel settings.The evaluation uses the rectenna in, a 5 m link, and Nakagami parameter m = 5.Source: B. Time-Switching RF Energy Harvesting… · p. 9, Figure 9 · p. 10

1) Numerical Results:

For both evaluated harvesting-efficiency models, the proposed approximation reproduces the true model’s expected charging time. Linear baselines can depart substantially from the true value and alter estimated duty cycles and communication resources.

1) Numerical Results:

  • For evaluating the two harvesting-efficiency models, harvested-power approximation uses M + 1 = 1171 data points for rectenna and M + 1 = 2201 points for rectenna, using V = 1.8 V and Tp = 50 msec.Source: 1) Numerical Results · p. 10
  • For both harvesting-efficiency models, the proposed approximation and the true nonlinear model give coincident expected charging times.The comparison covers the rectennas in and.Source: 1) Numerical Results · p. 10
  • Linear baseline models can place the estimated number of coherence periods needed for charging one order of magnitude from the true value.The comparison uses best-possible baseline efficiency values, yet their slopes still differ from the true nonlinear model.Source: 1) Numerical Results · p. 10

C. Power-Splitting RF Energy Harvesting Scenario: Passive RFID Tags

The passive RFID scenario considers power splitting for simultaneous harvesting and communication, with reception success depending on whether the tag can power itself and whether the interrogator meets a BER threshold. The paper reports accurate results for its methodology compared with linear harvesting models.

C. Power-Splitting RF Energy Harvesting Scenario: Passive RFID Tags

  • A passive RFID tag uses power splitting to harvest energy and communicate simultaneously, rather than harvesting first and communicating later.The tag communicates by switching its antenna load to reflect information to the interrogator.Source: C. Power-Splitting RF Energy… · p. 10, Figure 11 · p. 10
  • The absorbed input power is divided between harvesting and the tag’s downlink circuitry, while a fraction of incident power is used for uplink backscatter.The harvesting share is ζhar = χτd; the uplink fraction is ρu.Source: C. Power-Splitting RF Energy… · p. 11
  • Successful interrogator reception requires both harvested power above tag consumption and a bit-error rate at or below its threshold.Failure occurs if either the tag lacks operating power or the BER exceeds β.Source: C. Power-Splitting RF Energy… · p. 11
  • The proposed methodology provides accurate results in contrast with linear harvesting models.Success-probability expressions are presented for the linear baselines and the proposed nonlinear model.Source: C. Power-Splitting RF Energy… · pp. 11–12

VI. CONCLUSIONS

The conclusion argues that realistic RF harvesting models must account for sensitivity, nonlinearity, and saturation. Its piecewise-linear approximation agrees with real rectenna behavior, unlike linear and unlimited-sensitivity models.

VI. CONCLUSIONS

  • The study models RF harvesting with sensitivity limits, nonlinearity, and saturation, and proposes a tuning-free piecewise-linear approximation that agrees with two real rectenna models.Linear and nonlinear unlimited-sensitivity models deviate from reality.Source: §VI · p. 12

APPENDIX A PROOF OF PROPOSITION 1

The appendices derive the CDF for the proposed model and establish an approximation-error bound, with a numerical density-evolution procedure for sums of independent random variables.

APPENDIX A PROOF OF PROPOSITION 1

  • The CDF proof splits the integral over disjoint intervals, changes variables within each interval, and uses right-continuity to include x = v0 = 0.The proof also handles the intervals [0, vM) and [vM, x) separately.Source: Appendix A · p. 13

APPENDIX B PROOF OF PROPOSITION 2

  • The piecewise-linear approximation error is bounded using the second derivative of the interpolated function and the maximum second derivative of p over Pin.The bound's constant Cp depends on Pin and p(·), and is independent of M.Source: Appendix B · p. 13
  • Density evolution approximates the PDF of a sum of independent random variables by discretizing its support and using FFT-based convolution.The stated arithmetic complexity is O(N JFFT logJFFT).Source: Appendix B · pp. 13–14

APPENDIX D PROOF OF PROPOSITION 3

The proof differentiates the relation to show that R is decreasing and invertible for x > 0.

APPENDIX D PROOF OF PROPOSITION 3

  • Differentiating Eq. (35) and substituting the derivative of Q yields the derivative expression used for R.The proof then establishes that R′(x) < 0 for x > 0.Source: Appendix D · p. 14
  • Because R′(x) < 0 for x > 0, R is monotone decreasing and invertible on (0, ∞).Source: Appendix D · p. 14
  • The proof uses the monotonicity of Q when proceeding to the inverse of R.Source: Appendix D · p. 14

APPENDIX E PROOF OF PROPOSITION 4

The proof uses the proposed piecewise-linear model's monotonicity to evaluate successful-reception probability across two ranges of Pc.

APPENDIX E PROOF OF PROPOSITION 4

  • Ordered image points yield ordered slopes, making the piecewise-linear function monotone increasing and invertible over the stated ranges.Source: Appendix E · p. 14
  • For 0 < Pc < vM, the proof expresses successful-reception probability using the model's inverse and then substitutes the Nakagami-fading CDF.Source: Appendix E · p. 14
  • For Pc ≥ vM, successful-reception probability is zero under the stated non-decreasing model and harvesting factor condition.The proof uses ζhar ∈ (0, 1) and concludes P(eS) = 0.Source: Appendix E · p. 14
Loading 1707.07041v3…