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Millimeter Wave Energy Harvesting

Talha Ahmed Khan, Ahmed Alkhateeb, Robert W. Heath

arXiv:1509.01653v3cs.IT

TL;DR

The viability of millimeter-wave energy harvesting is unclear because its propagation differs from lower-frequency systems, including sensitivity to blockages. Using stochastic geometry, the paper analyzes energy and information transfer and finds that mmWave systems can potentially provide better energy coverage than lower-frequency solutions.

  • Problem

    Network-level design principles for mmWave energy harvesting systems remain insufficiently understood, despite their relevance to future cellular networks.

  • Method

    Using stochastic geometry, the paper derives analytical expressions for energy, harvested-power, and joint energy-information coverage in mmWave cellular networks.

  • Results

    Simulations suggest that mmWave cellular networks could potentially provide better energy coverage than lower-frequency solutions, while beamwidth and power-splitting optimization improve performance.

  • Takeaways & Limitations

    MmWave energy-harvesting performance depends on jointly selecting network antenna geometry and device-level signal splitting or multi-antenna strategies.

Abstract

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The millimeter wave (mmWave) band, which is a prime candidate for 5G cellular networks, seems attractive for wireless energy harvesting. This is because it will feature large antenna arrays as well as extremely dense base station (BS) deployments. The viability of mmWave for energy harvesting though is unclear, due to the differences in propagation characteristics such as extreme sensitivity to building blockages. This paper considers a scenario where low-power devices extract energy and/or information from the mmWave signals. Using stochastic geometry, analytical expressions are derived for the energy coverage probability, the average harvested power, and the overall (energy-and-information) coverage probability at a typical wireless-powered device in terms of the BS density, the antenna geometry parameters, and the channel parameters. Numerical results reveal several network and device level design insights. At the BSs, optimizing the antenna geometry parameters such as beamwidth can maximize the network-wide energy coverage for a given user population. At the device level, the performance can be substantially improved by optimally splitting the received signal for energy and information extraction, and by deploying multi-antenna arrays. For the latter, an efficient low-power multi-antenna mmWave receiver architecture is proposed for simultaneous energy and information transfer. Overall, simulation results suggest that mmWave energy harvesting generally outperforms lower frequency solutions.

I. INTRODUCTION … B. Channel Model

The paper develops a stochastic-geometry framework for wireless energy and information transfer in large-scale mmWave cellular networks, addressing blockage sensitivity and large antenna arrays. It analyzes network and device design choices under distinct mmWave network, user, and channel models.

  • I. INTRODUCTION: mmWave supports 5G through large spectrum resources, high data rates, directional beamforming, and densely packed large-dimensional antenna arrays.
  • A. Contributions: The paper derives tractable energy, information, and joint coverage analyses while accounting for blockage sensitivity and potentially large transmitter and receiver antenna arrays.
  • A. Contributions: Network-level results favor narrower beams with user–BS alignment, wider beams without alignment, and an optimum transmit beamwidth under typical conditions.
  • A. Contributions: Device-level performance improves through optimized power splitting and multi-antenna reception, supported by a low-power switch-based architecture for simultaneous energy and information transfer.
  • B. Related Work: Unlike prior lower-frequency energy-transfer studies, this work targets large-scale mmWave cellular networks whose distinct physical characteristics and design features prevent direct reuse of those results.
  • A. Network Model: The system model places mmWave BSs and wireless-powered users independently as homogeneous PPPs with densities λ and λu, respectively.
  • A. Network Model: Connected users associate with the BS maximizing average received power and assume perfect beam alignment, whereas users may experience energy outage below threshold ψ.
  • B. Channel Model: The channel model distinguishes LOS and NLOS links using separate path-loss exponents, incorporates blockage-dependent attenuation, and models independent Nakagami fading.

C. Antenna Model · III. MMWAVE WITH ENERGY HARVESTING · A. Stochastic Geometry Analysis

The paper models mmWave links with sectored directional antennas and analyzes energy harvesting at a typical user using stochastic geometry. It derives the distributions and assumptions needed to evaluate energy coverage for connected and nonconnected users.

  • C. Antenna Model: The sectored antenna model parameterizes main- and side-lobe directivity gains and half-power beamwidths for both BS and user antennas.BSs and users have Nt and Nr antenna elements, respectively.
  • C. Antenna Model: With uniformly distributed arrival and departure angles, the link directivity gain is modeled as a discrete random variable covering five antenna-alignment cases.The possible gains are MtMr, Mtmr, mtMr, mtmr, and 0, with probabilities determined by the beamwidth parameters.
  • C. Antenna Model: The zero-gain case represents complete beam misalignment, whereas a connected user has serving-link gain δ0 = MtMr under perfect beam alignment.The connected-mode assumption applies the maximum sectored-model gain to the serving BS link.
  • III. MMWAVE WITH ENERGY HARVESTING: The energy-harvesting section assumes users extract energy from incident mmWave signals without decoding information and analyzes connected and nonconnected users.Simultaneous information and power transfer is deferred to Section IV, while this section validates the analytical model after deriving energy coverage expressions.
  • A. Stochastic Geometry Analysis: The stochastic-geometry analysis characterizes nearest-LOS and nearest-NLOS BS distances using conditional PDFs and the probabilities of observing at least one BS of each type.LOS and NLOS association and link-distance distributions are developed through Lemmas 1–3.
  • A. Stochastic Geometry Analysis: The analysis evaluates a typical energy-harvesting user at the origin, with received power formed by summing BS transmit power, directivity, fading, and path gain across the network.Slivnyak’s theorem permits analysis at the origin without loss of generality.
  • A. Stochastic Geometry Analysis: Harvested energy depends on aggregate received power, the harvester activation threshold ψmin, and rectifier efficiency ξ ∈ (0, 1].The noise term is neglected because it is extremely small relative to the aggregate received signal.

Connected case:

For a connected user, the paper derives analytical and computationally simpler expressions for energy coverage and average harvested power. The analysis shows that LOS links dominate coverage and that harvested power scales with transmit power and, depending on α_L, with BS density.

  • Energy coverage: Theorem 1 gives the connected-case energy coverage probability P_con(λ, ψ) for energy outage threshold ψ, incorporating LOS and NLOS serving conditions.The probability is also the CCDF of harvested energy and depends on propagation, density, and antenna geometry parameters.
  • Energy coverage: Coverage is mainly influenced by LOS BSs, with λπR_B^2 representing the average number of LOS BSs seen by the user.The analytical approximation is relatively efficient to compute because it requires integration over a finite interval and evaluation of the Gamma function.
  • Average harvested power: Proposition 2 derives the useful average harvested power P̄_con(λ, ψ) for thresholds ψ ∈ [ψ_min, ∞), counting only incident signals that exceed the harvesting activation threshold.It follows by treating the energy coverage probability as the CCDF of the harvested-energy random variable.
  • Average harvested power: The limiting average harvested power is mainly determined by the serving LOS link and is independent of the small-scale fading parameters.The approximation is obtained by ignoring contributions from all but the serving LOS BS.
  • Scaling behavior: Average harvested power grows linearly with transmit power and may scale sublinearly to approximately linearly with BS density, depending on α_L.When α_L is large, increasing transmit power or BS density has almost the same effect; the text gives α_L = 3 as an example.

Nonconnected case:

For the nonconnected case, the paper derives energy-coverage and average-harvested-power expressions as functions of propagation conditions, network density, and antenna geometry. The average harvested power scales linearly with transmit power and BS density, unlike the connected case.

  • Nonconnected case:: Theorem 2 characterizes the nonconnected energy coverage probability Pncon(λ, ψ) for outage threshold ψ in a mmWave network of density λ.The expression is efficient to compute and depends on propagation conditions, network density, and antenna geometry parameters.
  • Nonconnected case:: Proposition 3 gives the average harvested power P̄ncon(λ, ψ) for energy outage thresholds ψ ∈ [ψmin, ∞).The result is expressed using the nonconnected energy coverage probability.
  • Nonconnected case:: The limiting-case average harvested power is characterized through ΨL(·) and ΨN(·).These functions are defined in equations (11) and (12), respectively.
  • Nonconnected case:: The average harvested power scales linearly with transmit power and BS density, so increasing either has the same effect.This follows because ΨL(·) and ΨN(·) depend linearly on transmit power and density through κ = 2πλPt; the behavior differs from the connected case.

B. Results and Design Insights

The results validate the analytical expressions and examine how antenna beam patterns affect energy coverage across connected and nonconnected networks. They also compare mmWave energy harvesting with lower-frequency solutions and report general-case energy coverage results.

  • Validation: Simulation results first verify the accuracy of the analytical expressions presented in Section III-A.The paper uses simulations as the initial validation step.
  • Antenna design: Antenna beam patterns are studied for their effects on energy coverage probability in purely connected and nonconnected networks.The cases correspond to ϵ →1 and ϵ →0, respectively.
  • Frequency comparison: The results compare mmWave energy harvesting with lower-frequency solutions and then provide energy coverage results for the general case.The comparison follows the connected and nonconnected scenario analysis.

Validation: … General case (0 < ϵ < 1):

Validation uses a 28 GHz mmWave system with single-antenna users and examines how beam geometry affects energy coverage across connected, nonconnected, and mixed user populations. Narrow beams favor connected users, wider beams favor nonconnected users, and the optimal BS array size depends on the user-population statistics.

  • Validation:: Validation assumes 28 GHz carrier frequency, blockage constant β = 0.0071, single omnidirectional receive antennas, ψ > ψmin, and rectifier efficiency ξ = 1.For ψ < ψmin, energy coverage probability flattens and is specified by Pcon(λ, ψmin) or Pncon(λ, ψmin).
  • Connected case (ϵ →1):: In the connected case, energy harvesting improves with narrower beams, corresponding to smaller beamwidths and larger directivity gains.Fewer neighboring-BS beams reach the user, but those that do have higher directivity gains.
  • Connected case (ϵ →1):: Under the stated comparison assumptions, mmWave energy harvesting provides considerable performance gain over UHF harvesting.The UHF baseline uses 8 transmit antennas per BS, maximal-ratio transmit beamforming, IID Rayleigh fading, path loss exponent 3.6, density 25 nodes/km2, 2.1 GHz carrier frequency, and 100 MHz bandwidth.
  • Nonconnected case (ϵ →0):: In the nonconnected case, wider beams improve mmWave energy harvesting because BS connectivity and alignment are critical.Wider beams increase the likelihood that a BS aligns with a receiver, at the expense of beamforming gain.
  • General case (0 < ϵ < 1):: The general case models a user population containing both connected and nonconnected users and characterizes beam patterns by half-power beamwidth and main- and side-lobe directivity gains.These antenna parameters are tuned to study overall energy coverage.
  • General case (0 < ϵ < 1):: The optimal transmit array size depends on user-population statistics: large BS arrays are desirable when ϵ is large, while small arrays are favorable when ϵ is small.The comparison uses overall energy coverage probability Λ(ϵ, ψ, λ) versus transmit array size Nt.

IV. MMWAVE SIMULTANEOUS INFORMATION AND POWER TRANSFER · A. Stochastic Geometry Analysis

The paper analyzes simultaneous wireless information and power transfer (SWIPT) in mmWave networks using stochastic geometry. It derives SINR coverage and joint success probabilities while examining power splitting, interference, and receiver antenna-array effects.

  • IV. MMWAVE SIMULTANEOUS INFORMATION AND POWER TRANSFER: SWIPT equips the energy-harvesting receiver with an information-decoding circuit and splits the received signal between energy harvesting and information decoding.A fraction √1 −ν is allocated to energy harvesting, while the remaining signal supports information decoding.
  • IV. MMWAVE SIMULTANEOUS INFORMATION AND POWER TRANSFER: A device is successful only when both SINR and harvested energy exceed their respective thresholds.The success probability Psuc(λ, T, ψ, ν) incorporates the SINR threshold T, energy threshold ψ, and splitting ratio ν.
  • A. Stochastic Geometry Analysis: The SINR coverage probability is modeled as a LOS/NLOS mixture weighted by the probabilities of being served by LOS and NLOS base stations.Pcov (λ, T, ν) = Pcov,L (λ, T, ν) ϱL + Pcov,N (λ, T, ν) ϱN.
  • A. Stochastic Geometry Analysis: Theorem 3 gives the analytical success probability Psuc(λ, T, ψ, ν) by combining SINR coverage with energy coverage.The SINR term follows from Lemma 4, whereas the energy term follows from Theorem 1.
  • A. Stochastic Geometry Analysis: The joint success probability depends on power splitting, SINR and energy thresholds, harvester activation, and rectifier efficiency.The interference CCDF also helps determine the system’s operating mode through parameter µ.
  • A. Stochastic Geometry Analysis: Interference harms information decoding but can benefit energy harvesting, so either SINR coverage or energy coverage can limit success.High interference typically makes SINR coverage limiting; when interference is low, energy coverage becomes the limiting factor.
  • A. Stochastic Geometry Analysis: Large receive antenna arrays can improve success probability, but the analytical model assumes ideal RF combining with power-hungry components.The cited components include phase shifters and multiple RF chains.

B. Low-power Receiver Architecture

The proposed low-power mmWave SWIPT receiver uses per-antenna power splitting, rectification, DC combining for energy harvesting, and RF combining for information reception. A greedy antenna-switching method avoids exhaustive-search complexity while retaining good combining gain with little performance loss.

  • Receiver Architecture: The architecture applies per-antenna power splitting, rectifies each signal, combines harvested DC energy, and combines information signals in the RF domain.The power-splitting parameter is ν.
  • Combining Design: Maximum post-combining SINR requires an optimum combining vector that may need global channel knowledge, which is challenging in practice.The receiver relaxes this requirement by using only the serving BS’s angle-of-arrival information.
  • Combining Design: Exhaustive search over all antenna-combining vectors can impose high computational cost and increase power consumption for large receive arrays.The proposed alternative activates antennas stepwise only when they improve the received SNR.
  • Combining Design: The low-complexity greedy approach provides good combining gain without substantial performance loss relative to more advanced, power-hungry solutions.This result is reported from numerical simulations.

C. Results

The results show that mmWave SWIPT can achieve reasonable overall success probability, with performance shaped by power splitting, SINR thresholds, and receive-array size. Optimizing the split and using larger receive arrays improve success probability under the evaluated conditions.

  • A reasonable overall success probability is achievable in the mmWave SWIPT system for typical propagation and system parameters.
  • The power splitting ratio ν must be optimized for the SINR outage threshold T to maximize overall success probability.As T increases, the system becomes SINR-limited and the optimum ν increases, favoring more received signal for information extraction.
  • Success probability improves as the receive antenna array size increases for the proposed low-power receiver architecture.The comparison includes fully digital maximal ratio combining (MRC) receivers, with curves averaged over the angle-of-arrival parameter.
  • When the SINR outage threshold T is small, success probability is mainly limited by energy outage and converges to a limit determined by the energy outage threshold.

V. CONCLUSIONS

The paper develops and validates a stochastic-geometry framework for mmWave energy and information transfer, using it to derive performance expressions and identify network- and device-level design insights. Device performance improves through optimized power splitting and large antenna arrays, enabled by a proposed low-power antenna-switching receiver architecture.

  • Analytical framework: The stochastic-geometry framework derives analytical expressions for mmWave energy and information transfer as functions of system, channel, and network parameters.Simulation results validate the accuracy of the derived expressions.
  • Device-level design: Optimizing the power splitting ratio and leveraging large antenna arrays can substantially improve device performance.These are identified as important device-related parameters affecting system performance.
  • Low-power receiver architecture: A low-power mmWave receiver architecture using antenna switches enables multiple antennas for simultaneous energy and information transfer while limiting power consumption.The architecture is proposed to support multi-antenna mmWave receivers under low-power constraints.

APPENDIX A: THEOREM 1

Theorem 1 is derived by approximating normalized-Gamma tail probabilities and evaluating conditional coverage distributions for LOS and NLOS serving links. The derivation uses PPP thinning, independent directivity gains, moment-generating functions, and the PPP probability generating functional.

  • Gamma approximation: A normalized-Gamma inequality upper-bounds Pr(u < x) by (1 − e^(−ax))^N, with a = N(N!)^−1.The substitution is approximate for finite N because u converges to 1 as N → ∞.
  • Conditional coverage distributions: The proof evaluates Pcon,L(λ, ψ) = Pr(S + I > ψ | L) for a receiver aligned with a LOS serving BS, where S is serving-BS power and I is interference power.The NLOS conditional distribution Pcon,N(λ, ψ) is derived similarly.
  • PPP decomposition: LOS and NLOS base stations are independently thinned into PPP tiers, and the user associates with the LOS or NLOS BS offering the maximum average received power.The LOS process is further split into four independent PPPs according to directivity gains.
  • Directivity modeling: Independent beam orientations assign directivity gain D_i with probability p_i, allowing received-power contributions from the resulting PPPs to be analyzed independently.This independence follows from the assumed independent beam orientations across links.
  • Theorem recovery: Conditioning on serving-link distance, normalized-Gamma moment-generating functions and the PPP probability generating functional simplify the LOS interference terms and recover the theorem expressions.The same framework yields the NLOS result using the corresponding conditional distribution and distance distribution from Lemma 3.

APPENDIX B: PROPOSITION 1 · APPENDIX C: COROLLARY 1 · APPENDIX D: THEOREM 3

The appendices simplify the mmWave analysis through a LOS-ball approximation, derive conditional mean received power, and establish the joint SINR-and-energy coverage expression. Theorem 3 additionally identifies an approximation arising from dropping interference-conditioning constraints.

  • APPENDIX B: PROPOSITION 1: A step-function LOS model marks base stations within radius RB as LOS and preserves the original LOS association probability ϱL.The approximation uses p(r) = 1{0<r<RB}, with ϱL = 1 − e−λπR2.
  • APPENDIX B: PROPOSITION 1: The Proposition 1 analysis neglects small-scale fading except on the serving link and ignores NLOS signals, leaving only LOS-ball base stations.This is described as likely in sufficiently dense networks.
  • APPENDIX B: PROPOSITION 1: Under the LOS-ball approximation, the serving-distance distribution simplifies to τL(x) = 2πλxϱL e−λπx2, with p5 = 0.The proof also invokes the PPP probability generating functional, a change of variables, and the generalized incomplete Gamma function.
  • APPENDIX C: COROLLARY 1: Corollary 1 derives the conditional mean received powers ¯PL = E[S + I|L] and ¯PN = E[S + I|N].The LOS conditional mean is evaluated by conditioning on the serving-link distance r0.
  • APPENDIX C: COROLLARY 1: The conditional means average over fading, apply Campbell’s theorem, and then average over r0 using Lemma 3 to obtain (9) and (10).The expressions use ΨL and ΨN as defined in (11) and (12).
  • APPENDIX D: THEOREM 3: Theorem 3 expresses harvested energy as γ = ξY 1{Y > ψmin} and evaluates joint success through Psuc(λ, T, ψ, ν) = Pr[SINR > T, γ > ψ].Y combines serving and interfering base-station contributions after signal splitting by ν.
  • APPENDIX D: THEOREM 3: Theorem 3’s approximation drops the conditions I > µ or I ≤ µ, effectively producing an upper bound while evaluating the expectation.The resulting SINR coverage follows from Lemma 4, energy coverage from Theorem 1, and ˜Pcon(λ, µ) is the interference CCDF at µ.
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