PaperlayerView exact revision on arXiv

Source-linked AI summary

On the Outage Performance of Ambient Backscatter Communications

Yinghui Ye, Liqin Shi, Xiaoli Chu, Guangyue Lu

arXiv:2005.07164v1cs.ITmath.IT

TL;DR

Prior analyses often did not jointly account for co-channel interference and nonlinear energy harvesting when evaluating outage in ambient backscatter systems. This paper analyzes a multi-link system with opportunistic selection and an adaptive reflection coefficient, and reports outage saturation and trade-offs involving link selection and harvesting-model choice.

  • Problem

    Prior work often assumed perfect cancellation or ignored co-channel interference, and commonly used a linear harvesting model despite the practical harvester’s nonlinearity.

    Source: §I · p. 2

  • Method

    The paper analyzes outage in a multi-link ambient-backscatter network with opportunistic link selection and proposes an adaptive reflection coefficient under nonlinear energy harvesting.

    Source: §I · p. 2

  • Results

    The paper reports outage saturation for both links at high legacy-transmitter power, slight legacy-outage degradation when the lowest-interference device transmits, and opposite outage-estimation biases from the linear harvesting model.

    Source: §I · p. 3

  • Takeaways & Limitations

    Within the considered network, outage depends on co-channel interference, harvesting-model choice, and device location, and the selected link can produce best- or worst-case outcomes for either transmission.

    Source: §I · p. 3, §VI · p. 11

Abstract

from arXiv · show

Ambient backscatter communications (AmBackComs) have been recognized as a spectrum- and energy-efficient technology for Internet of Things, as it allows passive backscatter devices (BDs) to modulate their information into the legacy signals, e.g., cellular signals, and reflect them to their associated receivers while harvesting energy from the legacy signals to power their circuit operation. {\color{black} However, the co-channel interference between the backscatter link and the legacy link and the non-linear behavior of energy harvesters at the BDs have largely been ignored in the performance analysis of AmBackComs. Taking these two aspects, this paper provides a comprehensive outage performance analysis for an AmBackCom system with multiple backscatter links}, where one of the backscatter links is opportunistically selected to leverage the legacy signals transmitted in a given resource block. For any selected backscatter link, we propose an adaptive reflection coefficient (RC), which is adapted to the non-linear energy harvesting (EH) model and the location of the selected backscatter link, to minimize the outage probability of the backscatter link. In order to study the impact of co-channel interference on both backscatter and legacy links, for a selected backscatter link, we derive the outage probabilities for the legacy link and the backscatter link. Furthermore, we study the best and worst outage performances for the backscatter system where the selected backscatter link maximizes or minimizes the signal-to-interference-plus noise ratio (SINR) at the backscatter receiver. We also study the best and worst outage performances for the legacy link where the selected backscatter link results in the lowest and highest co-channel interference to the legacy receiver, respectively.

I. INTRODUCTION

Ambient backscatter reuses legacy signals for information and energy, but prior outage analyses often idealized interference and energy harvesting. This paper analyzes a multi-link system with opportunistic link selection, a nonlinear harvesting model, and an adaptive reflection coefficient.

I. INTRODUCTION

  • Prior analyses often assumed perfect interference cancellation or ignored interference, while many also used a linear harvesting model; the paper identifies a lack of comprehensive outage analysis for both links.The introduction notes that inaccurate harvesting models affect the SINRs of both legacy and backscatter links.Source: §I · p. 2
  • The paper proposes an adaptive reflection coefficient under a practical nonlinear energy-harvesting model, derives outage probabilities for both links, and evaluates best- and worst-case link selections.The backscatter cases are selected by receiver SINR, while the legacy cases are selected by interference at the legacy receiver.Source: §I · pp. 2–3
  • The introduction reports outage saturation at high legacy-transmitter power, a slight legacy-outage degradation when the lowest-interference device transmits, and opposing biases from a linear harvesting model.The linear model overestimates backscatter-link outage and slightly underestimates legacy-link outage.Source: §I · p. 3

II. SYSTEM MODEL

  • The system has one legacy transmitter, one legacy receiver, and K backscatter devices with receivers; one backscatter link is selected per resource block while the others remain silent.This selection is described as avoiding severe interference among backscatter links.Source: §I · p. 2, §II · p. 3
  • The model treats channels as quasi-static with path loss and Rayleigh fading, and accounts for both harvested-energy sufficiency and receiver decoding.A device that lacks enough harvested energy stays silent; when it has enough, it backscatters information.Source: §II · pp. 3–4

III. OUTAGE ANALYSIS FOR AMBACKCOMS

Backscatter-link outage combines insufficient harvested energy with decoding failure when the device has enough energy. The paper chooses the reflection coefficient adaptively to minimize this outage while satisfying the device’s circuit-energy requirement.

III. OUTAGE ANALYSIS FOR AMBACKCOMS

  • Backscatter-link outage consists of energy outage plus the probability of decoding failure when harvested energy is sufficient for circuit operation.The outage definition separates a device lacking energy from a receiver failing to decode backscattered information.Source: §III · p. 4

A. Adaptive RC Scheme

  • The adaptive reflection-coefficient scheme minimizes backscatter-link outage for each selected link under a practical nonlinear energy-harvesting model.The paper states that the resulting closed-form optimal coefficient provides a setting guideline for practical systems.Source: A. Adaptive RC Scheme · p. 4
  • The coefficient must satisfy the harvested-energy requirement for circuit operation; if harvested energy is insufficient, the device is inactive and its backscatter link is in outage.The paper formulates successful transmission as requiring both adequate energy and an SINR above the decoding threshold.Source: A. Adaptive RC Scheme · p. 4

B. Outage Analysis for the k-th Backscatter Link

The section derives outage probabilities for an individual backscatter link, then provides approximations and a high-transmit-power bound to analyze their behavior. It also identifies outage saturation from legacy-transmission interference.

B. Outage Analysis for the k-th Backscatter Link

  • The outage probability is derived using the distribution of the multiplicative and additive channel gain S_k.The section first gives the CDF and PDF of S_k, then uses them to calculate the k-th link's outage probability.Source: B. Outage Analysis for the k-th… · p. 5
  • Because the outage expression still contains a non-closed-form integral, the section considers Gaussian-Chebyshev quadrature and a high-transmit-power approximation.The quadrature parameter M trades complexity against accuracy.Source: B. Outage Analysis for the k-th… · p. 5
  • The Gaussian-Chebyshev expression can evaluate outage accurately with a small M, avoiding Monte Carlo simulations and supporting analysis of parameter effects.The passage also describes the expression and resulting numerical evaluations as useful for assessing practical system performance.Source: B. Outage Analysis for the k-th… · p. 5
  • The high-transmit-power bound reveals outage saturation caused by legacy-transmission interference at the k-th backscatter link.The bound also identifies diversity gain and shows that its limiting outage probability decreases as the stated channel-gain product increases.Source: B. Outage Analysis for the k-th… · p. 6

1) Outage Probability under the Best Case:

The best case selects the backscatter link with the maximum SINR at the backscatter receiver, and the section gives a lower bound on its outage probability.

1) Outage Probability under the Best Case:

2) Outage Probability under the Worst Case:

The worst case selects the backscatter link with the minimum SINR at the backscatter receiver, and the section gives a lower bound on its outage probability.

2) Outage Probability under the Worst Case:

IV. OUTAGE ANALYSIS FOR LEGACY TRANSMISSION

The legacy-link outage analysis distinguishes whether the backscatter device has enough energy and compares cases where the selected backscatter link causes the least or greatest interference at the legacy receiver.

IV. OUTAGE ANALYSIS FOR LEGACY TRANSMISSION

  • Legacy-link outage occurs if the received SNR is below threshold when the device lacks energy, or the received SINR is below threshold when it has enough energy.Source: §IV · p. 6
  • The outage expression separates the cases where harvested energy is at least the circuit consumption and where it is below that consumption.The section then gives a lower bound for legacy-transmission outage probability.Source: §IV · pp. 6–7
  • The legacy-link best case uses the selected backscatter link with minimum interference at the legacy receiver; the worst case uses maximum interference.These cases bound legacy-link outage performance.Source: §IV · p. 7

A. Outage Probability under the Best Case

The best-case legacy outage analysis distinguishes whether backscatter links have enough energy to operate. When all are active, it selects the link with minimum interference; the outage probability is built from the corresponding energy and outage events.

A. Outage Probability under the Best Case

  • When all backscatter links are active, the best case selects the link with minimum interference Gmin; if any link lacks energy, it selects an inactive link.The active-link case uses the minimum of G1 through GK.Source: A. Outage Probability under the Best… · p. 7
  • The best-case legacy outage probability combines the probability that all links have enough energy, the conditional probability of legacy outage, and the outage probability with backscatter inactive.The inactive-link term is the legacy outage probability when backscatter has no impact on legacy transmission.Source: A. Outage Probability under the Best… · p. 7
  • The analysis obtains the distribution of minimum interference conditioned on all links having enough energy, then uses it to compute the conditional outage probability.The derivation applies Gaussian-Chebyshev quadrature to approximate the resulting probability.Source: A. Outage Probability under the Best… · pp. 7–8
  • The best-case legacy outage lower bound is assembled from the two event probabilities and the inactive-backscatter outage term.The section states that the lower bound can be written after computing P1 and P2.Source: A. Outage Probability under the Best… · pp. 7–8

B. Outage Probability under the Worst Case

The worst-case outage analysis considers selection that maximizes interference and derives a legacy-link outage lower bound. The accompanying simulation section specifies the evaluated system settings.

B. Outage Probability under the Worst Case

  • The worst-case legacy outage analysis uses the maximum interference across the K backscatter links and derives its CDF.The analysis uses that distribution to approximate the outage probability and compute a lower bound.Source: B. Outage Probability under the Worst… · p. 8
  • Table II summarizes the meanings of the derived outage probabilities, including the lowest and highest backscatter-system outage probabilities.Its notation includes the best- and worst-case backscatter outage probabilities.Source: Table II · p. 8, B. Outage Probability under the Worst… · p. 8

V. SIMULATION AND DISCUSSION

  • The simulations use K = 3 links, a 1 MHz bandwidth, 8.9 µW circuit power per device, and a 10 Mbps legacy transmission rate.The stated nonlinear energy-harvesting parameters set Emax to 240 µW for each device.Source: §V · p. 9
  • The simulation setting specifies link distances, a 915 MHz legacy signal, and antenna gains of 1.8 dBi for BDs and 6 dBi for the LT, LR, and BRs.The distances are listed for the LT, BDs, LR, and BRs.Source: §V · p. 9

A. Outage performance analysis for the backscatter links

The outage analysis finds interference-driven saturation and location-dependent trade-offs between legacy and backscatter links. Link selection, energy-harvesting assumptions, and deployment geometry shape the resulting performance.

A. Outage performance analysis for the backscatter links

  • Monte Carlo simulations match the derived backscatter outage probabilities; increasing LT power reduces outage only until an interference-driven error floor, which maximum-BR-SINR selection can lower.The simulations use more than 1 × 10^6 trials, and M = 10 is sufficient for accurate Gaussian-Chebyshev approximation.Source: A. Outage performance analysis for the… · p. 9
  • The adaptive RC scheme achieves better outage capacity than fixed and random RC schemes as circuit power consumption increases.The comparison uses the third BD with LT power set to 20 dBm.Source: A. Outage performance analysis for the… · p. 9

B. The impact of backscatter links on the legacy transmission

C. Trade-off for the outage performance between the legacy transmission and the backscatter link

  • BD angle creates both win-win and trade-off regions: θ ∈ [π/2, π] improves both links, whereas θ ∈ [3π/2, 2π] worsens both.The outage minima occur at θ = π for the legacy link and θ = 3π/2 for the backscatter link.Source: C. Trade-off for the outage… · p. 10
  • As LT–BD distance increases, legacy outage decreases while backscatter outage increases; under a legacy outage constraint, a smaller distance favors backscatter.The paper attributes the opposite trends to lower received RF power at greater distance.Source: C. Trade-off for the outage… · p. 11

VI. CONCLUSIONS

  • Co-channel interference saturates outage in both links and backscatter imposes a legacy rate ceiling; minimum-interference selection minimizes legacy loss, while linear EH overestimates backscatter outage.The conclusion reports that the linear EH model has very little impact on legacy-link outage.Source: §VI · p. 11

APPENDIX A

These appendices work through distribution calculations used in the outage analysis, including conditional CDF/PDF expressions and special-function evaluations.

APPENDIX A

  • Appendix A derives FSk(x) using variable substitutions and identities involving modified Bessel functions K1 and K0.Source: Appendix A · p. 11

APPENDIX B

  • Appendix B uses a proposition for the conditional CDF and PDF of Sk given |h1k|^2 ≥ bk/ak to calculate I2.Source: Appendix B · pp. 11–12

APPENDIX C

  • Appendix C evaluates I2−2 using gamma- and Whittaker-function identities.The text defines Γ(x) as the gamma function and identifies Wμ,ν(x) as a Whittaker function.Source: Appendix C · p. 12

APPENDIX D

The appendices approximate an otherwise non-closed-form integral at high LT power and derive CDFs for minimum- and maximum-based quantities.

APPENDIX D

  • Appendix D approximates a non-closed-form integral for high LT transmit power, with noise power treated as very small.Source: Appendix D · p. 12

APPENDIX E

  • Appendix E derives the CDF of Gk and then the CDF of min(G1, G2, …, GK), including a conditioned form.Source: Appendix E · p. 12

APPENDIX F

  • Appendix F derives the CDF of bGk and uses it to calculate the CDF of bGmax.Source: Appendix F · p. 13
Loading 2005.07164v1…