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Optimal Reflection Coefficients for ASK Modulated Backscattering from Passive Tags

Amus Chee Yuen Goay, Deepak Mishra, Aruna Seneviratne

Abstract

This paper studies backscatter communication (BackCom) systems with a passive backscatter tag. The effectiveness of these tags is limited by the amount of energy they can harness from incident radio signals, which are used to backscatter information through the modulation of reflections. To address this limitation, we adopt a practical Constant-Linear-Constant (CLC) energy harvesting model that accounts for the harvester's sensitivity and saturation threshold, both of which depend on the input power. This paper aims to maximize this harvested power at a passive tag by optimally designing the underlying M-ary amplitude-shift keying (ASK) modulator in a monostatic BackCom system. Specifically, we derive the closed-form expression for the global optimal reflection coefficients that maximize the tag's harvested power while satisfying the minimum symbol error rate (SER) requirement, tag sensitivity, and reader sensitivity constraints. We also proposed optimal binary-ASK modulation design to gain novel design insights on practical BackCom systems with readers having superior sensitivity. We have validated these nontrivial analytical claims via extensive simulations. The numerical results provide insight into the impact of the transmit symbol probability, tag sensitivity constraint, and SER on the maximum average harvested power. Remarkably, our design achieves an overall gain of around 13% over the benchmark, signifying its utility in improving the efficiency of BackCom systems. Moreover, our proposed solution methodology for determining the maximum average harvested power is applicable to any type of energy harvesting model that exhibits a monotonic increasing relationship with the input power.

Optimal Reflection Coefficients for ASK Modulated Backscattering from Passive Tags

Abstract

This paper studies backscatter communication (BackCom) systems with a passive backscatter tag. The effectiveness of these tags is limited by the amount of energy they can harness from incident radio signals, which are used to backscatter information through the modulation of reflections. To address this limitation, we adopt a practical Constant-Linear-Constant (CLC) energy harvesting model that accounts for the harvester's sensitivity and saturation threshold, both of which depend on the input power. This paper aims to maximize this harvested power at a passive tag by optimally designing the underlying M-ary amplitude-shift keying (ASK) modulator in a monostatic BackCom system. Specifically, we derive the closed-form expression for the global optimal reflection coefficients that maximize the tag's harvested power while satisfying the minimum symbol error rate (SER) requirement, tag sensitivity, and reader sensitivity constraints. We also proposed optimal binary-ASK modulation design to gain novel design insights on practical BackCom systems with readers having superior sensitivity. We have validated these nontrivial analytical claims via extensive simulations. The numerical results provide insight into the impact of the transmit symbol probability, tag sensitivity constraint, and SER on the maximum average harvested power. Remarkably, our design achieves an overall gain of around 13% over the benchmark, signifying its utility in improving the efficiency of BackCom systems. Moreover, our proposed solution methodology for determining the maximum average harvested power is applicable to any type of energy harvesting model that exhibits a monotonic increasing relationship with the input power.

Paper Structure

This paper contains 28 sections, 9 theorems, 45 equations, 15 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. State-of-the-Art
  3. Motivation and Contributions
  4. Paper Organization and Notations
  5. System Description
  6. System Model and Transmission Protocol
  7. M-ary ASK Modulation
  8. Performance Metrics for BackCom
  9. Tag Power Sensitivity
  10. Reader Sensitivity
  11. Symbol Error Rate
  12. Problem Definition
  13. Optimization Formulation for the General Case
  14. Optimization with BASK Modulation
  15. Solution Methodology
  16. ...and 13 more sections

Key Result

Lemma 1

The average harvested power is maximized when either $\Gamma_{{\rm a}i}=0$ or $\Gamma_{{\rm b}i}=0$, $\forall i \in \mathbb{M}$.

Figures (15)

  • Figure 1: Monostatic BackCom system model.
  • Figure 2: Equivalent Thevenin Circuit of the Backscatter Tag with Minimum Scattering Antenna for $M$-ASK Modulation.
  • Figure 3: The descending order sequence of $\Gamma_{\left(k\right)}$ on number line
  • Figure 4: Design insights on $P^\ast_{\rm L,avg}$ for 4-ASK.
  • Figure 5: Design insights on $P^\ast_{\rm L,avg}$ for 8-ASK.
  • ...and 10 more figures

Theorems & Definitions (20)

  • Lemma 1
  • Proof
  • Lemma 2
  • Proof
  • Lemma 3
  • Proof
  • Corollary 1
  • Proof
  • Theorem 1
  • Proof
  • ...and 10 more