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Joint Transmit Signal and Beamforming Design for Integrated Sensing and Power Transfer Systems

Kenneth MacSporran Mayer, Nikita Shanin, Zhenlong You, Sebastian Lotter, Stefan Brückner, Martin Vossiek, Laura Cottatellucci, Robert Schober

TL;DR

An accurate non-linear circuit-based energy harvesting (EH) model is adopted and the proposed approach significantly outperforms a heuristic baseline scheme based on a linear EH model, which linearly combines energy beamforming with the beamsteering vector in the direction to the ST as its transmit strategy.

Abstract

Integrating different functionalities, conventionally implemented as dedicated systems, into a single platform allows utilising the available resources more efficiently. We consider an integrated sensing and power transfer (ISAPT) system and propose the joint optimisation of the rectangular pulse-shaped transmit signal and the beamforming vector to combine sensing and wireless power transfer (WPT) functionalities efficiently. In contrast to prior works, we adopt an accurate non-linear circuit-based energy harvesting (EH) model. We formulate and solve a non-convex optimisation problem for a general number of EH receivers to maximise a weighted sum of the average harvested powers at the EH receivers while ensuring the received echo signal reflected by a sensing target (ST) has sufficient power for estimating the range to the ST with a prescribed accuracy within the considered coverage region. The average harvested power is shown to monotonically increase with the pulse duration when the average transmit power budget is sufficiently large. We discuss the trade-off between sensing performance and power transfer for the considered ISAPT system. The proposed approach significantly outperforms a heuristic baseline scheme based on a linear EH model, which linearly combines energy beamforming with the beamsteering vector in the direction to the ST as its transmit strategy.

Joint Transmit Signal and Beamforming Design for Integrated Sensing and Power Transfer Systems

TL;DR

An accurate non-linear circuit-based energy harvesting (EH) model is adopted and the proposed approach significantly outperforms a heuristic baseline scheme based on a linear EH model, which linearly combines energy beamforming with the beamsteering vector in the direction to the ST as its transmit strategy.

Abstract

Integrating different functionalities, conventionally implemented as dedicated systems, into a single platform allows utilising the available resources more efficiently. We consider an integrated sensing and power transfer (ISAPT) system and propose the joint optimisation of the rectangular pulse-shaped transmit signal and the beamforming vector to combine sensing and wireless power transfer (WPT) functionalities efficiently. In contrast to prior works, we adopt an accurate non-linear circuit-based energy harvesting (EH) model. We formulate and solve a non-convex optimisation problem for a general number of EH receivers to maximise a weighted sum of the average harvested powers at the EH receivers while ensuring the received echo signal reflected by a sensing target (ST) has sufficient power for estimating the range to the ST with a prescribed accuracy within the considered coverage region. The average harvested power is shown to monotonically increase with the pulse duration when the average transmit power budget is sufficiently large. We discuss the trade-off between sensing performance and power transfer for the considered ISAPT system. The proposed approach significantly outperforms a heuristic baseline scheme based on a linear EH model, which linearly combines energy beamforming with the beamsteering vector in the direction to the ST as its transmit strategy.
Paper Structure (15 sections, 2 theorems, 22 equations, 2 figures, 1 table, 1 algorithm)

This paper contains 15 sections, 2 theorems, 22 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Transmit Signal Model
  4. Wireless Power Transfer System
  5. Sensing System
  6. Bounds on $\tau$ and $T$
  7. Sensing accuracy
  8. Problem Formulation and Proposed Solution
  9. Problem Formulation
  10. Feasibility Region of Problem \ref{['P1: Original Problem']}
  11. Problem Reformulation and Proposed Solution
  12. Results and Performance Evaluation
  13. Optimal Pulse Duration
  14. Performance Evaluation and Trade-Off Between Sensing Accuracy and Harvested Power
  15. Conclusion

Key Result

Proposition 1

The pulse duration $\tau$ has the feasible region $\mathcal{T} = \left[ \tau_\mathrm{min}, \tau_\mathrm{max} \right]$, where the minimum pulse duration $\tau_\mathrm{min}$ is given by with $z_3 =P_\mathrm{p} \| \boldsymbol{u} \|_2^2 \hat{R}_\mathrm{max}^2 / z^2 > 0$ and $z_4 = 4R_\mathrm{max}/c > 0$.

Figures (2)

  • Figure 1: Average harvested power $\phi(A^*_\tau \boldsymbol{w}^*_\tau, \tau)$ for $\tau \in \mathcal{T}_{n_\tau}$. The optimal pulse duration $\tau^*$ is highlighted in red.
  • Figure 2: Average harvested power $\phi(A^*_{\tau^*} \boldsymbol{w}^*_{\tau^*}, \tau^*)$ vs. $\hat{R}_\mathrm{max}$. Solid lines with crosses correspond to the proposed solution, while dash-dotted lines with circles indicate the baseline scheme.

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof