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Power Beacon-Assisted Millimeter Wave Ad Hoc Networks

Xiaohui Zhou, Jing Guo, Salman Durrani, Marco Di Renzo

TL;DR

A tractable model for PB-assisted millimeter wave (mmWave) wireless ad hoc networks, where each transmitter (TX) harvests energy from all PBs and then uses the harvested energy to transmit information to its desired receiver, confirms that it is feasible and safe to power TXs in an mmWave ad hoc network using PBs.

Abstract

Deployment of low cost power beacons (PBs) is a promising solution for dedicated wireless power transfer (WPT) in future wireless networks. In this paper, we present a tractable model for PB-assisted millimeter wave (mmWave) wireless ad hoc networks, where each transmitter (TX) harvests energy from all PBs and then uses the harvested energy to transmit information to its desired receiver. Our model accounts for realistic aspects of WPT and mmWave transmissions, such as power circuit activation threshold, allowed maximum harvested power, maximum transmit power, beamforming and blockage. Using stochastic geometry, we obtain the Laplace transform of the aggregate received power at the TX to calculate the power coverage probability. We approximate and discretize the transmit power of each TX into a finite number of discrete power levels in log scale to compute the channel and total coverage probability. We compare our analytical predictions to simulations and observe good accuracy. The proposed model allows insights into effect of system parameters, such as transmit power of PBs, PB density, main lobe beam-width and power circuit activation threshold on the overall coverage probability. The results confirm that it is feasible and safe to power TXs in a mmWave ad hoc network using PBs.

Power Beacon-Assisted Millimeter Wave Ad Hoc Networks

TL;DR

A tractable model for PB-assisted millimeter wave (mmWave) wireless ad hoc networks, where each transmitter (TX) harvests energy from all PBs and then uses the harvested energy to transmit information to its desired receiver, confirms that it is feasible and safe to power TXs in an mmWave ad hoc network using PBs.

Abstract

Deployment of low cost power beacons (PBs) is a promising solution for dedicated wireless power transfer (WPT) in future wireless networks. In this paper, we present a tractable model for PB-assisted millimeter wave (mmWave) wireless ad hoc networks, where each transmitter (TX) harvests energy from all PBs and then uses the harvested energy to transmit information to its desired receiver. Our model accounts for realistic aspects of WPT and mmWave transmissions, such as power circuit activation threshold, allowed maximum harvested power, maximum transmit power, beamforming and blockage. Using stochastic geometry, we obtain the Laplace transform of the aggregate received power at the TX to calculate the power coverage probability. We approximate and discretize the transmit power of each TX into a finite number of discrete power levels in log scale to compute the channel and total coverage probability. We compare our analytical predictions to simulations and observe good accuracy. The proposed model allows insights into effect of system parameters, such as transmit power of PBs, PB density, main lobe beam-width and power circuit activation threshold on the overall coverage probability. The results confirm that it is feasible and safe to power TXs in a mmWave ad hoc network using PBs.

Paper Structure

This paper contains 24 sections, 3 theorems, 34 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Approach and Contributions
  4. Notation and Paper Organization
  5. System Model
  6. Power Transfer and Information Transmission Model
  7. MmWave Blockage Model
  8. MmWave Channel Model
  9. Beamforming Model
  10. Metrics
  11. Power Transfer
  12. Information Transmission
  13. Transmit Power and Locations of Active TX
  14. Channel Coverage Probability
  15. Total Coverage Probability
  16. ...and 9 more sections

Key Result

Theorem 1

Following the system model in Section sec:model, the Laplace transform of the aggregate received power at the typical TX from all the PBs in a mmWave ad hoc network is where and $\Gamma(\cdot)$ is the complete gamma function, $\,_2F_1(\cdot,\cdot;\cdot;\cdot)$ is the Gaussian (or ordinary) hypergeometric function, $\delta_\mathrm{L}\triangleq\frac{2}{\alpha_\mathrm{L}}$ and $\delta_\mathrm{N}\tr

Figures (8)

  • Figure 1: Illustration of mmWave blockage model.
  • Figure 2: Power coverage probability versus power circuit activation threshold $\gamma_{\mathrm{PT}}$for different PB densities. Other system parameters follow Table \ref{['tab:values']}.
  • Figure 3: Channel coverage probability and total coverage probability versus SINR threshold $\gamma_{\mathrm{TR}}$. The PB density is 50 and 10 per $\textrm{km}^2$ and the TX density is 500, 100, 250 and 50 per $\textrm{km}^2$.
  • Figure 4: Coverage probabilities versus PB transmit power $P_p$.
  • Figure 5: Channel coverage probability and total coverage probability versus power circuit activation threshold $\gamma_{\mathrm{PT}}$ with different TX and RX beamforming parameters.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Definition 1
  • Remark 1
  • Theorem 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Definition 2
  • Remark 5
  • Proposition 1
  • Corollary 1