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Spatially-aware Secondary License Sharing in mmWave Networks

Shuchi Tripathi, Abhishek K. Gupta

Abstract

In this work, we consider a multi-operator mmWave network implementing secondary license sharing (SLS) where a primary license holder leases secondary licenses to secondary users, allowing them to access its licensed spectrum under some pre-defined transmission constraints. The highly directional nature of mmWaves, along with their sensitivity to blockages, naturally confines the interference to/from devices to narrow angular sectors within a certain range around themselves. This motivates us to consider a spatially-aware SLS that determines a secondary link's activity based on its distance/orientation relative to the primary link, as well as blockages around it. By leveraging the tools of stochastic geometry, we develop an analytical framework to design and study such spatially-aware SLS in mmWave networks. Our analysis quantifies the transmission opportunities available to secondary users and the resulting coverage probabilities for both primary and secondary links. We characterize the effect of directionality and blockage conditions, along with transmission restrictions and secondary users' density, on the performance of both operators. Via numerical investigation, we derive various insights. We show that blockage conditions can change the shape of coverage plots and thus affect key conclusions. Further, blockage and directionality can increase the transmission opportunities for secondary users, improving the feasibility and gains of SLS.

Spatially-aware Secondary License Sharing in mmWave Networks

Abstract

In this work, we consider a multi-operator mmWave network implementing secondary license sharing (SLS) where a primary license holder leases secondary licenses to secondary users, allowing them to access its licensed spectrum under some pre-defined transmission constraints. The highly directional nature of mmWaves, along with their sensitivity to blockages, naturally confines the interference to/from devices to narrow angular sectors within a certain range around themselves. This motivates us to consider a spatially-aware SLS that determines a secondary link's activity based on its distance/orientation relative to the primary link, as well as blockages around it. By leveraging the tools of stochastic geometry, we develop an analytical framework to design and study such spatially-aware SLS in mmWave networks. Our analysis quantifies the transmission opportunities available to secondary users and the resulting coverage probabilities for both primary and secondary links. We characterize the effect of directionality and blockage conditions, along with transmission restrictions and secondary users' density, on the performance of both operators. Via numerical investigation, we derive various insights. We show that blockage conditions can change the shape of coverage plots and thus affect key conclusions. Further, blockage and directionality can increase the transmission opportunities for secondary users, improving the feasibility and gains of SLS.
Paper Structure (30 sections, 11 theorems, 40 equations, 12 figures, 4 tables)

This paper contains 30 sections, 11 theorems, 40 equations, 12 figures, 4 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Sectorized beam pattern
  4. Ideal beam pattern
  5. Analysis
  6. Medium access probability (MAP)
  7. Activity factor (AF)
  8. Coverage of primary link
  9. Coverage of secondary links
  10. Secondary coverage at a given location
  11. Coverage of the typical secondary link
  12. Numerical Results and Insights
  13. MAP of secondary links
  14. AF of the secondary network
  15. Impact of spatially-aware SLS
  16. ...and 15 more sections

Key Result

Lemma 1

The MAP of the $i^{\mathrm{th}}$ secondary transmitter at location $\mathbf{X}_{\mathrm{s}i} = x_{\mathrm{s}i} \angle{ \theta_{\mathrm{s}i} }$ is given as where $p_\mathrm{L} (x_{\mathrm{s} i}) = \exp(-\mu x_{\mathrm{s} i} - p)$, $p_\mathrm{N} (x_{\mathrm{s} i}) = 1 - p_\mathrm{L} (x_{\mathrm{s} i})$, $\kappa_T = (\rho/p_\mathrm{s})/(C_T)$ and $\kappa_{i\mathrm{0}} = g_{\mathrm{pr}} ( \theta_{\ma

Figures (12)

  • Figure 1: An illustration of the system model for analysis of (a) the primary coverage network and (b) the channel fading model.
  • Figure 2: An illustration of (a) the new coordinate reference for the secondary links' coverage analysis and (b)the three set-ups for the primary link's location with parameters $\{\angle \delta_{\mathrm{p}\mathrm{0}}, x_{\mathrm{p}\mathrm{0}}, \angle{\omega_{\mathrm{p}\mathrm{0}}}\}$ taken as (i) $\{\pi/2, 50 \,\text{m}, \pi/12\}$, (ii) $\{\pi/2, 80 \, \text{m}, -\pi/2\}$ and (iii) $\{\pi/2, 10 \,\text{m}, \pi/2\}$.
  • Figure 3: The spatial variation of $p_{\mathrm{m}i}$ with $\lambda_\mathrm{s} = 8 \times 10^{-3}$ /$\text{m}^2$ and $M = (4, \, 4)$ for (a) $\rho = 10$ femto-Watts and (b) $\rho = 1$ femto-Watts. Both ends of the primary and secondary links have antennas and each $\bullet\!\!\!-\!\!\!-\!\!\!\blacklozenge$ represents a primary receiver-transmitter pair.
  • Figure 4: The variation of secondary AF $\eta_\mathrm{s}$ with average LOS distance $L_\mu = 1/\mu$ (in meters) for different values of interference-threshold $\rho$ with (a) $M = (1,1)$ and (b) $M = (4,4)$. Here, radius of region of interest $R = 1000$ m.
  • Figure 5: The variation of secondary AF $\eta_\mathrm{s}$ with the interference-threshold $\rho$ for $M = (4,4)$ by varying (a) the value of $L_\mu$ (in m) with $R = 1000$ m and (b) the values of region-of-interest radius $R$ with $L_\mu = 200$ m.
  • ...and 7 more figures

Theorems & Definitions (22)

  • Lemma 1
  • Remark 1
  • Remark 2
  • Corollary 1
  • Theorem 1
  • Remark 3
  • Corollary 2
  • Remark 4
  • Example 1
  • Theorem 2
  • ...and 12 more