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EVT-enriched Radio Maps for URLLC

Dian Echevarría Pérez, Onel L. Alcaraz López, Hirley Alves

TL;DR

This paper introduces a sophisticated and adaptable framework combining extreme value theory with radio maps to spatially model extreme channel conditions accurately and evaluates the performance of this method in a rate maximisation problem with defined outage constraints and compares it with a benchmark in the literature.

Abstract

This paper introduces a sophisticated and adaptable framework combining extreme value theory with radio maps to spatially model extreme channel conditions accurately. Utilising existing signal-to-noise ratio (SNR) measurements and leveraging Gaussian processes, our approach predicts the tail of the SNR distribution, which entails estimating the parameters of a generalised Pareto distribution, at unobserved locations. This innovative method offers a versatile solution adaptable to various resource allocation challenges in ultra-reliable low-latency communications. We evaluate the performance of this method in a rate maximisation problem with defined outage constraints and compare it with a benchmark in the literature. Notably, the proposed approach meets the outage demands in a larger percentage of the coverage area and reaches higher transmission rates.

EVT-enriched Radio Maps for URLLC

TL;DR

This paper introduces a sophisticated and adaptable framework combining extreme value theory with radio maps to spatially model extreme channel conditions accurately and evaluates the performance of this method in a rate maximisation problem with defined outage constraints and compares it with a benchmark in the literature.

Abstract

This paper introduces a sophisticated and adaptable framework combining extreme value theory with radio maps to spatially model extreme channel conditions accurately. Utilising existing signal-to-noise ratio (SNR) measurements and leveraging Gaussian processes, our approach predicts the tail of the SNR distribution, which entails estimating the parameters of a generalised Pareto distribution, at unobserved locations. This innovative method offers a versatile solution adaptable to various resource allocation challenges in ultra-reliable low-latency communications. We evaluate the performance of this method in a rate maximisation problem with defined outage constraints and compare it with a benchmark in the literature. Notably, the proposed approach meets the outage demands in a larger percentage of the coverage area and reaches higher transmission rates.
Paper Structure (16 sections, 1 theorem, 28 equations, 11 figures, 2 tables, 1 algorithm)

This paper contains 16 sections, 1 theorem, 28 equations, 11 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. EVT for URLLC
  3. Radio Maps and applications for URLLC
  4. Contributions
  5. System model
  6. Problem definition
  7. EVT and radio maps integration
  8. EVT preliminaries
  9. EVT-based constraint reformulation
  10. Radio map construction
  11. Definition of predictive constraint
  12. Optimization framework
  13. Proposed algorithm
  14. Benchamrk
  15. Numerical Results
  16. ...and 1 more sections

Key Result

Theorem 1

For a given random variable $X$ from a non-degenerative distribution and for a large enough threshold $\mu$, the cumulative distribution function (CDF) of $Z =X-\mu$ conditioned on $X>\mu$ is given by defined on $\{z: z>0 \ \text{and} \ 1+\xi z/\sigma > 0\}$. The distribution in GPD is known as the GPD with shape and scale parameters $\xi$ and $\sigma$, respectively.

Figures (11)

  • Figure 1: System model. The BS serves $K$ UEs in the DL, guaranteeing URLLC quality-of-service demands. The crosses depict the locations where SNR measurements are available from previous UEs in the network. Notice that the density of observation points in the figure does not match the number of localisations with available samples in a real scenario and is only used for visualisation purposes. The GPS provides the localisation of the SNR measurements and UEs.
  • Figure 2: Predictive mean of the threshold $\hat{\mu}$ (left) at each location in the coverage area, and actual threshold $\mu$ (right) obtained from the test data. The number of samples used is $N=10^5$ and $\rho = 0.99$.
  • Figure 3: Predictive mean of the scale $\hat{\sigma}$ (left) at each location in the coverage area, and actual scale $\sigma$ (right) obtained from the test data. The number of samples used is $N=10^5$ and $\rho = 0.99$.
  • Figure 4: Predictive mean of the shape $\hat{\xi}$ (left) at each location in the coverage area, and actual shape $\xi$ (right) obtained from the test data. The number of samples used is $N=10^5$ and $\rho = 0.99$.
  • Figure 5: Empirical CDF of the Bhattacharyya distance between predicted GPD and actual GPD with a common threshold value for a different number of samples with $\rho=0.99$.
  • ...and 6 more figures

Theorems & Definitions (1)

  • Theorem 1: Theorem for Exceedances Over Thresholds coles2001introduction