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The Rendezvous Between Extreme Value Theory and Next-generation Networks

Srinivas Sagar, Athira Subhash, Chen-Feng Liu, Ahmed Elzanaty, Yazan H. Al-Badarneh, Sheetal Kalyani, Mohamed-Slim Alouini, Mehdi Bennis, Lajos Hanzo

TL;DR

This paper surveys how extreme value theory (EVT) can model and analyze rare, extreme events in next-generation wireless networks. It provides a cohesive view of EVT fundamentals—i.i.d. and i.n.i.d. settings, peak-over-threshold, and convergence rates—and maps them to a wide range of NG applications, including multi-user diversity, spectrum sharing, relays, massive MIMO, URLLC, and ML-enabled systems. The key contribution is a unified treatment showing that maxima/minima often converge to Gumbel, Frechet, or Weibull laws, with exceedances well modeled by the generalized Pareto distribution, enabling simple yet powerful tail-based performance analyses and design insights. The article also discusses practical limitations (dependencies, finite samples, correlations) and outlines promising future directions, such as green networking, non-terrestrial and ISAC systems, and deeper integration of EVT with AI/ML for robust NG network design.

Abstract

Promising technologies such as massive multiple-input and multiple-output, reconfigurable intelligent reflecting surfaces, non-terrestrial networks, millimetre wave communication, ultra-reliable lowlatency communication are envisioned as the enablers for next-generation (NG) networks. In contrast to conventional communication systems meeting specific average performance requirements, NG systems are expected to meet quality-of-service requirements in extreme scenarios as well. In this regard, extreme value theory (EVT) provides a powerful framework for the design of communication systems. In this paper, we provide a comprehensive survey of advances in communication that utilize EVT to characterize the extreme order statistics of interest. We first give an overview of the history of EVT and then elaborate on the fundamental theorems. Subsequently, we discuss different problems of interest in NG communication systems and how EVT can be utilized for their analysis. We finally point out the open challenges and future directions of EVT in NG communication systems.

The Rendezvous Between Extreme Value Theory and Next-generation Networks

TL;DR

This paper surveys how extreme value theory (EVT) can model and analyze rare, extreme events in next-generation wireless networks. It provides a cohesive view of EVT fundamentals—i.i.d. and i.n.i.d. settings, peak-over-threshold, and convergence rates—and maps them to a wide range of NG applications, including multi-user diversity, spectrum sharing, relays, massive MIMO, URLLC, and ML-enabled systems. The key contribution is a unified treatment showing that maxima/minima often converge to Gumbel, Frechet, or Weibull laws, with exceedances well modeled by the generalized Pareto distribution, enabling simple yet powerful tail-based performance analyses and design insights. The article also discusses practical limitations (dependencies, finite samples, correlations) and outlines promising future directions, such as green networking, non-terrestrial and ISAC systems, and deeper integration of EVT with AI/ML for robust NG network design.

Abstract

Promising technologies such as massive multiple-input and multiple-output, reconfigurable intelligent reflecting surfaces, non-terrestrial networks, millimetre wave communication, ultra-reliable lowlatency communication are envisioned as the enablers for next-generation (NG) networks. In contrast to conventional communication systems meeting specific average performance requirements, NG systems are expected to meet quality-of-service requirements in extreme scenarios as well. In this regard, extreme value theory (EVT) provides a powerful framework for the design of communication systems. In this paper, we provide a comprehensive survey of advances in communication that utilize EVT to characterize the extreme order statistics of interest. We first give an overview of the history of EVT and then elaborate on the fundamental theorems. Subsequently, we discuss different problems of interest in NG communication systems and how EVT can be utilized for their analysis. We finally point out the open challenges and future directions of EVT in NG communication systems.
Paper Structure (36 sections, 2 theorems, 29 equations, 17 figures, 7 tables)

This paper contains 36 sections, 2 theorems, 29 equations, 17 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Overview of EVT
  3. Overview of EVT in Communications
  4. History of EVT in Communications
  5. Related Review Articles
  6. Notations
  7. Organization
  8. Mathematics behind Extreme Value Theory
  9. EVT for i.i.d. RVs
  10. EVT for i.n.i.d. RVs
  11. Peak over Threshold Using EVT
  12. Rate of Convergence
  13. EVT for NG Applications
  14. Multi-User Diversity
  15. Spectrum Sharing
  16. ...and 21 more sections

Key Result

Theorem 1

The class of EVDs is $G_{\beta}\left(ax+b\right)$ with $a>0$ and $b \in \mathbb{R}$, where with $\beta \in \mathbb R$ and for $\beta=0$, the right-hand side is interpreted as $\exp\left[-\exp\left(-x\right)\right]$.

Figures (17)

  • Figure 1: EVT evolution and Communication Pyramid
  • Figure 2: Various mathematical tools across different disciplines are required to utilize EVT for communications engineering.
  • Figure 3: PDF of EVDs for $a=0$, $b=1$.
  • Figure 4: llustration of the limiting distributions of the maximum and minimum for an exponential random variable. (a) shows the Gumbel distribution as the limiting distribution for the maximum of $K$i.i.d. exponential RVs, while (b) presents the corresponding PDF. (c) displays the Weibull distribution as the limiting distribution for the minimum of $K$i.i.d. exponential RVs, and (d) shows the corresponding PDF.
  • Figure 5: Order statistics for NG
  • ...and 12 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • proof