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Multivariate Extreme Value Theory Based Rate Selection for Ultra-Reliable Communications

Niloofar Mehrnia, Sinem Coleri

TL;DR

This paper tackles ultra-reliable low-latency communication with spatial diversity by modeling the joint tail statistics of multiple channels via multivariate extreme value theory (MEVT). It introduces a BGPD-based framework grounded in a Poisson point process to capture inter-channel dependencies in rare events, and derives an optimal transmission rate that satisfies a target outage probability while incorporating bootstrap-based confidence intervals to cope with limited training data. Through a bi-variate tail estimation pipeline (threshold selection, UGPD fitting, Fréchet and Pickands transforms, BGPD construction) and a CI-enabled rate selection mechanism, the approach yields substantially higher rates (up to ~$10^3$) than traditional extrapolation methods, with reduced training data needs. Numerical results based on engine-compartment measurements from a Fiat Linea demonstrate improved rate performance and reliable outage control, highlighting the method's potential for practical URLLC deployments and guiding future work in transfer learning and digital-twin based offline training.

Abstract

Diversity schemes play a vital role in improving the performance of ultra-reliable communication systems by transmitting over two or more communication channels to combat fading and co-channel interference. Determining an appropriate transmission strategy that satisfies ultra-reliability constraint necessitates derivation of statistics of channel in ultra-reliable region and, subsequently, integration of these statistics into rate selection while incorporating a confidence interval to account for potential uncertainties that may arise during estimation. In this paper, we propose a novel framework for ultra-reliable real-time transmission considering both spatial diversities and ultra-reliable channel statistics based on multivariate extreme value theory. First, tail distribution of joint received power sequences obtained from different receivers is modeled while incorporating inter-relations of extreme events occurring rarely based on Poisson point process approach in MEVT. The optimum transmission strategies are then developed by determining optimum transmission rate based on estimated joint tail distribution and incorporating confidence intervals into estimations to cope with the availability of limited data. Finally, system reliability is assessed by utilizing outage probability metric. Through analysis of data obtained from the engine compartment of Fiat Linea, our study showcases the effectiveness of proposed methodology in surpassing traditional extrapolation-based approaches. This innovative method not only achieves a higher transmission rate, but also effectively addresses stringent requirements of ultra-reliability. The findings indicate that proposed rate selection framework offers a viable solution for achieving a desired target error probability by employing a higher transmission rate and reducing the amount of training data compared to conventional rate selection methods.

Multivariate Extreme Value Theory Based Rate Selection for Ultra-Reliable Communications

TL;DR

This paper tackles ultra-reliable low-latency communication with spatial diversity by modeling the joint tail statistics of multiple channels via multivariate extreme value theory (MEVT). It introduces a BGPD-based framework grounded in a Poisson point process to capture inter-channel dependencies in rare events, and derives an optimal transmission rate that satisfies a target outage probability while incorporating bootstrap-based confidence intervals to cope with limited training data. Through a bi-variate tail estimation pipeline (threshold selection, UGPD fitting, Fréchet and Pickands transforms, BGPD construction) and a CI-enabled rate selection mechanism, the approach yields substantially higher rates (up to ~) than traditional extrapolation methods, with reduced training data needs. Numerical results based on engine-compartment measurements from a Fiat Linea demonstrate improved rate performance and reliable outage control, highlighting the method's potential for practical URLLC deployments and guiding future work in transfer learning and digital-twin based offline training.

Abstract

Diversity schemes play a vital role in improving the performance of ultra-reliable communication systems by transmitting over two or more communication channels to combat fading and co-channel interference. Determining an appropriate transmission strategy that satisfies ultra-reliability constraint necessitates derivation of statistics of channel in ultra-reliable region and, subsequently, integration of these statistics into rate selection while incorporating a confidence interval to account for potential uncertainties that may arise during estimation. In this paper, we propose a novel framework for ultra-reliable real-time transmission considering both spatial diversities and ultra-reliable channel statistics based on multivariate extreme value theory. First, tail distribution of joint received power sequences obtained from different receivers is modeled while incorporating inter-relations of extreme events occurring rarely based on Poisson point process approach in MEVT. The optimum transmission strategies are then developed by determining optimum transmission rate based on estimated joint tail distribution and incorporating confidence intervals into estimations to cope with the availability of limited data. Finally, system reliability is assessed by utilizing outage probability metric. Through analysis of data obtained from the engine compartment of Fiat Linea, our study showcases the effectiveness of proposed methodology in surpassing traditional extrapolation-based approaches. This innovative method not only achieves a higher transmission rate, but also effectively addresses stringent requirements of ultra-reliability. The findings indicate that proposed rate selection framework offers a viable solution for achieving a desired target error probability by employing a higher transmission rate and reducing the amount of training data compared to conventional rate selection methods.
Paper Structure (16 sections, 1 theorem, 28 equations, 6 figures, 1 algorithm)

This paper contains 16 sections, 1 theorem, 28 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. MEVT-based Rate Selection Framework
  4. Bi-variate Channel Estimation
  5. Bi-variate Rate selection
  6. Outage Probability of the Transmission Rate
  7. Confidence interval
  8. Fundamentals of bootstrap-based BCA
  9. BCA in CI determination of UGPD parameters
  10. BCA in CI determination of the transmission rate
  11. Numerical Results
  12. Benchmark Extrapolation-based Algorithm
  13. Measurement Setup and Simulation Platform
  14. Transmission Rate
  15. Confidence Interval
  16. ...and 1 more sections

Key Result

Theorem 1

Let $G_{pp}(\hat{\tilde{x}},\hat{\tilde{y}}) \approx G_{pp}(\hat{\omega})$ be the estimated BGPD model fitted to the training samples $X^{n} = \{x_1,x_2,...,x_n\}$ and $Y^{n} = \{y_1,y_2,...,y_n\}$. Then, the inverse joint CDF function $F^{-1} \sim G_{pp}^{-1}(\varepsilon_n)$ can be obtained as where $\hat{\Tilde{x}}$ and $\hat{\Tilde{y}}$ are the estimated Fréchet transformation of $G_x(\hat{\ti

Figures (6)

  • Figure 1: Flow diagram of the proposed MEVT-based rate selection framework.
  • Figure 2: Measurement setup with the transmitter (TX) and receiver (RX) antennas located in the engine compartment of Fiat Linea: (a) Engine compartment, and (b) VNA setup.
  • Figure 3: The transmission rate of BGPD fitted to the filtered i.i.d. samples of the group $1$ at different sample numbers, and targeted PER $\epsilon \in \{10^{-5},10^{-4},10^{-3}\}$.
  • Figure 4: The estimated Pareto parameters along with their CI considering $\alpha=0.05,0.2,0.5$ for stationary group $1$, receivers Rx$1$ and Rx$2$, at different sample numbers: (a) Scale parameter and the corresponding CI for Rx$1$, and (b) Shape parameter and the corresponding CI for Rx$1$; the horizontal black line refer to the $-0.5$ minimum acceptable value for the shape parameter of UGPD.
  • Figure 5: The CDF of pseudo-polar Pickands angular component based on empirical results along with $0.01$ confidence interval, the Beta distribution $\beta_1$ fitted to the sample numbers $\approx 1.3 \times 10^{-5}$, and the Beta distribution $\beta_2$ fitted to the sample number $\approx 5 \times 10^{-5}$.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof