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Extreme Value Theory Based Rate Selection for Ultra-Reliable Communications

Niloofar Mehrnia, Sinem Coleri

TL;DR

URLLC demands extremely low PER; the paper uses EVT to model the channel tail with a GPD and derives a rate that guarantees outage probability below $\epsilon$; it provides a full Estimation-Rate-Validation pipeline and validates it with engine-compartment data, showing it outperforms extrapolation-based methods. The approach hinges on tail fitting via MLE, threshold selection by mean residual life and stability, and a closed-form rate expression $R_{GPD}(X^n)=\log_2\bigl(1+u+\frac{\hat\sigma}{\hat\xi}[1-\varepsilon_n^{-\hat\xi}]\bigr)$; it demonstrates reliable ultra-reliable communication under varying engine vibrations. The work offers a practical EVT-based tool for URLLC rate adaptation in non-ideal channels.

Abstract

Ultra-reliable low latency communication (URLLC) requires the packet error rate to be on the order of $10^{-9}$-$10^{-5}$. Determining the appropriate transmission rate to satisfy this ultra-reliability constraint requires deriving the statistics of the channel in the ultra-reliable region and then incorporating these statistics into the rate selection. In this paper, we propose a framework for determining the rate selection for ultra-reliable communications based on the extreme value theory (EVT). We first model the wireless channel at URLLC by estimating the parameters of the generalized Pareto distribution (GPD) best fitting to the tail distribution of the received powers, i.e., the power values below a certain threshold. Then, we determine the maximum transmission rate by incorporating the Pareto distribution into the rate selection function. Finally, we validate the selected rate by computing the resulting error probability. Based on the data collected within the engine compartment of Fiat Linea, we demonstrate the superior performance of the proposed methodology in determining the maximum transmission rate compared to the traditional extrapolation-based approaches.

Extreme Value Theory Based Rate Selection for Ultra-Reliable Communications

TL;DR

URLLC demands extremely low PER; the paper uses EVT to model the channel tail with a GPD and derives a rate that guarantees outage probability below ; it provides a full Estimation-Rate-Validation pipeline and validates it with engine-compartment data, showing it outperforms extrapolation-based methods. The approach hinges on tail fitting via MLE, threshold selection by mean residual life and stability, and a closed-form rate expression ; it demonstrates reliable ultra-reliable communication under varying engine vibrations. The work offers a practical EVT-based tool for URLLC rate adaptation in non-ideal channels.

Abstract

Ultra-reliable low latency communication (URLLC) requires the packet error rate to be on the order of -. Determining the appropriate transmission rate to satisfy this ultra-reliability constraint requires deriving the statistics of the channel in the ultra-reliable region and then incorporating these statistics into the rate selection. In this paper, we propose a framework for determining the rate selection for ultra-reliable communications based on the extreme value theory (EVT). We first model the wireless channel at URLLC by estimating the parameters of the generalized Pareto distribution (GPD) best fitting to the tail distribution of the received powers, i.e., the power values below a certain threshold. Then, we determine the maximum transmission rate by incorporating the Pareto distribution into the rate selection function. Finally, we validate the selected rate by computing the resulting error probability. Based on the data collected within the engine compartment of Fiat Linea, we demonstrate the superior performance of the proposed methodology in determining the maximum transmission rate compared to the traditional extrapolation-based approaches.
Paper Structure (10 sections, 2 theorems, 15 equations, 4 figures)

This paper contains 10 sections, 2 theorems, 15 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Rate Selection Framework
  4. Channel Estimation
  5. Rate Selection
  6. Validation of Selected Rate
  7. Numerical Results
  8. Optimum transmission rate
  9. Reliability assessment
  10. Conclusions

Key Result

Theorem 1

Let GPD($\sigma$,$\xi$) be the Pareto model fitted to the training samples $X^{n} = \{x_1,x_2,...,x_n\}$. Then, the MLE of $\sigma$ and $\xi$ can be obtained as where $k$ is the number of samples in the tail, i.e., exceeding the optimum threshold; $y_i = u-x_{i}$ for all $x_{i}<u$, where $i\in \{1,...,n\}$; and $\hat{\theta}$ is the root of the following equation:

Figures (4)

  • Figure 1: Flowchart of the proposed rate selection framework.
  • Figure 2: Measurement setup with the transmitter (TX) and receiver (RX) antennas located in the engine compartment of Fiat Linea.
  • Figure 3: Normalized transmission rate for: (a) group $1$ at $u=-10$ dBm, (b) group $1$ at $u=-5$ dBm, and (c) group $2$ at $u=-25$ dBm. The single Extrapolated and Mismatch plots correspond to all $\epsilon$ values. Extrapolated and Mismatch plots are both based on the Rayleigh assumptions.
  • Figure 4: Reliability measure of the proposed model and the traditional extrapolation approach for: (a) group $1$, and (b) group $2$; The dashed-black lines are the reference lines at targeted error rate $\epsilon \in \{10^{-3},10^{-4},10^{-5}\}$. Extrapolated and Mismatch plots are both based on the Rayleigh assumptions.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof