Incorporation of Confidence Interval into Rate Selection Based on the Extreme Value Theory for Ultra-Reliable Communications

TL;DR

The paper tackles URLLC rate selection under ultra-reliability constraints by integrating confidence intervals into an extreme value theory framework. It models the channel tail with a generalized Pareto distribution and derives CI bounds for the GPD parameters, which are then propagated into a rate expression $R_{GPD}(X^n)=\log_2\left(1+u+\frac{\hat{\sigma}}{\hat{\xi}}\left[1-\varepsilon_n^{-\hat{\xi}}\right]\right)$ to guarantee a target outage probability $ε$. The authors derive CI for the GPD parameters via a $t$-distribution-based approach using multiple iterations of MLE, and demonstrate that incorporating CI reduces the required training sample size on Fiat Linea data at 60 GHz. They show how parameter and rate CI tighten with more data and/or higher allowable error, highlighting a trade-off between estimation uncertainty and data collection cost, with future work on multivariate EVT extensions.

Abstract

Proper determination of the transmission rate in ultra-reliable low latency communication (URLLC) needs to incorporate a confidence interval (CI) for the estimated parameters due to the large amount of data required for their accurate estimation. In this paper, we propose a framework based on the extreme value theory (EVT) for determining the transmission rate along with its corresponding CI for an ultra-reliable communication system. This framework consists of characterizing the statistics of extreme events by fitting the generalized Pareto distribution (GPD) to the channel tail, deriving the GPD parameters and their associated CIs, and obtaining the transmission rate within a confidence interval. Based on the data collected within the engine compartment of Fiat Linea, we demonstrate the accuracy of the estimated rate obtained through the EVT-based framework considering the confidence interval for the GPD parameters. Additionally, we show that proper estimation of the transmission rate based on the proposed framework requires a lower number of samples compared to the traditional extrapolation-based approaches.

Figures (5)

• Figure 1: 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 2: CI range for the estimated Pareto parameters considering different $\alpha$ values for groups $1$ and $2$ at different sample numbers: (a) CI range of the scale parameter for group $1$, (b) CI range of the shape parameter for group $1$, (c) CI range of the scale parameter for group $2$, and (d) CI range of the shape parameter for group $2$. The CI range refers to the difference between the upper and lower bounds of the CI.
• Figure 3: The estimated Pareto parameters along with their CI considering $\alpha=0.01,0.5$ for groups $1$ and $2$ at different sample numbers: (a) Scale parameter and the corresponding CI for group $1$, (b) Shape parameter and the corresponding CI for group $1$, (c) Scale parameter and the corresponding CI for group $2$, and (d) Shape parameter and the corresponding CI for group $2$. Blue plot is the estimated parameter; circle/pentagram corresponds to $\alpha=$$0.5$/$0.01$; filled/empty plot corresponds to upper/lower bound of CI.
• Figure 4: CI range for the estimated transmission rate considering different $\alpha$ values and different sample numbers for: (a) group $1$, and (b) group $2$.
• Figure 5: Estimated transmission rate with the corresponding CI at $\alpha = 0.5, 0.01$ and different sample numbers for: (a) group $1$, and (b) group $2$. Blue plot is the estimated parameter; circle/pentagram corresponds to $\alpha=$$0.5/0.01$; filled/empty plot corresponds to upper/lower bound of CI.