Multivariate Extreme Value Theory Based Channel Modeling for Ultra-Reliable Communications

TL;DR

This work tackles the challenge of deriving accurate statistics for the lower tail of multichannel MIMO channels in ultra-reliable communications (URC) by employing a multivariate extreme value theory (MEVT) framework. It develops two BGPD constructions—logistic-family BGPD and Poisson point process BGPD—built atop uni-variate GPD tails transformed via a Fréchet transform and Pickands coordinates, to model joint tail behavior. The methodology is validated on real 60 GHz Fiat Linea engine-compartment data, showing substantially better tail fit than conventional extrapolation to the $10^{-9}$–$10^{-5}$ PER regime, with mean-constraint validation supporting model validity. The results imply a practical pathway to quantify and exploit multivariate tail events for MIMO-URC, while pointing to future work in real-time deployment, confidence intervals, and transfer learning for data-limited settings.

Abstract

Attaining ultra-reliable communication (URC) in fifth-generation (5G) and beyond networks requires deriving statistics of channel in ultra-reliable region by modeling the extreme events. Extreme value theory (EVT) has been previously adopted in channel modeling to characterize the lower tail of received powers in URC systems. In this paper, we propose a multivariate EVT (MEVT)-based channel modeling methodology for tail of the joint distribution of multi-channel by characterizing the multivariate extremes of multiple-input multiple-output (MIMO) system. The proposed approach derives lower tail statistics of received power of each channel by using the generalized Pareto distribution (GPD). Then, tail of the joint distribution is modeled as a function of estimated GPD parameters based on two approaches: logistic distribution, which utilizes logistic distribution to determine dependency factors among the Frechet transformed tail sequence and obtain a bi-variate extreme value model, and Poisson point process, which estimates probability measure function of the Pickands angular component to model bi-variate extreme values. Finally, validity of the proposed models is assessed by incorporating the mean constraint on probability measure function of Pichanks coordinates. Based on the data collected within the engine compartment of Fiat Linea, we demonstrate the superiority of proposed methodology compared to the conventional extrapolation-based methods in providing the best fit to the multivariate extremes.

Figures (6)

• Figure 1: Flowchart of the proposed multi-channel modeling framework.
• Figure 2: Transmitter and receiver antennas in the engine compartment.
• Figure 3: CDF of the received power tail samples transformed based on the Fréchet transformation: (a) for the transformed samples of receiver Rx$1$, $x \rightarrow \tilde{x}$, and (b) for the transformed samples of receiver Rx$2$, $y \rightarrow \tilde{y}$.
• Figure 4: Joint bi-variate CDF of the normalized tail power of empirical, extrapolation-based, logistic-based BGPD, and Poisson point process-based BGPD.
• Figure 5: $r$-$\omega$ plot. The Horizontal black line corresponds to $r_0 \approx -0.47$.

Theorems & Definitions (14)

• Definition 1: Fréchet transformation
• Theorem 1
• proof
• Theorem 2
• proof
• Definition 2: Pickands coordinates
• Theorem 3
• proof
• Remark 1
• Definition 3: Pickands constraints