Statistical Tools and Methodologies for Ultrareliable Low-Latency Communication—A Tutorial

Abstract

This article provides a tutorial on several statistical tools and methodologies that are useful for designing and analyzing ultrareliable low-latency communication systems.

Extreme Value Theory-based Robust Minimum-Power Precoding for URLLC

“…EVT deals with the stochastic behavior of events that arise in the tail of probability distributions, thus, it is a handy tool for URLLC [3]. For instance, the authors in [5] presented a methodology to model extreme fade events on the channel.…”

“…. Herein, J(ξ k ) and J(υ k ) represent the Fisher information 3 , which grows with the sample size. Notice that the estimates' variance goes to zero as the number of samples grows.…”

“…Notice that the use of confidence bounds of the parameters, i.e., [υ k,LB , ξk,LB ] and [υ k,UB , ξk,UB ], and their associated outage probability bounds O k,LB and O k,U B , instead of the actual estimates [υ k , ξk ] as in most EVT-related works, allows to cope with the uncertainties associated with the use of a 3 For a full definition of the Fisher information, please refer to [25]. For UE k compute γ k,N and ψ k according to ( 10) and ( 13), respectively…”

“…However, achieving reliability and low latency simultaneously, e.g., for supporting applications like factory automation, vehicular communications, and telesurgery with latency-reliability pairs of (10 ms, 1−10 −4 ), (1 ms, 1−10 −5 ), and (1 ms, 1−10 −9 ) [2], respectively, is extremely challenging. Indeed, efficiently supporting URLLC services requires an accurate statistical model characterization of the operational system, including channel conditions, interference statistics, user mobility, and the behavior of the communication protocols [3].…”