  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.
