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

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 Fréchet 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.

Extreme Value Theory Based Rate Selection for Ultra-Reliable Communications

“…Then, EVT is applied to each stationary sequence for estimating the shape and scale parameters of UGPD as a change-point function of time, as explained in detail in [19]. The parameters of UGPDs obtained for the received powers of Rx1 and Rx2 are then mutually used to determine the tail distribution of the joint probability distribution of multiple channel sequences and by using MEVT techniques to characterize the statistics of the inter-relationships of extreme events [14]. The transmitter assumes that the main source in the block fading channel is link outage [5], [6], [23].…”

“…where Λ( ˜ , ˜ ) is defined on space {(0, ∞) × (0, ∞)\(0, ˜ ) × (0, ˜ )}, denoting space {(0, ∞) × (0, ∞)} excluding sub-space {(0, ˜ )×(0, ˜ )}. Finally, the BGPD model based on the Poisson point process approach is determined as [14] (…”

“…In a URC system with spatial diversity, a proper channel model can be derived by i) estimating the channel statistic within a more nuanced notation of coherence distance for ultra-reliable communication [12], ii) using machine learning data-driven frameworks [13], or iii) incorporating novel techniques to the characteristics associated with extreme events across multiple variables, such as proposing the utilization of power law expression techniques by extrapolating from channel data [5] and multivariate extreme value theory (MEVT) [14]. In [12], adjustments to the coherence distance definitions are made to accurately capture the distance at which wireless channels can be reliably predicted.…”

“…Nevertheless, these initial studies still rely on average statistics channels, such as Gaussian, Rayleigh, or Rician, to characterize channel behavior in the ultra-reliable region. Only recently, a novel methodology utilizing MEVT has been introduced in [14] to model multiple channels in a multiple-input multiple-output (MIMO)-URC system by deriving the lower tail statistics of received power. MEVT is a statistical discipline specializing in formulating methods for modeling dependencies among infrequent events by leveraging multidimensional boundary relationships.…”

“…Moreover, [16] develops a data-driven rate selection framework where federated learning (FL) training has been used to estimate the transmission rate and assess the reliability of the system with minimum training time in the absence of knowledge about the channel state information (CSI). However, all of these designs use the extrapolation of average-statistics channel models, which have been demonstrated not to fit the empirical data in the ultrareliable region [14], [17]- [19]. We have recently proposed a novel extreme value theory (EVT)-based framework in [17] for estimating and validating the optimal transmission rate to address the constraints of ultra-reliable communications for a single transmitter-receiver pair.…”