Wireless Channel Modeling Based on Extreme Value Theory for Ultra-Reliable Communications

A key building block in the design of ultra-reliable communication systems is a wireless channel model that captures the statistics of rare events occurring due to significant fading. In this paper, we propose a novel methodology based on extreme value theory (EVT) to statistically model the behavior of extreme events in a wireless channel for ultra-reliable communication. This methodology includes techniques for fitting the lower tail distribution of the received power to the generalized Pareto distribution (GPD), determining the optimum threshold over which the tail statistics are derived, ascertaining the optimum stopping condition on the number of samples required to estimate the tail statistics by using GPD, and finally, assessing the validity of the derived Pareto model. Based on the data collected within the engine compartment of Fiat Linea under various engine vibrations and driving scenarios, we demonstrate that the proposed methodology provides the best fit to the collected data, significantly outperforming the conventional extrapolation-based methods. Moreover, the usage of the EVT in the proposed method decreases the required number of samples for estimating the tail statistics by about $7 \times 10^5$.