Level crossing rate (LCR) is a well-known statistical tool that is related to the duration of a random stationary fading process \emph{on average}. In doing so, LCR cannot capture the behavior of \emph{extremely rare} random events. Nonetheless, the latter events play a key role in the performance of ultra-reliable and low-latency communication systems rather than their average (expectation) counterparts. In this paper, for the first time, we extend the notion of LCR to address this issue and sufficiently characterize the statistical behavior of extreme maxima or minima. This new indicator, entitled as extreme LCR (ELCR), is analytically introduced and evaluated by resorting to the extreme value theory and risk assessment. Capitalizing on ELCR, some key performance metrics emerge, i.e., the maximum outage duration, minimum effective duration, maximum packet error rate, and maximum transmission delay. They are all derived in simple closed-form expressions. The theoretical results are cross-compared and verified via extensive simulations whereas some useful engineering insights are manifested.

翻译：电平穿越率（LCR）是一种广为人知的统计工具，它描述的是随机平稳衰落过程在平均意义下的持续时间。然而，LCR无法刻画极端罕见随机事件的行为特征。对于超可靠低延迟通信系统而言，后者比其平均（期望）统计量更关键地影响着系统性能。本文首次拓展了LCR的概念以解决此问题，并充分刻画了极值极大值或极小值的统计特性。这一新指标被称为极端LCR（ELCR），通过借助极值理论和风险评估进行解析推导与评估。基于ELCR，衍生出若干关键性能指标，包括最大中断持续时间、最小有效持续时间、最大分组错误率和最大传输时延，这些指标均以简洁的闭式表达式给出。通过大量仿真对理论结果进行交叉验证，并揭示了若干工程启示。