Higher-Order Meta Distribution Analysis of Wireless Systems with Application to the Reliability of UWB THz Networks

Communication reliability, as defined by 3GPP, refers to the probability of providing a desired quality of service (QoS). This metric is typically quantified for wireless networks by averaging the QoS success indicator over spatial and temporal random variables. Recently, the meta distribution (MD) has emerged as a two-level performance analysis tool for wireless networks, offering a detailed examination of the outer level (i.e., system-level) reliability assessment versus the inner level (i.e., link-level) reliability thresholds. Most existing studies focus on first-order spatiotemporal MD reliability analyses, and the benefits of leveraging MD reliability for applications beyond this structure remain unexplored, a gap addressed in this paper. We present wireless application examples that can benefit the higher-order MD reliability analysis. Specifically, we provide the analysis and numerical results for a second-order spatial-spectral-temporal MD reliability of ultra-wideband THz communication. The results demonstrate the value of the hierarchical representation of MD reliability across three domains and the impact of the inner-layer target reliability on the overall MD reliability measure.