Copula-Based Analysis of Outage Probability: Assessing Redundancy for Improved Resiliency

The advent of 6G wireless networks promises to rev-olutionize communication with ultra-reliable, high-throughput, and low-latency services for applications like autonomous systems and immersive media. A critical aspect of 6G is network resiliency, which ensures reliable performance under challenging conditions such as extreme weather, congestion, and interference. The outage probability, which quantifies the likelihood of a communication link failing to meet its required Quality of Service (QoS), is a key metric for assessing resiliency. One strategy for improving resiliency is adding redundancy, such as introducing new transmitters. However, the impact of redundancy on outage probability is complex. Traditional models often assume independent fading channels, which oversimplify the real-world dependencies between transmitters. To address this, we use copulas, a mathematical tool that models joint distributions while accounting for various dependence structures between fading channels. This approach is particularly useful in complex environments where correlations between links vary. Our results show that less dependency between links leads to a lower outage probability, while more dependency results in higher outage probabilities. Additionally, we apply Fréchet- Hoeffding bounds to derive bounds for the outage probability that show how adding redundancy, such as additional link, can affect outage probability, enhancing our analysis of network resiliency.