kth Distance Distributions of n-Dimensional Matern Cluster Process

In this letter, we derive the CDF (cumulative distribution function) of kth contact distance (CD) and nearest neighbor distance ( NND) of the n-dimensional (n-D) Matern cluster process (MCP). We present a new approach based on relationship between the probability mass function (PMF) and the probability generating function (PGF) of the random variable (RV) denoting the number of points in a ball of arbitrary radius to derive these CDFs. We also validate our analysis via numerical simulations and provide insights using the presented analysis. We also discuss two applications, namely-macro-diversity in cellular networks and caching in D2D networks, to study the impact of clustering on the performance.

Automated summary

This letter discusses the derivation of cumulative distribution functions for the kth contact distance and nearest neighbor distance of the n-dimensional Matern cluster process, as well as a new approach based on the relationship between probability mass and generating functions. The analysis is validated through numerical simulations and provides insights into the impact of clustering on performance, with applications in cellular networks and D2D networks highlighted for further study.