kth Distance Distributions of n-Dimensional Matérn Cluster Process

Abstract: In this letter, we derive the CDF (cumulative distribution function) of $k$th contact distance (CD) and nearest neighbor distance (NND) of the $n$-dimensional ($n$-D) Mat\'ern cluster process (MCP). We present a new approach based on the probability generating function (PGF) of the random variable (RV) denoting the number of points in a ball of arbitrary radius to derive its probability mass function (PMF). The proposed method is general and can be used for any point process with known probability generating functional (PGFL). 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.