Regularizing Random Points: Complementary Mat\'ern Hard-Core Point Process

In this paper we present a tractable approach for regularizing randomly placed points, by splitting them into two subsets: the first is generated by means of the Mat\'ern hard-core point process, while the remaining points constitute the complementary Mat\'ern hard-core point process. We study the characteristics of these processes, deriving its pair-correlation functions, and the distribution of the distance to the nearest neighbour. The results have several applications in wireless communications, including the modeling of wireless sensor networks, where we investigate an example of regularizing such networks and illustrate its advantage in reducing the energy consumption of wireless nodes.