Unified Analytical Volume Distribution of Poisson-Delaunay Simplex and its Application to Coordinated Multi-Point Transmission

TL;DR

This paper derives an exact, unified probability density function for the volume of typical cells in Poisson-Delaunay triangulations across any dimension, and applies it to develop a novel coordinated multi-point transmission scheme.

Contribution

It provides the first unified analytical PDF for Poisson-Delaunay cell volumes in arbitrary dimensions and demonstrates its application in advanced wireless communication schemes.

Findings

Exact PDF and CDF derived for Poisson-Delaunay cell volumes in any dimension.

Shape characteristics of the distribution are thoroughly analyzed.

Application to a new coordinated multi-point transmission scheme with precise void cell effect evaluation.

Abstract

For Poisson-Delaunay triangulations in $d$-dimensional Euclidean space $\mathbb{R}^{d}$, a structured and computationally efficient form of the probability density function (PDF) of the volume of a typical cell is analytically derived in this paper. In particular, the ensuing PDF and the corresponding cumulative density function (CDF) are exact and unified, applicable to spaces of arbitrary dimension ($d \ge 1$). Then, the special cases and shape characteristics of the resulting PDF are thoroughly examined. Finally, various applications of the obtained distribution functions are outlined and, in particular, a novel coordinated multi-point transmission scheme based on Poisson-Delaunay triangulation is developed and the pertinent void cell effect is precisely evaluated by using the obtained distribution functions.