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

For Poisson-Delaunay triangulations in d-dimensional Euclidean space 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 are exact and unified, applicable to spaces of arbitrary dimension (d ≥ 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.