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

For Poisson-Delaunay triangulations in <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-dimensional Euclidean space <inline-formula> <tex-math notation="LaTeX">$\mathbb {R}^{d}$ </tex-math></inline-formula>, 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 (<inline-formula> <tex-math notation="LaTeX">$d \ge 1$ </tex-math></inline-formula>). 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.

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