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