Distance distributions in random networks

By Dmitri Moltchanov. Ad hoc networks, 2012

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Channel Hardening and Favorable Propagation in Cell-Free Massive MIMO With Stochastic Geometry (2017, background): “From existing results on the distance distribution in Poisson networks, the joint PDF of the distances r = [ r 1 , r 2 , . . . , r M c ] T from the M c nearest antennas to the typical user is f r ( x 1 , . . . , [30].”
Estimating the intrinsic dimension of datasets by a minimal neighborhood information (2017, background): “1 Distribution of shells volumes for a homogeneous Poisson process Let Φ be a homogeneous Poisson process in R(2) with intensity λ (see [1] for more information about Poisson processes); in particular Φ satisfies the following properties:”
Power Control for D2D Underlaid Cellular Networks: Modeling, Algorithms, and Analysis (2013, methodology): “As we assume the uplink user and the D2D receiver are randomly positioned in the disk with radiusR, the pdffdk,0(r) is given by [25]”