In wireless networks, the knowledge of nodal distances is essential forseveral areas such as system configuration, performance analysis and protocoldesign. In order to evaluate distance distributions in random networks, theunderlying nodal arrangement is almost universally taken to be an infinitePoisson point process. While this assumption is valid in some cases, there arealso certain impracticalities to this model. For example, practical networksare non-stationary, and the number of nodes in disjoint areas are notindependent. This paper considers a more realistic network model where a finitenumber of nodes are uniformly randomly distributed in a general d-dimensionalball of radius R and characterizes the distribution of Euclidean distances inthe system. The key result is that the probability density function of thedistance from the center of the network to its nth nearest neighbor follows ageneralized beta distribution. This finding is applied to study networkcharacteristics such as energy consumption, interference, outage andconnectivity.
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