Communication Neighbors Comparison in a Poisson Field of Nodes

The statistics of the ratio between the propagation losses of a given node and its i-th and j-th least-propagation-loss neighbors are obtained assuming that the spatial distribution of the neighboring nodes follows a two-dimensional homogeneous Poisson point process. It is shown that these statistics, unlike those for each individual propagation loss, are independent of the environmental fading type as well as the density of the neighbor nodes. The analytical results are validated and illustrated through numerical results and computer simulations. Some applications of the derived statistics are also presented.