Distance Statistics of the Communication Best Neighbor in a Poisson Field of Nodes

In a wireless network, while the signal attenuation due to the distance-related path loss is minimum between a node and its nearest neighbor, this is not the case for the overall attenuation when the fading effect is also taken into account. Hence, the communication best neighbor (CBN) of a node is defined as the neighbor of that node with which it has the highest channel power gain. Recently, the statistics of the physical neighborhood index of the CBN have been derived for a general fading environment in which the nodes have two-dimensional Poisson distribution. In this paper, the statistics of the distance between a node and its CBN as well as the joint CBN distance-index statistics are obtained for the same scenario. Then, the analytical expressions are specialized for the case where the communication channels follow the generalized gamma fading model. Also, the results are verified and illustrated by computer simulations and numerical results. Further, it is shown how the obtained analytical results can be used to identify the CBN more efficiently by limiting the search region and the number of neighbors that are examined.