Best Neighbor Communication in a Poisson Field of Nodes

The communication channel power gain to the nearest neighbor of a node in a wireless communication network is not necessarily the largest among all neighbors due to fading. The probability that the kth nearest neighbor of a node has the best communication channel with the highest power gain in a 2-D network with homogeneous Poisson distribution of nodes is derived for a general fading environment. The result is specialized to the case where the communication links are modeled as generalized-gamma fading channels. The analytical results are verified and illustrated by computer simulations and numerical results. Some applications of the new theory are also presented. A novel criterion that represents the fading severity, i.e., the generalized amount of fading (GAF), is defined, and its value as an important measure for fading channels is justified.