On k-th nearest neighbor distance distribution of random ad-hoc network

The internodal distance is an important characteristic of ad-hoc wireless networks and sensor networks. Some important properties like propagation delay, like capacity etc. are depending on the internodal distance. In this paper we consider a d-dimensional binomial point process (BPP) having N points distributed uniformly over a compact space S ⊂ Rd. Here we prove that the kth nearest neighbor distance in binomial point process converges weakly to the nth nearest neighbor distance in Poisson point process, which follows a generalize gamma density.